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An empirical characterisation of the Bombay Stock Exchange

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An empirical characterisation of the Bombay Stock Exchange

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Content AN EMPIRICAL CHARACTERISA TION OF THE BOMBA Y STOCK EXCHANGE
by
Susan Thomas
A Dissertation Presented to the
F ACUL TY OF THE GRADUA TE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial F ulllment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(Economics)
August 2017
Copyrigh t 2017 Susan Thomas
Contents
List Of T ables 3
List Of Figures 5
1 Prologue 6
1.1 Motiv ation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 In Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2 Institutional Backdrop 15
2.1 The Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.1 Equit y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.2 Fixed Income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.3 Mutual F unds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1.4 F oreign Institutional Investors . . . . . . . . . . . . . . . . . . . . . 20
2.2 Listing Categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3 T rading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.1 Brok ers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.2 Badla . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3.3 Brok erage Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3.4 The Scam: Septemb er 1991 to July 1992 . . . . . . . . . . . . . . . 29
2.3.5 Electronic trading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4 The Institutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.4.1 The Securities Exc hanges Board of India, sebi . . . . . . . . . . . . 30
2.4.2 The National Stock Exchange, nse . . . . . . . . . . . . . . . . . . 31
2.5 In summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3 Mark et Eciency on the bse 35
3.1 Data Description and Univ ariate Summary Statistics . . . . . . . . . . . . 40
3.2 Returns Predictability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.2.1 Serial Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2.1.1 Analysis by Size . . . . . . . . . . . . . . . . . . . . . . . 51
3.2.2 Runs T ests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.2.3 Long-term Mean Rev ersion and V ariance Ratio T ests . . . . . . . . 61
3.2.4 Seasonality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
1
3.2.4.1 The \January Eect" . . . . . . . . . . . . . . . . . . . . 69
3.2.4.2 Day of week eects . . . . . . . . . . . . . . . . . . . . . . 71
3.3 Event Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.3.1 Bonus Issues on the bse . . . . . . . . . . . . . . . . . . . . . . . . 75
3.3.1.1 Data Description . . . . . . . . . . . . . . . . . . . . . . . 78
3.3.1.2 More-stringent sample selection . . . . . . . . . . . . . . . 78
3.3.1.3 Less-stringent sample selection . . . . . . . . . . . . . . . 82
3.3.1.4 T rading frequency before and after XB-date . . . . . . . . 84
3.3.2 GDR Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.4 T ests of insider-information . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.4.1 Mutual F und Performance . . . . . . . . . . . . . . . . . . . . . . . 90
3.4.1.1 The Ev aluation Strategy . . . . . . . . . . . . . . . . . . . 92
3.4.1.2 The Data Describ ed . . . . . . . . . . . . . . . . . . . . . 93
3.4.1.3 Estimation Results . . . . . . . . . . . . . . . . . . . . . . 97
3.5 In Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4 Heteroskedasticit y Models 105
4.1 Motiv ation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.1.1 Wh y Heteroskedasticit y in Returns Matters . . . . . . . . . . . . . 106
4.2 Statistical character of the returns vector . . . . . . . . . . . . . . . . . . . 107
4.3 arch Models for the bse Sensex . . . . . . . . . . . . . . . . . . . . . . . 109
4.3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
4.3.2 Estimation and Model Selection Criteria . . . . . . . . . . . . . . . 111
4.3.3 Specication of the Mean Equation . . . . . . . . . . . . . . . . . . 112
4.3.4 Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
4.3.5 Inference and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.3.6 Structural changes in the Indian Economy . . . . . . . . . . . . . . 122
4.3.7 Estimation of Shifts in levels of V olatility . . . . . . . . . . . . . . . 126
4.4 Complications on the simple arch theme . . . . . . . . . . . . . . . . . . . 133
4.4.1 Is volatility on the bse priced? . . . . . . . . . . . . . . . . . . . . 133
4.4.2 garch -in-mean, or garchm Models . . . . . . . . . . . . . . . . . 133
4.4.3 Estimation and Analysis of garchm Models . . . . . . . . . . . . . 134
4.4.3.1 Event Study Analysis . . . . . . . . . . . . . . . . . . . . 136
4.4.4 Mutiv ariate Garch ( mvgarch ) Mo dels . . . . . . . . . . . . . . . . 139
4.4.5 Cross-correlation Analysis of the bse and the s&p500 . . . . . . . 142
4.4.6 Estimation and Analysis of mvgarch Models . . . . . . . . . . . . 145
4.5 In Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
5 Epilogue 150
5.1 Synopsis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
5.2 F uture research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Reference List 163
2
List Of T ables
1.1 F oreign Capital Inows ($ million) . . . . . . . . . . . . . . . . . . . . . . 11
2.1 Yields on gov ernmen t securities . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Mutual F und Market Capitalisation, January 1994 . . . . . . . . . . . . . . 19
2.3 Listing Categories on the BSE . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4 Example of the cost of purchasing one portfolio . . . . . . . . . . . . . . . 28
2.5 T rading days per y ear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1 Univ ariate statistics for the bse Sensex and Index-250. . . . . . . . . . . 42
3.2 Univ ariate statistics of daily returns on A companies . . . . . . . . . . . . 43
3.3 Univ ariate statistics of daily returns on 250 companies . . . . . . . . . . . 44
3.4 acf for bse Sensex and Index-250 . . . . . . . . . . . . . . . . . . . . . . 48
3.5 Number of rejections of H
0
: k
= 0 . . . . . . . . . . . . . . . . . . . . . . 49
3.6 acf for 30 companies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.7 Size-Returns(%) analysis of companies by Quartiles . . . . . . . . . . . . . 52
3.8 Asymptotic V ariance Bounds violations in Size Quartiles . . . . . . . . . . 53
3.9 Prob V alues for H
0
: E (runs) = for bse Sensex and Index-250 . . . . . 55
3.10 Run lengths for the indexes classication by Scam Even t . . . . . . . . . . 57
3.11 Run Lengths of indexes classied b y years . . . . . . . . . . . . . . . . . . 58
3.12 Cross-sectional distribution of Prob V alues of H
0
: E (runs) = . . . . . . 60
3.13 Estimates of vr(k) and normalised statistics . . . . . . . . . . . . . . . . . 63
3.14 Daily vr and b ounds for the bse Sensex and s&p500 . . . . . . . . . . . . 65
3.15 Daily v ariance ratios and Monte Carlo simulated bounds . . . . . . . . . . 67
3.16 Monthly vr and Monte Carlo simulated b ounds . . . . . . . . . . . . . . . 68
3.17 Eect of Month Dummies on returns of the bse Sensex . . . . . . . . . . . 70
3.18 Eect of Day Dummies on returns of the bse Sensex . . . . . . . . . . . . 72
3.19 Event study around Bonus Issue for the Restricted Sample . . . . . . . . . 79
3.20 V olatility of Excess Returns around the Bonus Issue for the Restricted Sample 81
3.21 Event study around Bonus Issue for the Unrestricted Sample . . . . . . . . 82
3.22 T rading F requency around XB dates . . . . . . . . . . . . . . . . . . . . . 85
3.23 Abnormal returns from GDR around Pricing Date (%) . . . . . . . . . . . 87
3.24 Summary Statistics for the Mutual F unds . . . . . . . . . . . . . . . . . . 94
3.25 Risk of common stock: some illustrations (11 April 1994) . . . . . . . . . 95
3.26 Estimation of the mark et mo del . . . . . . . . . . . . . . . . . . . . . . . 98
3
3.27 Analysis of v ariance of ( r
j
r
f
) . . . . . . . . . . . . . . . . . . . . . . . . 99
3.28 Sharp e’s Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.1 Selection of mean equation lagged terms . . . . . . . . . . . . . . . . . . . 115
4.2 ar(1)- garch model statistics . . . . . . . . . . . . . . . . . . . . . . . . . 116
4.3 ar(1)- garch : diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4.4 garch parameter estimates . . . . . . . . . . . . . . . . . . . . . . . . . . 119
4.5 Structural change on the bse . . . . . . . . . . . . . . . . . . . . . . . . . 123
4.6 garch with a single dummy in the v ariance equation . . . . . . . . . . . . 128
4.7 garch with single dummy in the v ariance, Post 1985 . . . . . . . . . . . . 131
4.8 garch with all the dummies in the v ariance, P ost 1985 . . . . . . . . . . . 132
4.9 ar-garch (1,1)-in-mean estimation . . . . . . . . . . . . . . . . . . . . . . 135
4.10 ar(1)- mvgarch (1,1) diagnostics . . . . . . . . . . . . . . . . . . . . . . . 146
4.11 ar(1)- mvgarch (1,1) diagnostics: P ost 1990 . . . . . . . . . . . . . . . . . 147
5.1 T ransactions costs in India’s equity market (percent) . . . . . . . . . . . . 158
4
List Of Figures
1.1 Capital Issues by the Priv ate Sector, 1980 to 1994 . . . . . . . . . . . . . . 9
1.2 F oreign Inv estmen t in to India . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1 T-bill yields in 1993-94 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Yield curve: Government debt instruments . . . . . . . . . . . . . . . . . . 18
2.3 Growth in Mark et Capitalisation across Listing Categories . . . . . . . . . 23
2.4 Histogram of the Market Capitalisation in Listing Categories, December 1997 24
3.1 Day of w eek eects: Co ecien ts . . . . . . . . . . . . . . . . . . . . . . . . 73
3.2 Day of w eek eects: Prob v alues . . . . . . . . . . . . . . . . . . . . . . . . 73
4.1 Daily acf : lags 1 to 40 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.2 acf of daily residuals: lags 1 to 20 . . . . . . . . . . . . . . . . . . . . . . 118
4.3 Daily data: April 1979 to March 1995 . . . . . . . . . . . . . . . . . . . . . 121
4.4 CAR around budget announcemen ts: April 1979 to March 1995 . . . . . . 137
4.5 Squared residuals around budget announcements: April 1979 to March 1995 137
4.6 Correlation b et ween the bse Sensex and the SP500 in three time periods . 144
5
Chapter 1
Prologue
This thesis studies stock markets in India. Here, the behaviour of the Indian markets is
analysed using the returns on an index calculated for the perio d from April 1979 to Marc h
1995. This series characterises market behaviour across a reasonably long time p eriod in
which there have b een a v ast number of p olicy and structural changes in the economic
climate in India. In the course of this perio d, the Indian investor has seen the birth of an
IPO mark et which oered him a viable investment alternative. The Indian economy has
been opened up to the international econom y by the remov al of barriers to the inow of
foreign capital and investment.
In this thesis, we aim to document the statistical behaviour of the Bomba y Sto c k Ex-
change ( bse), the largest and most active stock mark et in India, and analyse the economic
implications thereof.
6
1.1 Motiv ation
Previous W ork done
The rst studies on Indian stock markets were published in the late seven ties and the
eighties (Mookerjee 1988, Y alawar 1988, Cooper 1982, Sharma & Kennedy 1977). The bse
being the most developed sto ck market in India, researc h on the Indian Stock Mark ets
has typically been about the bse. Most of this work was done using data of the largest
companies and the bse Sensex Index, a stock market index which has been published b y
the bse since the late 1970’s. The studies ha ve been conducted along the lines of tests
of weak form mark et eciency in F ama (1965). A broad consensus emerging from these
pap ers is that after transactions costs, arbitrage opportunities on the bse are not readily
discernible.
In this dissertation, we ha ve access to data-sets which are an order of magnitude ahead
of these earlier studies. With this in hand, we can update studies, long overdue, on Indian
stock exchanges.
An equally important motiv ation for this work derives from changes in the economic
policy environmen t. Although active trading on the bse began in 1876, making it one
of the oldest stock markets in the w orld, in the paradigm of post{independence economic
policy in India, the stock mark et w as not allo wed to play a ma jor role in guiding resource
allocation in the coun try . This constraint w orked its eect at several levels:
Go v ernmen t regulation and go v ernmen t{con trolled nancial institutions pla y ed a dominan t
role in resource allo cation.
7
Public issues of sto c k w ere sub ject to price con trols.
A w eak mark et micro-structure that did not facilitate the trading pro cess.
In this economic landscap e, sto c k mark ets w ere not a particularly imp ortan t feature. This has
c hanged substan tially with recen t p olitical ev en ts. Due to these ev en ts, describ ed further on, it
is pruden t to re-examine the eciency of the mark et b oth from the Indian and the in ternational
p ersp ectiv e.
The Indian Economy
The paradigm of economic p olicy in India started c hanging from around 1985 on w ard, with a shift
to w ards mark et{orien ted p olicies (Bhagw ati 1993). A host of p olicy c hanges ha v e b een instituted
that ha v e gradually shifted con trol of resource allo cation from the go v ernmen t to mark ets. Some
of the sp ecic p olicy measures in the lib eralisation pro cess include the ab olition of industrial
licensing, elimination of (the o ccasional) price con trols, and elimination of go v ernmen t con trol of
the exc hange rate. There is a strong consensus underlying the lib eralisation pro cess, and eac h
y ear the econom y b ecomes more mark et{driv en, and less inuenced b y bureaucratic or p olitical
con trol.
These c hanges ha v e had a ma jor impact on rms in India and hence on the ev aluation of their
traded shares. Of these, the t w o most imp ortan t c hanges for the sto c k mark et are:
1. Ab olition of the Con troller of Capital Issues, cci, on 29th Ma y 1992.
The cci w as the regulatory b o dy on public issues b efore 1992.
One of the tasks of the cci w as to price all securities sold b y rms. This w as done to ensure
that shares w ere only sold at \fair" prices. The cci had a form ula whic h used accoun ting
8
information and emerged with the \fair price" whic h w ould, in general, b e far b elo w the
mark et price.
This led to systematic under-pricing of public issues, b y a factor of 50{300%. In this
en vironmen t, public issues w ere o v ersubscrib ed, often b y a factor of more than ten times.
In the ev en t of o v er-subscription, applican ts for the purc hase of the issue w ere selected b y
lottery . While this pro duced go o d opp ortunities for those in v estors who participated in
these lotteries, it made rms less in terested in raising money via sto c k mark ets.
With the ab olition of the cci, rms ha v e increasingly c hosen to use sto c k mark ets to raise
resources. This is suggested b y the gro wth of public issues b y the priv ate sector in absolute
terms and as a p ercen tage of net sa vings, as depicted in Figure 1.1.
1
1979-80 1982-83 1985-86 1988-89 1991-92
10
% of Net Savings
Figure 1.1: Capital Issues by the Priv ate Sector, 1980 to 1994
1
This data is based on CMIE (1993 a), supplemen ted with more recen t data.
9
2. Reduction of restrictions on foreign presence in the econom y .
F or all practical purp oses, foreign in v estmen t w as not w elcome in to India b efore 1991.
Apart from the bureaucratic appro v als required, foreign companies w ere not allo w ed to
o wn more than 40% of a compan y . F oreign participation on the bse w as prohibited.
T o da y , foreign in v estors are able to either set up or purc hase companies in India. F or-
eign institutional in v estors w ere allo w ed to op erate on the bse from Septem b er 1992. As
of Jan uary 1994, 132 foreign nancial institutions had setup nancial op erations in Bom-
ba y . They purc hased and sold sto c ks of Indian rms listed on the bse, on b ehalf of their
in ternational clien ts as w ell as those within the coun try .
The pace of foreign in v estmen t in to India has b een transformed as a consequence of the
lib eralisation pro cess. This is illustrated b y these graphs, deriv ed from CMIE (1993 b).
1990-91 1991-92 1992-93 1993-94
0
1
10
% of Total Investment
Figure 1.2: F oreign Investment into India
10
W e see that b oth the quantity of foreign in v estmen t and the shar e of foreign in v estmen t in
total domestic in v estmen t ha v e exp erienced strong gro wth.
F oreign in v estmen t has en tered India in three w a ys: through direct in v estmen t in pro jects,
through purc hases of sto c k on the bse, and through Global Dep ository Receipts ( gdr)
2
and
External Commercial Borro wings ( ecb)
3
issued b y Indian companies on Europ ean mark ets
(CMIE 1993 b). T able 1.1 together with Figure 1.2 sho ws that capital o ws in to the sto c k
mark et ha v e increased with the en try of foreign in v estmen t in to India.
1991-92 1992-93 1993-94 1994-95
F oreign Direct In v estmen t 154 233 620 1000
P ortfolio In v estmen t 0 0 1665 1200
GDR and ECBs 0 0 2374 2000
T otal 154 233 4659 4200
CMIE estimates
T able 1.1: F oreign Capital Ino ws ($ million)
All this has led to an increase in the mark et capitalisation of the bse. F or a frame of reference,
the mark et capitalisation of the bse w as Rs. 67 billion in 1980 and Rs. 520 billion in 1988.
Ination through this p erio d a v eraged 10% a y ear.
Th us, structural p olicy shifts ha v e resulted in sto c k exc hanges and mark ets assuming a greater
imp ortance in the Indian econom y . If the sto c k mark et is to pla y a role in the w a y resource
allo cation is done, esp ecially in the con text of w orld mark ets and in ternational capital o ws, then
2
These are sto c ks that are sold b y Indian companies in exc hanges in Europ e. These sto c ks are traded
only on these exc hanges, and can only b e held b y foreign clien ts.
3
These are b onds that are sold b y Indian companies to foreign clien ts.
11
it is imp ortan t for us to re-ev aluate and impro v e on the w ork done previously to ascertain the
eciency of the bse.
Institutional F ramework
A basic argumen t motiv ating the idea of ecien t mark ets is simple and p o w erful: In the absence of
legal or institutional constrain ts, agen ts seek and eliminate arbitrage opp ortunities (ineciencies).
Hence a \sucien t n um b er" of arbitrage-seek ers ensures that mark ets are ecien t.
The nyse has b een the fo cus of eciency researc h for a quarter of a cen tury or more. A
class of eciency h yp otheses ha v e b een established as c haracterising the nyse , particular to the
institutional structure that go v erns it. The bse is c haracterised b y a totally unique set of legal
and institutional constrain ts up on the b eha viour of agen ts.
4
F urther, the to ols used b y traders
and analysts on the bse (theoretical, informational, and computational to ols) are decades b ehind
those used on the nyse .
Th us, it is quite lik ely that some of the h yp otheses, whic h are empirically defensible on the
nyse , will b e statistically rejected b y price data on the bse. In addition, the results of tests
of these h yp otheses w ould serv e as a starting p oin t for economists who seek to understand the
causalit y from institutional arrangemen ts to resource allo cation outcomes.
W orldwide Portfolio F ormation
Mo dern in v estors are alw a ys on the searc h for nancial instrumen ts whic h are uncorrelated with
the sources of risk in their existing p ortfolios. Because the Indian econom y is relativ ely insulated
from disturbances in w orld trade and output, the bse index is quite uncorrelated with the s&p500 .
4
W e outline details of the institutional asp ects of the bse in the next c hapter.
12
F or example, on the da y of the Octob er 1987 crash on W all Street, the bse index fell b y a mere
0.2%, and rose b y 0.5% at the end of the w eek.
Another direction of reasoning whic h suggests that capital is lik ely to o w from the rest of the
w orld in to the bse deriv es from neo classical reasoning: Capital is relativ ely scarce in India. The
risk-less rate of return and the equit y premium are b oth higher in India than in the dev elop ed
coun tries in the W est. This will b e b orne out sharply when w e examine risk-less rates of return
in the follo wing c hapters.
Both the higher rates of return as w ell as the lac k of correlation of Indian sto c k mark ets with
other, global equit y mark ets w ould mak e in v estmen ts in to India attractiv e from the viewp oin t of
a w ell-div ersied p ortfolio con trolled in New Y ork. As seen in Figure 1.2 and T able 1.1, foreign
in v estmen t in to India has b een gro wing rapidly . A rigorous empirical c haracterisation of the
mark et b eha viour w ould b e useful in p ortfolio optimisation in v olving Indian sto c ks.
1.2 In Summary
In recen t y ears, the Bom ba y Sto c k Exc hange has come out from under some institutional shac kles
imp osed on the w orking of the mark et. These restrictions ha v e b een in suc h con trast to that of
mark ets in dev elop ed coun tries that it w ould b e illuminating to carefully examine the mark et
b eha viour in terms of returns: as a precursor to tests of con temp orary mo dels of asset pricing;
as a basis for creating new in v estmen t mo dels; from the viewp oin t of studying the relationship
b et w een a new institutional framew ork and mark et b eha viour; and, as a source of new assets for
in ternational p ortfolio formation. In addition to institutional dierences, the bse is also one of
13
the largest emerging nancial mark ets in the w orld, with a v ery small b o dy of w ork ha ving b een
done to c haracterise it.
The aim of this thesis is th us to do cumen t the features of the bse with a view to measuring the
degree of eciency of the mark et, using newly constructed data from original sources. Researc h
will b e done b oth from the p oin t of view of individual companies
5
as w ell as the bse Sensex. The
time p erio d for the data-set is v e y ears of daily data from 1990 to 1994 for individual compan y
returns. Most of the individual compan y researc h w as done using a set of 92 compan y returns
data. Daily bse Sensex returns data is a v ailable from April 1979 to April 1995.
5
These companies accoun t for at least the top 40% or more of the mark et capitalization of the bse at
an y one p oin t in time.
14
Chapter 2
Institutional Backdrop
In this c hapter, w e commence our researc h on the bse with a description of the structure of
the exc hange co v ering the instrumen ts that are traded, ho w trading actually tak es place, the
regulatory practices, and institutional structures.
2.1 The Instruments
The instrumen ts traded on the bse are equit y issued b y companies, xed{income pap er (including
con v ertibles) and closed{end m utual funds. There are no deriv ativ es.
2.1.1 Equity
Equit y can b e issued at dieren t p oin ts in the life cycle of a generic compan y:
It starts with the initial public oering, the ipo. This issue is co ordinated b y a merc han t
banking compan y .
15
Companies can announce sto c k splits, whic h are called b onus shar es in India. Bon us Shares
ma y con tain a signal of higher dividend pa y outs in the future, for the p ost{split mark et
capitalisation is generally higher than b efore the split. W e do cumen t the eects of this
ev en t in greater detail in Section 3.3.
Companies can sell shares to the public at large.
Companies can sell shares to their curren t shareholding, oering shareholders an opp ortu-
nit y to main tain their claim on the future cash-o ws of the compan y .
Often, the previous t w o strategies are implemen ted through con v ertible b onds.
In the last t w o y ears, man y companies listed on the bse ha v e done Euro-issues of Global
Dep ository Receipts ( gdrs), whic h represen ts a completely new mec hanism of selling equit y in
in ternational mark ets. This is a recen t dev elopmen t and will b e discussed in more detail in Section
3.3.2.
2.1.2 Fixed Income
Debt is issued b oth b y companies and b y the go v ernmen t. But in general,there has b een little
liquidit y in debt mark ets in India. Most purc hasers at the public issue hold the instrumen t to
maturit y . Go v ernmen t debt is traded at a mark et named the Discoun t Finance House of India,
(dhfi ), and corp orate debt (including con v ertibles) is traded on the sto c k exc hanges. More
recen tly , the trading of go v ernmen t debt has started taking place on the newly op ened National
Sto c k Exc hange ( nse) in Bom ba y . W e discuss the nse later in this c hapter.
16
Government debt
Short{term go v ernmen t debt in India is sold as T-bills, and long{term debt is called go v ernmen t
securities. T-bills come with 91{da y and 364{da y terms to maturit y . Go v ernmen t securities come
with maturities of t w o through nine y ears.
T-bill yields observ ed in 1993-94 are summarised in Figure 2.1. Yields on the longer-term
go v ernmen t securities as on 1 Jan uary 1994 are summarised in T able 2.1. These are nominal
rates. The yield curv e implied b y all these instrumen ts, as of 1 Jan uary 1994, is in Figure 2.2.
7
8
9
10
11
12
Yield (%)
91 days
364 days
Figure 2.1: T-bill yields in 1993-94
Maturit y Yield
(y ears) (%)
2 12.75
5 13.00
7 13.25
9 13.40
T able 2.1: Yields on government securities
17
0 2 4 6 8 10
Years to maturity
11
12
13
Rates of Return
Figure 2.2: Yield curve: Government debt instruments
Corp orate Debt
Companies sell debt instrumen ts of t w o t yp es:
Commer cial Pap er
This is unsecured short-term debt pap er issued b y corp orations as loans to other corp ora-
tions. These ha v e time to maturit y of usually under a y ear. As of 1 Jan uary 1994, CPs of
highly rated companies w ere issued at rates of 11.5% or so.
Deb entur es
These are b onds and ha v e terms from t w o to ten y ears. Deb en tures are non-c onvertible or
p artly c onvertible or ful ly c onvertible . Con v ertible b onds giv es the b ondholder the option
of con v erting the b ond in to a share at a pre-determined price, and a pre-determined future
time. These constitute the most sophisticated nancial instrumen ts traded in India.
Deriv ativ es based on these debt instrumen ts are not traded.
18
This dissertation will fo cus on equit y b ecause it mak es up the bulk of trading v olume on the
bse. W e do not explore Indian xed income mark ets in this thesis.
2.1.3 Mutual F unds
F rom 1964 on w ard, the m utual fund industry w as restricted b y go v ernmen t regulation to consist
of a single state{o wned monop oly named the Unit T rust of India (UTI). En try in to the m utual
fund industry w as only p ermitted from 1988. Since then, man y other m utual fund companies
that ha v e started selling pro ducts (see T able 2.2).
Mutual Mark et V alue of % share in % share in
F und in v estmen ts (T otal Mark et (Mutual F und Mark et
(Rs. Billion) Capitalisation) Capitalisation)
uti 353.80 13.61 80.32
Can bank 41.94 1.18 9.52
sbi 16.41 0.70 3.73
Indian Bank 6.39 0.18 1.45
lic 4.21 0.15 0.96
gic 2.27 0.06 0.52
boi 1.48 0.06 0.34
icici 1.00 0.04 0.23
Kothari 1.00 0.04 0.23
20
th
Cen tury
1.00 0.04 0.23
Morgan Stanley
10.00 0.38 2.27
T aurus
1.00 0.04 0.23
T otal 440.51 16.51 100.00
Mutual F unds run b y foreign companies
T able 2.2: Mutual F und Market Capitalisation, January 1994
Eac h of these companies runs m ultiple sc hemes. Both op en{ended and closed{ended sc hemes
exist. The ab o v e 12 companies had 136 dieren t sc hemes as of Jan uary 10, 1994. In all, the m utual
19
fund industry is a crucial in termediary in carrying in v estable funds from the la y consumer in to
nancial mark ets.
As seen in T able 2.2, ev en after the barriers to en try in to the m utual fund industry w ere
eliminated, UTI remains the dominan t pla y er in the m utual fund industry . With assets of Rs.400
billion (around $13 billion) it comprises 80% of the total mark et capitalisation of the m utual fund
industry . It is a large nancial institution ev en b y w orld standards.
The trac k{record of the m utual fund industry is one of the few metho ds of assessing strong
form eciency of a giv en sto c k mark et. W e will attempt this in Section 3.4.1. In the Indian
con text, p erformance ev aluation of m utual funds is particularly in teresting when applied to uti,
since uti is large enough to p ossess mark et p o w er in the bse { a unique status in the class of
m utual funds the w orld o v er.
2.1.4 F oreign Institutional Investors
Lastly , there are m utual funds oered b y the F oreign Institutional In v estor or fiis. In 1992,
the Go v ernmen t of India, ( goi), started gran ting p ermissions to foreign institutional in v estors
to op erate on the bse. As of 4 Jan uary 1993, 132 institutions had b een gran ted p ermission.
The funds con trolled b y the fiis in Bom ba y amoun t to ab out Rs.38 billion, or $1.2 billion. This
amoun ts to ab out 1% of the mark et capitalisation of the bse.
Equit y instrumen ts traded on an exc hange are further dieren tiated b y Listing Categories.
20
2.2 Listing Categories
The bse categorizes listed companies in to four classes based on the daily v olumes of shares traded
as w ell as daily v olatilit y of trading v olumes. The classes are :
, or A gr oup : These shares ha v e v ery high daily v olumes traded but lo w v olatilit y in
v olumes traded. The exc hanges p ermitted a lo cal v ersion of forw ards trading for A group
securities.
The set of A companies are \up dated" appro ximately ev ery t w o y ears. There are curren tly
92 A group companies.
, or B gr oup : These shares ha v e high daily v olumes traded with v ery high v olatilit y in
the v olumes traded.
, or G gr oup : These shares ha v e lo w daily v olumes as w ell as lo w v olatilit y in n um b er of
shares traded.
\Other", or O gr oup : These shares ha v e lo w daily v olumes and high v olatilit y of v olumes
traded. This category tends to largely include shares of companies that are newly issued
on the bse. \Other" is also otherwise dened as those shares listed on the bse that do not
fall under the categories of , or .
There are appro ximately 6,000 companies that are listed on the bse. Of these, appro ximately
2,000 companies are small companies oated b y brok erage houses in order to ev ade tax pa ymen t.
These companies do not trade during the y ear and w e will consisten tly ignore these companies in
our w ork. The follo wing table 2.3 sho ws the distribution of companies b y listing category . Here,
21
w e only use those companies that ha v e had some trading activit y on the bse on 13 Decem b er
1993.
Listing Mark et Capitalisation Num b er
Category $ billion Rs. Crore % %
A 44 137,801 42.47 92 4.5
B 7 21,444 6.61 130 6.4
G 22 68,529 21.12 239 11.7
O 31 96,718 29.81 1581 77.4
T otal 104 324,491 100.00 2042 100.0
T able 2.3: Listing Categories on the BSE
F or August 1992 on w ard, public sector priv atisation eorts, where the State sold around 20% of
shares to the public, ha v e caused the listing of extremely large-sized companies on the bse. These
ha v e en tered the mark et listed as G companies, and has led to a rise in the mark et capitalisation
of this category . This has also c hanged the distribution of mark et capitalisation among listing
categories. T raditionally the A group companies w ere the largest companies on the bse. After
the public sector units disin v estmen t pro cess b egan, the largest mark et capitalisations w ere in
the G group.
This is illustrated b y the follo wing t w o gures.
In Figure 2.3, w e see the ev olution of the mark et capitalisation b y listing category from the
start of 1990 on w ard. The rise of the G companies is sharply visible in August 1992 here.
Figure 2.4 sho ws a snapshot (as of 24 Decem b er 1993) of the distribution of mark et capi-
talisation among the listing categories. In it, w e see that the largest of all companies are
no w in the G group rather than the A group.
22
5Jan90 20Apr90 3Aug90 16Nov90 1Mar91 14Jun91 27Sep91 10Jan92 24Apr92 7Aug92 20Nov92 5Mar93 18Jun93 1Oct93
100
1000
Overall
A group
B group
G group
Others
Figure 2.3: Gro wth in Market Capitalisation across Listing Categories
23
0 2 4 6 8 10
log(Market Capitalisation)
0.0
0.1
0.2
0.3
Overall distribution
0.0
0.1
0.2
0.3
A group
0.0
0.1
0.2
0.3
B group
0.0
0.1
0.2
0.3
G group
0.0
0.1
0.2
0.3
O group
Figure 2.4: Histogram of the Market Capitalisation in Listing Categories, Decem ber 1997
2.3 T rading
Prior to No v em b er 1994, trading on the exc hanges started from 12 no on and lasted for three
hours, on v e da ys of the w eek. The closing prices w ere published b y the exc hange at eigh t
in the ev ening when all the transactions w ould b e accoun ted for. There w as activ e o-mark et
24
trading whic h to ok place b et w een the closing of trading and the publication of the prices. After
No v em b er 1994, trading has b een done o v er a longer p erio d in the da y , starting from 10 in the
morning, lasting for v e hours.
Settlemen t t ypically tak es place fortnigh tly on a F rida y . The bse has a clearing house through
whic h all pa ymen ts of cash or deliv ery are enforced. The clearing house tak es three to six da ys
for deliv ery .
2.3.1 Brokers
The bse has b een set up on the mo del of the British sto c k exc hange, whic h is a brok er-based
system. T rading is done b y brok ers who tak e orders from in v estors or from other brok ers. Brok ers
trade on their o wn accoun ts as w ell. There are no designated sp ecialists on the exc hange. Some
asp ects of the role of the sp ecialist is assumed, on o ccasion, b y a class of brok ers who are called
jobb ers .
Jobb ers ooad orders from brok ers when the orders cannot b e instan tly lled and ha v e them
matc hed during the course of the trading da y . Ho w ev er, the main dierence b et w een the jobb er
and the sp ecialist is that jobb ers cannot carry forw ard an y order to the trading session of the next
da y . Also, unlik e the sp ecialist on the nyse , there is no xed jobb er for an y share. Therefore, in
an essen tial sense, jobb ers are not mark et-mak ers.
The jobb er c harges a premium on ev ery trade that he accepts. This premium is a function of
the risk the jobb er p erceiv es at ev ery momen t, and is a v ariable addition to the trading costs on
the bse.
It is estimated that 70% of the trades that w ere carried out on the bse in August 1993 w ere
jobbing trades.
25
2.3.2 Badla
On the bse, a form of forw ard trading in shares existed called badla. In this system, an in v estor
who had b ough t shares had the exibilit y of deferring the settlemen t of his trade. This w ould
b e useful in situations where the in v estor did not ha v e the money for the immediate purc hase of
the sto c k, but w ould b e able to mak e the pa ymen t some time later. badla w as restricted to A
shares only . This w as similar to the rip orti system prev alen t in coun tries lik e Italy , F rance and
Belgium, whic h w as eectiv ely a mec hanism of lending and b orro wing money and shares to and
from the mark et (Williams & Barone 1991).
In Marc h 1994, amidst m uc h con tro v ersy , badla w as banned (Shah 1995 a). F rom Marc h 1994
on w ard, all trading on the BSE has b een for sp ot deliv ery .
2.3.3 Brokerage Costs
T rading on the bse lac k ed transparency un til around April 1995. Orders w ere placed with brok ers.
Prices w ere not observ ed in real-time, and brok ers w ould not rev eal the exact time at whic h the
trades w ere made. The exc hanges published information ab out the op en{high{lo w{close prices
at the end of the trading da y , whic h customers w ere forced to use as a b enc hmark for the prices
that they migh t ha v e receiv ed or paid for their trade. Brok ers commonly c harged prices close to
the da ys high on purc hase order, and paid prices close to the da ys lo w on sell orders.
F urther, brok ers did not rep ort the v arious c harges on a customers trade in a dis-aggregated
form. The transaction c harges w ould include jobb ers margin, the brok erage fee, and the price
paid for the sto c k. In principle, brok ers promised that the fee w as \roughly 1%", but on an y one
trade a customer could not kno w the role of brok erage fee. Therefore prior to b eing billed, the
26
brok erage fee w as an uncertain n um b er. F or example, the jobb ers margin v aried with the trading
v olume of the sto c k. Th us, the cost of trading small companies w as t ypically m uc h higher than
the cost of trading larger companies.
Since data on trading cost is not readily a v ailable, w e are reduced to anecdote to illustrate
the size of the costs of trading on Indian sto c k exc hanges.
One episo de of trading in v olv ed the purc hase of a p ortfolio of A group companies, w orth
Rs.0.5 million ($16,000). The order to purc hase this p ortfolio w as placed on 8 Dec 1993, and
the en tire execution of the order w as observ ed in detail. The brok er w as ask ed to purc hase
the p ortfolio at the next da ys op ening price (the idea b eing that this w ould reduce the
brok er’s exibilit y to c harge prices close to the da y’s high price).
If v alued at op ening prices of the da y , the p ortfolio should ha v e cost Rs.526,112 or $16,702.
The nal price paid, inclusiv e of all trading costs, w as Rs.531,720 or $16,882. T rading costs
w ere hence eectiv ely 1.08% of the p ortfolio v alue.
The dis-aggregated bill sen t b y the brok er sho w ed these trading costs:
27
Compan y Op ening Purc hase Markup
Price price (%)
Asso ciated Cemen t Cos. Ltd. 2820.00 2800.00 -0.71
Ba ja j Auto Ltd. 695.00 720.00 3.60
Bro ok e Bond India Ltd. 407.50 410.00 0.61
Cen tury T extiles & Inds. Ltd. 6900.00 7000.00 1.45
Co c hin Reneries Ltd. 280.00 276.00 -1.43
Colgate-P almoliv e (India) Ltd. 820.00 815.00 -0.61
Great Eastern Shipping Co. Ltd. 106.00 107.00 0.94
Hindustan Lev er Ltd. 540.00 545.00 0.93
I.T.C. Ltd. 690.00 700.00 1.45
I.C.I.C.I. 1580.00 1580.00 0.00
Larsen & T oubro Ltd. 256.25 257.00 0.29
Nestle India Ltd. 330.00 330.50 0.15
Reliance Industries Ltd. 301.00 306.50 1.83
S.C.I.C.I. Ltd. 152.00 157.50 3.62
T ata Chemicals Ltd. 465.00 476.25 2.42
T ata Engineering & Lo comotiv e Co. Ltd. 340.00 343.50 1.03
T ata Iron & Steel Co. Ltd. 222.00 221.50 -0.23
T able 2.4: Example of the cost of purchasing one portfolio
One of the brok erage houses, Prabh udas Lilladhar, c harges around 0.5% for trading in A
group companies on b ehalf of T empleton, whic h is a large sized asset managemen t compan y
in India. The trading costs for B group companies are near 1%. These are t ypically orders
with a size in man y millions of dollars.
On the blac k mark et, a mem b ership on the bse sells for around USD one million, illustrating the
returns to b eing a brok er.
The distinct lac k of transparency in trading costs has b een the cause of m uc h v o cal customer
dissatisfaction in the past. The gro wing dissen t migh t ha v e ultimately led to the go v ernmen t
instituting c hanges in the brok er monitoring system. But the issue of reforming the existing
systems w as brough t to the fore v ery abruptly b y the Scam of 1992.
28
2.3.4 The Scam: September 1991 to July 1992
Prices on the bse w ere manipulated b y an individual brok er for a p erio d of sev en mon ths from
No v em b er, 1991 to June, 1992. The brok er to ok adv an tage of a w eakly monitored banking system
to mo v e money from banks in to the sto c k mark et in a non-transparen t manner. Prices on the
bse rose substan tially , causing a price bubble in the equit y mark et all across the coun try .
A t the start of the bubble in No v em b er 1991, the total mark et capitalization w as Rs.1,944.42
billion (or $64.8 billion). The p eak during this p erio d of June 1992 had the mark et capitalisation
at Rs.4,481.15 billion (or $149 billion). This had dropp ed almost completely to No v em b er 1991
lev els b y the end of June 1992.
Since then, the GOI had tak en a relativ ely b enign p osition on the reforms of the sto c k ex-
c hanges in India. The price bubble pro v ed to b e nal stra w inuencing the p olicy stance to w ards
the bse. Tw o imp ortan t new institutions w ere created as part of Go v ernmen t p olicy to w ards
nancial mark ets: an equit y mark et regulator, the Sto c k Exc hanges Board of India, sebi and a
new national equit y exc hange, the National Sto c k Exc hange, nse. A consequence of the start of
nse had a direct and immediate impact on trading practices on the bse, whic h w as the onset of
ele ctr onic tr ading on the exc hanges.
2.3.5 Electronic trading
When the nse started sto c k mark et op erations in No v em b er 1994, it started as an electronic
exc hange. By April 1995, the bse had also adopted electronic trading systems. The mark et
micro-structure prev alen t to da y on these electronic trading systems is v ery dieren t from the
mark et micro-structure whic h w as prev alen t in the last t w o decades. Electronic trading has not
29
y et fully stabilised on the bse, and trading v olumes on the nse are still quite lo w. Ho w ev er, the
o v erall costs of execution on b oth these systems are lo w er than they used to b e: anecdotes from
brok ers on the mark et suggests that brok erage fees ha v e fallen from \roughly 1%" to \roughly
0.25%".
Ho w ev er, the price data used in this thesis is en tirely based on the p erio d in whic h there w as
no electronic trading on the bse. Our discussion in the remainder of this thesis hence assumes
trading mec hanisms from the pre-electronic era.
When w e discuss mark et eciency , and transactions costs as a barrier to arbitrage, our ndings
are relev an t for the y ears prior to the shift to electronic trading. W e ha v e ev ery reason to b eliev e
that the lo w ered transactions costs implied b y the new online trading systems should generate
substan tially altered equilibrium and observ ed mark et eciency prop erties in the y ears to come.
2.4 The Institutions
2.4.1 The Securities Exchanges Board of India, sebi
One of the k ey institutional dev elopmen ts to strengthen the equit y mark ets has b een the creation
of an indep enden t regulator for securities mark ets. sebi w as set up in 1992 to replace the Con-
troller of Capital Issues ( cci) whic h w as the departmen t in the Ministry of Finance that regulated
the equit y mark ets. In comparison with the cci whose main role w as the o v ersigh t of the primary
mark et issues, sebi w as originally set up with an emphasis on the restructuring of the bse and
the other sto c k exc hanges in India. But with the bubble of 1992, the sebi mandate has b een
mo died to include protecting the in v estor against suc h misuse of resources from taking place.
sebi p erforms three additional functions:
30
One of the results of the pressure of increased in v estmen ts in Indian equit y has b een an
exp osure of sev eral brok er malpractices of on the bse. A new role of the sebi as compared
to the earlier role of the cci is to register, monitor and regulate equit y mark et brok ers.
sebi sets guidelines for, and monitors, merc han t banks.
sebi monitors the b eha viour of m utual funds.
2.4.2 The National Stock Exchange, nse
Another institutional dev elopmen t is the creation of a new exc hange, the nse. It has b een
promoted b y three large state{o wned nancial institutions. In the short run, the ob jectiv e of
the nse is to pro vide a single national platform to trade xed income securities, particularly
go v ernmen t securities; these are nancial instrumen ts in whic h gen uine mark ets in India are
absen t. The nse is the rst exc hange not to b e a lo cal exc hange. It is also the rst exc hange that
is electronic, and not an op en outcry exc hange. The nse b egan trading go v ernmen t b onds from
mid{1994, and equit y from end 1994.
2.5 In summary
Based on the ab o v e description of the institutional framew ork of the bse, what is the prior that
w e can dev elop ab out mark et eciency?
Mark et eciency dep ends on availability and the pr o c essing of information. Th us, the mark et
is ecien t, dep ending on the lac k of arbitrage opp ortunities. Arbitrage opp ortunities are those
in v estmen ts where the in v estor gets prots with no risk. Here, the prots ha v e to b e calculated
net of tr ansactions c osts .
31
A vailability of Information
The frequency of disclosure of accoun ting information b y companies is lo w. Complete
ann ual rep orts app ear with a lag of around v e to six mon ths after the scal y ear is
complete, and summary results (of around ten n um b ers) are released eac h six mon ths with
a lag of one to t w o mon ths.
1
Sto c k prices rst b ecame a v ailable in real-time in late 1994.
Go o d qualit y databases of compan y{lev el information are rare: There is only one compan y
making a serious eort in building databases ab out the Indian econom y . While there are
h undreds of users of the information in the nance industry , these databases are still not
ubiquitous.
In this framew ork, one of the mec hanisms through whic h information en ters price formation
is insider trading, whic h is widely considered to b e a common feature on the bse.
Me chanisms of Information Pr o c essing
There is an accen t on pre{computer metho ds of analysing information (in part, this is
b ecause data-sets in computer form are hard to nd).
A sound mark et index is absen t. The bse Sensex is the most widely used index, whic h is a
mark et capitalisation{w eigh ted index using 30 companies. There are no analogues to the
s&p500 or Wilshire 5000 indexes.
Ineciencies c annot b e arbitr age d away due to tr ading c osts
1
The scal y ear ends on Marc h 31. Most ann ual rep orts arriv e at cmie b y end{Septem b er or early{
Octob er. The rst half of the y ear ends on 30 Septem b er. Most rst{half results b ecome a v ailable b y early
No v em b er.
32
In Section 2.3.3 w e sa w ho w one{trip trading costs are around 1% for small in v estors and
around 0.5% for large in v estors. These costs are v ery large compared with the US, where
large in v estors face costs lik e 2 cen ts p er shar e .
The problem of large trading costs is accen tuated b y w eak brok erage services. The trading
cost is somewhat unpredictable; this is seen in the last column of T able 2.4. This in tro duces
additional uncertain t y in arbitrage. Man y statistical ineciencies cannot b e arbitraged
a w a y at suc h trading costs.
The bse sta ys closed for a remark ably large n um b er of da ys eac h y ear:
Y ear T rading Da ys
1990 199
1991 206
1992 190
1993 214
1994 230
T able 2.5: T rading days per year
Net of 104 w eek end da ys, w e w ould normally exp ect the mark et to trade for 261 da ys a y ear.
Man y times, the bse is closed for sev eral da ys on end. The instan taneit y of information
dissemination in to prices is inhibited b ecause of this.
Finally , if some agen ts p ossess mark et p o w er, they can con taminate price pro cesses.
Market Power
33
While the bse has a total mark et capitalisation of $110 billion or so, trading v olumes are
relativ ely small { in the region of $100 million a da y .
2
It is clearly within the capabilit y
of the largest m utual fund, uti, or an y of the foreign institutional in v estors, to manipulate
prices.
3
T o da y , the gro wth rates of b oth the mark et capitalisation and daily trading v olume are
high, m uc h higher than the gro wth rate of assets con trolled b y agen ts with mark et p o w er.
This b o des w ell for the future of the mark et eciency of the bse.
The question w e seek to analyse is whether this mark et b e ecien t? The information pro cess-
ing going in to the bse seems to b e a collection of prot maximisers, w orking in an atmosphere
with lo w transparency of information, but with the a v ailabilit y of frequen t insider trading. W e
w ould exp ect signican t arbitrage opp ortunities to go unexploited giv en the una v ailabilit y of in-
formation. W e exp ect that it will p erhaps not b e unlik e the situation in the United States at the
time of F ama (1965). In addition, the high trading costs imp ose sharp b ounds on the class of
ineciencies whic h can b e arbitraged a w a y . Th us, w e exp ect the bse of 1994 to b e a inecien t
mark et as compared with the nyse of 1994.
In the follo wing c hapter, w e will use data in standard statistical tests dened in the literature
to shed more ligh t on these questions.
2
This implies that one thousandth of the mark et capitalisation is traded daily . On the nyse , roughly
$10 billion is traded daily .
3
As men tioned ab o v e, uti con trols assets of $13 billion.
34
Chapter 3
Market Eciency on the bse
In this c hapter, w e empirically examine mark et eciency on the Bom ba y Sto c k Exc hange. A t
the outset, w e will la y out the theoretical bac kdrop.
The ecien t mark ets h yp othesis, ( emh ), is a statemen t ab out the absence of arbitrage opp or-
tunities in an econom y p opulated b y rational, prot-maximising agen ts. T o quote Jensen (1978),
\an ecien t mark et is dened with resp ect to an information set F
t
if it is imp ossible to earn
economic prots b y trading on the basis of F
t
." The h yp othesis of mark et eciency is as basic to
nance as the h yp othesis of rationalit y in economics { it do es not dep end on the sup erstructure
of assumptions ab out preferences and tec hnology that go in to setting up a mo del of an econom y .
Mark et eciency merely implies that opp ortunities for systematically earning prots without risk
do not exist.
The early literature in the US in mark et eciency emphasised statistical tests whic h w ere
relativ ely free of economic theory underpinnings (F ama 1965). This phase of researc h w as v ery
successful in establishing a consensus ab out some prop erties of the data generating pro cess under-
lying returns. Kno wledge of these prop erties then enabled the second generation of researc hers
35
to approac h b oth mark et eciency and asset pricing theory more fruitfully . The theory that w as
subsequen tly dev elop ed w as used to further rene tests to examine mark et eciency .
In the case of the bse w e use a new data-set whic h is w ell-suited for mark et eciency researc h,
but ill-suited for testing asset pricing theory .
Curren t tests of mark et eciency , based on an asset pricing mo del, are joint tests of e-
ciency and the mo del. If the n ull h yp othesis is rejected, it ma y b e either b ecause of the
failure of eciency of the mark et or b ecause the asset pricing mo del is missp ecied. Th us
far, none of the studies ha v e succeeded in disen tangling these t w o asp ects of the n ull. Giv en
the p ossibilit y that the mo del is missp ecied, the rejection of the n ull h yp othesis do es not
necessarily presen t an y clear rejection of the ecien t mark et h yp othesis.
The v ery success of the mark et eciency literature in the US has led to the follo wing
phenomenon: when the literature rejects the n ull h yp othesis in a test whic h in v olv es asset
pricing theory , the conclusion tends to b e that the sp ecication of the asset pricing theory
is at fault, and not mark et eciency itself.
Examples can b e found in b oth theoretical (F ama 1970, Roll 1977, Jensen 1978) and empir-
ical (Ball 1978, Charest 1978, Banz 1981, Sc h w ert 1983, F ama & F renc h 1989, F ama 1991,
F ama, F renc h, Bo oth & Sinqueeld 1993) literature, to cite a few. Here, the t ypical con-
clusion is that diculties in asset pricing theory , rather than mark et ineciency , underlie
the rejections of the n ull h yp othesis.
There ha v e b een some exceptions, where researc hers ha v e explicitly dev elop ed mo dels with
inecien t mark ets built in. In these mo dels, in v estors are mo deled as b eing \irrational"
36
in displa ying a herd men talit y in their decision to buy or sell sto c ks. Beha vioural c harac-
teristics of returns in these mo dels are sho wn to b e similar to those observ ed in real-w orld
nancial mark ets (Grossman & Stiglitz 1980, Summers 1986 a, P oterba & Summers 1988, Lo
& MacKinla y 1988).
In building to w ards a theory-free paradigm of non-parametric testing of mark et eciency ,
tests are based on the premise of no-arbitrage, i.e., that opp ortunities for earning un usual
returns do not exist. These tests target consisten t statistical c haracteristics of the price
and returns pro cess using few in ter-link ages with a sp ecic mo del of asset pricing. Th us
in this t yp e of test, the rejection of the n ull sp eaks as direct evidence of lac k of mark et
eciency , without the confusion caused b y a parametric asset pricing theory in the picture.
Our fo cus will b e to establish st ylised empirical facts ab out mark et eciency , and help pa v e
the w a y for future researc h in to asset pricing theory . The eciency testing strategy in this thesis
will emphasise \non-parametric" strategies of testing for the absence of arbitrage opp ortunities,
with little emphasis on the greater sup erstructure of the established economic theories of asset
pricing.
The form ulation of mark et eciency used here is similar to that of F ama (1991). T ests
of mark et eciency are categorised in to three sets using dieren t denitions of the a v ailable
information set (denoted b y F
t
). The three categories are as follo ws:
1. R eturns pr e dictability : Based on the premise that past prices encapsulate all the infor-
mation ab out the sto c k, mark et eciency means that no p ossible arbitrage opp ortunities
37
can unco v ered through an analysis of the time series of returns. In these tests for mark et
eciency , w e test for returns predictabilit y .
1
One of the rst pap ers to dene the n ull for a price pro cess arising from an ecien t mar-
k et w as Sam uelson (1965). He concluded that giv en rationalit y of the in v estor and zero
transactions costs, prices could b e mo deled as a random w alk. This in turn, implies that
returns are a white noise pro cess. Based on this denition, w e can construct t w o sets of
tests of returns predictabilit y:
Non-parametric tests suc h as serial correlation, runs analysis and v ariance ratio.
T ests of seasonalit y suc h as testing for the Jan uary eect and the w eek end eect.
2. Event Studies : These tests study the eect of an economic ev en t on the b eha viour of
returns. The ev en t here is a corp orate action, examples of whic h are announcemen ts of
dividend, new sto c k issues or sto c ks splits. In these tests (whic h are also referred to as
\semi-strong tests of mark et eciency"), F
t
con tains prices as w ell as publicly a v ailable
corp orate information.
The ecien t mark et h yp othesis p ostulates a certain eect on the b eha viour of returns due
to these ev en ts. If there is a consisten t deviation from the exp ected b eha viour, it w ould
mean an arbitrage opp ortunit y for an in v estor to prot from. An ecien t mark et w ould
mean that the opp ortunit y w ould disapp ear v ery quic kly . F ailure to do so implies there
exists some mark et ineciency that prev en ts adjustmen t to new announcemen ts b y rms
(Charest (1978), Banz (1981) ha v e b een some of the rst few studies in this area).
1
This suite of tests, based on F
t
con taining only the price v ector, is also referred to in the literature as
the \w eak form tests of mark et eciency".
38
Ev en t studies ha v e b een an explosiv e eld of study in sto c k mark ets in recen t y ears. The
initial w ork of F ama, Fisc her, Jensen & Roll (1969), Bro wn & W arner (1980) and Bro wn
& W arner (1985) has led to a plethora of w ork on v arious ev en ts aecting the sto c k price
b eha viour (Dra vid 1987, Karp o & W alkling 1990, Lang & Stulz 1994, Karaath 1994,
Armitage 1995).
One unique feature of ev en t studies is that, unlik e all other forms of mark et eciency re-
searc h, these allo w us to pinp oin t the sequence of ho w mark ets assimilate information. This
allo ws us to capture mark et eciency qualitativ ely , as the sp eed with whic h information
is assimilated in to prices. On the bse, a recen t ev en t study on gdr issues (Shah 1995 c)
analyses whether the common sto c k of rms issuing Global Dep ository Receipts ( gdrs,
whic h are issues listed and traded in exc hanges outside the home coun try) w ere mispriced
at the time of issue (Section 3.3.2).
In this thesis, w e examine the eect of b on us issues of sto c k in the framew ork of ev en t
study analysis. Bon us issues are equiv alen t to sto c k splits in the u.s. and ha v e b een found
in the literature to b e instances with un usual excess returns.
3. T ests of Insider Information : The previous t w o tests of mark et eciency illustrates no-
arbitrage within the framew ork of publicly a v ailable information. The last set of tests of
mark et ineciency includes information that is not publicly a v ailable in F
t
(these are called
the \strong form tests of mark et eciency").
The tests apply to situations where information is made a v ailable to only a subset of
in v estors who, if the mark et is ecien t, will still not b e able to a v ail of arbitrage opp ortuni-
ties. The only observ able instance of suc h situations is in the p erformance of m utual funds.
39
Managers of suc h funds migh t ha v e priv ate information a v ailable, p erhaps b y virtue of large
institutional purc hases (Jae 1974, Lacey & Phillips-P atric k 1992). The tests are based
on the premise that the sup erior information set should result in a consisten tly sup erior
p erformance of the fund.
W e will test the strong form of mark et eciency using a p erformance ev aluation study of
the t w en t y oldest closed-end funds in India, that ha v e the longest time-series of returns
data a v ailable.
3.1 Data Description and Univ ariate Summary
Statistics
In the thesis, our main fo cus is on the empirical analysis of mark et eciency as measured b y
returns on a mark et index. The data-set con tains returns on t w o mark et indexes. The rst index
is the bse Sensex, where the time-series starts from April 1979. This is a v alue-w eigh ted index of
30 companies, the comp osition of whic h has b een c hanged v ery sligh tly across this time p erio d.
The other index is the Index-250, whic h is a shorter time series from Ma y 1992 on w ard. This is a
v alue-w eigh ted index of 250 companies, whic h will serv e to capture the b eha viour of the smaller
companies and the companies that ha v e en tered the mark et since the lib eralization to ok place.
The time in terv al of 1990 to 1995 has b een a tum ultuous one for the Indian econom y . The
ev en t with the largest impact in this p erio d w as the Scam of 1992. W e exp ect the statistical
c haracteristics of the Scam p erio d to b e dieren t from the other time p erio ds. In this section,
w e examine returns for the p erio ds of Jan uary 1990 up to Septem b er 1991 (whic h is called the
40
Pr e-Sc am p erio d), Septem b er 1991 up to July 1992 ( Sc am) and after July 1992 ( Post-Sc am )
separately .
When w ork on this thesis w as started, the data-set con tained rm lev el data for 92 \A"
companies, with daily price data from Jan uary 1990 to Ma y 1994. These 92 companies accoun ted
for Rs. 2 trillion of the total mark et capitalization of the bse of Rs. 5 trillion in 1994. Most of
the eciency tests ha v e b een done using this data.
In Jan uary 1995, a larger data-set of 250 companies w as made a v ailable, with data up to
Decem b er 1994. These 250 companies accoun t for Rs.3.7 trillion of the total mark et capitalisation
of the bse of Rs.5.1 trillion; they are hence an excellen t sample to w ork with to c haracterise the
time structure of the bse. The smallest corp oration used here has a mark et capitalisation of
Rs.3.1 billion, or $100 million. The data for this set of companies ha v e dieren t starting p oin ts
of time and mak e for a less con tin uous time series.
2
W e b egin the analysis with T able 3.1 b elo w that outlines the univ ariate statistics for daily
returns of the t w o indexes.
2
These additions are new companies that en tered the mark et later or suered from more non-
sync hronous trading.
41
Median Mean Standard Sk ewness Excess
Deviation Kurtosis
1990{1994 bse Sensex 0.1389 0.1853 2.2905 0.1343 3.3263
July 1992{Dec 1994 Index-250 0.0540 0.0841 1.5405 -0.1021 0.7629
1990 bse Sensex 0.1297 0.1494 2.5517 -0.2726 1.7905
1991 bse Sensex 0.1476 0.2900 1.9720 0.1580 4.2240
1992 bse Sensex 0.2596 0.2401 3.2516 0.3067 1.6462
1993 bse Sensex 0.1980 0.1157 1.8578 -0.2134 0.0916
Index-250 0.2208 0.1541 1.6138 -0.4671 0.9076
1994 bse Sensex 0.0492 0.1326 1.4957 0.5477 1.5667
Index-250 -0.019 0.0811 1.2714 0.6351 1.7250
1990{1994 bse Sensex 0.1380 0.1183 1.7468 0.2432 5.1220
July 1992{Dec 1994 Index-250 0.0540 0.0841 1.5405 -0.1021 0.7629
Pre-Scam bse Sensex 0.2258 0.2465 2.3766 -0.2216 2.7208
(Jan90{Sep91)
Scam bse Sensex 0.0693 0.4334 3.1793 0.4387 2.5163
(Sep91{Jul92)
P ost-Scam bse Sensex 0.0400 0.0401 1.8096 -0.0384 0.5468
(Jul92{Dec94) Index-250 0.0540 0.0794 1.5324 -0.1102 0.7815
T able 3.1: Univ ariate statistics for the bse Sensex and Index-250.
In k eeping with our exp ectations of scam-related c hanges, there seems to b e a rather abrupt
increase in the mean return of the bse Sensex from 1990 to 1991, with a decrease in the standard
deviation ( ). In 1992, the more p erceptible c hange is in the increase of . These c hanges are
more mark ed when the time in terv als are categorized with resp ect to the scam ev en t.
T able 3.2 and T able 3.3 tabulates the rst four momen ts of the t w o rm lev el price data.
42
Median Mean Standard Sk ewness Kurtosis
Deviation 1990 0.062 0.033 4.143 -0.035 10.166
0.304 2.634 2.420 29.219
1991 0.330 0.348 3.444 0.968 6.834
0.202 1.236 1.217 12.255
1992 0.177 0.187 5.522 0.614 9.529
0.241 2.054 1.641 14.238
1993 0.144 0.151 3.052 0.129 4.671
0.150 0.833 1.036 6.928
1994 0.033 0.031 3.408 0.149 2.766
0.271 1.110 0.984 5.615
1990{1994 0.166 0.163 4.174 -0.138 35.621
0.111 1.392 4.505 107.163
Pre-Scam 0.188 0.199 3.995 0.202 15.783
0.213 2.085 3.080 47.036
Scam 0.313 0.370 5.582 0.810 7.484
0.323 1.971 1.018 5.605
P ost-Scam 0.062 0.068 3.442 -0.149 11.343
0.141 1.257 2.151 33.394
Note: The smaller n um b er en tered b elo w the estimated co ecien t is the standard deviation of the statistic.
T able 3.2: Univ ariate statistics of daily returns on A companies
43
P erio d Num b er Median Mean Standard Sk ewness Kurtosis
Deviations 1990 177 0.102 0.223 4.697 0.366 5.533
0.822 3.604 0.878 6.849
1991 186 0.363 0.499 4.374 0.789 7.130
1.2477 3.6768 1.263 14.087
1992 202 0.164 0.367 7.382 0.437 7.646
2.077 7.397 1.335 11.490
1993 225 0.172 0.178 4.629 -0.081 7.110
0.918 4.408 1.466 14.847
1994 246 0.086 0.137 3.830 0.514 6.720
0.375 2.460 1.415 17.199
1990{1994 250 0.186 0.255 5.064 0.504 23.055
0.777 2.916 2.257 57.541
Pre-Scam 250 0.211 0.321 4.518 0.663 8.745
0.430 2.510 1.224 16.477
Scam 250 0.383 0.910 7.365 0.556 7.411
3.986 8.351 1.231 9.836
P ost-Scam 250 0.086 0.136 4.491 0.093 13.099
0.906 3.285 1.643 30.304
Note: The smaller n um b er en tered b elo w the estimated co ecien t is the standard deviation of the statistic.
T able 3.3: Univ ariate statistics of daily returns on 250 companies
44
3.2 Returns Predictability
The no-arbitrage principle expresses the idea that if mispriced assets exist in an econom y p op-
ulated b y rational agen ts, they will b e able to earn prots with no risk. Under this condition,
in v estors will con tin ue trading un til the prots are driv en do wn to zero. In the pro cess, the mis-
pricing will b e eliminated. Since this will happ en ev ery time an arbitrage opp ortunit y arises, price
lev els will b e con tin uously main tained at what Sam uelson (1965) referred to as price outcomes
from a \fair game". Sam uelson (1965) mo deled this prop ert y as the random w alk prop ert y of
prices, where the b est prediction of price at the next time p erio d ( P
t+1
) is the price at the curren t
time (P
t
).
P
j t
= P
j (t 1)
+ j t
where j t
D (0; )
or E (P
j t
) = P
j (t 1)
Here, P
j t
is the price of sto c k j at time t. j t
is the information inno v ation to the price.
If prices are a random w alk, then p ercen tage c hanges in the price ough t to b e white noise.
If w e follo w the ab o v e random w alk mo del of prices P
t
, the n ull h yp othesis of mark et eciency
is equiv alen t to testing returns for the standard statistical prop erties of a homosk edastic white
noise pro cess as follo ws:
H
0
: E (r
t
) = 0;
E (r
t
r
t
) = 2
r
;
E (r
t
r
s
) = 0; 8t 6= s
45
The condition whic h sets the exp ected v alue of r
t
to b e 0 is not economically v ery sensible,
since these are risky instrumen ts and m ust oer p ositiv e returns to attract in v estors. Th us
the n ull b ecomes H
0
: E (r
t
) = r
. The sample mean ^ m is a consisten t estimator of r
.
3
The second condition on the v ariance of returns is a v ery imp ortan t one from more than
one p oin t of view. Kno wledge ab out the v ariance is of considerable imp ortance in the area
of asset pricing mo del form ulation and ev aluation; p ortfolio formation whic h crucially relies
on kno wledge of v ariance and co v ariance of returns; in the pricing of deriv ativ e instrumen ts.
An estimator often used is the sample v ariance, ^ s
2
r
.
Estimation of a constan t 2
r
is sub ject to the same problems as that of estimating r
, since
it is practically imp ossible to nd a series that has constan t v ariance across dieren t p erio ds
of time. The profession has partially resolv ed this problem using sto c hastic pro cesses with
conditional heterosk edasticit y . Th us, the fo cus of researc h has shifted to a study of the
conditional second momen ts of the returns pro cess. If the returns pro cess is dened as
r
t
= r
+ t
where t
jF
t 1
D (0; h
t
)
the conditional v ariance h
t
of the series is found to ha v e a v ery w ell dened time dep enden t
structure that helps explain some of the statistical b eha vioural c haracteristics of the returns.
The time-series structure is giv en in one relativ ely general form ulation as:
3
The estimation of the rst momen t has b een the fo cus of a lot of the asset pricing mo dels suc h as the
capm. In our con text, w e are not in terested in the v alue of r
, but rather in the time series prop erties of
the r
t
pro cess.
46
h
t
= +
p
X
i=1
i
2
t i
+
q
X
j =1
j
h
t j
This is kno wn as the Generalized Auto-regressiv e Heterosk edasticit y (GAR CH) form of
error and is widely used in iden tifying nancial time series.
4
These mo dels ha v e b een
successful, in no mo derate measure, in explaining the amoun t of sk ewness and kurtosis
found in returns data all o v er the w orld.
W e will explore the notion of conditional second momen t of the returns pro cess in greater
depth in the next c hapter on the v olatilit y structure of bse returns. In this c hapter, w e will
fo cus en tirely on the returns and excess returns b eha viour, assuming homosk edasticit y .
The last condition for the pro cess to b e white noise comes from the structure of the auto-
correlation co ecien ts k
at dieren t lags k . White noise pro cesses are uncorrelated across
time. Th us, the n ull is dened as H
0
: k
= 0:0; 8k . Giv en T observ ations, the rejection
region is outside 2=
p
T , as T ! 1. This is the sub ject that w e will study in the next
section.
3.2.1 Serial Correlation
The acf of the returns of the mark et index are examined for the rst eigh t lags in T able 3.4.
Ov erall, data for the bse Sensex is 3325 observ ations, data for the Index-250 is 667 observ ations.
The asymptotic b ounds 2
p
T ev aluate to 0:0347 for the bse Sensex and 0:076 for the Index-
250. The o v erall auto-correlation function is:
4
Bollerslev, Chou & Kroner (1992)
47
Lag bse Sensex Index-250
1 0.114 0.331
2 -0.039 0.031
3 0.001 0.011
4 0.008 0.031
5 -0.014 0.067
6 0.003 0.011
7 0.001 0.018
8 0.010 -0.037
T able 3.4: acf for bse Sensex and Index-250
1
lies outside the asymptotic b ounds for b oth the indexes. This suggests deviations from
mark et eciency in the v ery short run, i.e., a da y . The more pronounced rejection of H
0
: 1
= 0
in the case of Index-250 is lik ely to b e caused b y non-sync hronous trading to some exten t.
5
The acf of the daily returns for the 250 individual companies are also examined. Daily
returns for these companies are observ ed from 1 Jan uary 1990 on w ard, whic h is v e y ears of
data. The mark et w as op en for business for 1039 da ys in these v e y ears.
6
T otally , there are
186,879 observ ations of returns in this data-set.
In the acfs in T able 3.5, the largest n um b er of rejections of the asymptotic b ounds are found
at a lag of one, with 44% of the companies ha ving co ecien ts outside the asymptotic b ounds. Of
the companies with rejections, 34% ha v e negativ e correlations. The lags ha ving the next largest
n um b er of companies with out of b ound co ecien ts are at lags of nine and t w o. A t lags t w o and
three, the p ositiv e rejections substan tially outn um b er the negativ e, whereas it is vice-v ersa for
the remaining lags examined.
5
The issue of non-sync hronous trading is dealt with in greater detail in the c hapter on v olatilit y mo dels,
Chapter 4. In a n utshell, this is the dela y ed impact of sho c ks to the econom y through companies that
trade at a lag with resp ect to information inno v ation or less frequen tly with resp ect to other companies
on the mark et.
6
The n um b er of traded da ys for whic h these companies are observ ed, ho w ev er, v aries substan tially; 60%
of the companies ha v e data for more than 904 trading da ys, and the highest observ ed is 994 traded da ys.
48
But, b oth in the case of the index and the individual companies, the o v erall b eha viour of the
acf is the same, with strongly signican t correlations at lag of one. The presence of large correla-
tion in all these cases - with dieren t c haracteristics of trading patterns, size, nancing structure,
mark et reputation - strengthens the notion that there is strong rst order time dep endence in
returns. F rom this, w e admit the p ossibilit y of mark et ineciency on the bse.
Lag Negativ e P ositiv e T otal
rejections rejections
1 84 25 109
33.6% 10.0% 43.6%
2 8 39 47
3.2% 15.6% 18.8%
3 4 29 33
1.6% 11.6% 13.2%
4 14 15 29
5.6% 6.0% 11.6%
5 20 14 34
8% 5.6% 13.6%
6 17 11 28
6.8% 4.4% 11.2%
7 11 24 35
4.4% 9.6% 14%
8 26 19 45
10.4% 7.6% 18%
9 8 42 50
3.2% 16.8% 20%
10 4 33 37
1.6% 13.2% 14.8%
11 9 18 27
3.6% 7.2% 10.8%
12 14 8 22
5.6% 3.2% 8.8%
13 26 10 36
10.4% 4.0% 14.4%
14 15 11 26
6.0% 4.4% 10.4%
15 15 9 24
6.0% 3.6% 9.6%
T otal 275 307 582
47.25% 52.75% 100.00%
P ercen tages are of total n um b er of rejections
T able 3.5: Number of rejections of H
0
: k
= 0
49
Ho w signican t are these deviations from = 0 in an economic sense? W e can get a practical
in tuition for this b y observing the acf for the 30 companies whic h mak e up the bse Sensex
mark et index, presen ted in decreasing order of mark et size.
Compan y 1 2 3 4 5 6 7 8 asymptotic
b ounds
I.T.C. -0.004 0.088 0.062 0.023 -0.019 -0.036 0.075 -0.033 0.048
Reliance 0.055 0.061 -0.007 0.032 -0.037 -0.068 0.092 -0.016 0.053
HLL 0.028 0.019 0.126 0.011 -0.108 -0.077 0.117 -0.117 0.094
TISCO 0.072 -0.027 -0.020 0.031 -0.008 -0.037 0.043 -0.079 0.048
Colgate -0.045 -0.001 0.050 0.037 -0.088 -0.047 0.092 -0.091 0.064
L&T -0.016 0.026 0.029 0.084 -0.024 -0.000 -0.035 -0.025 0.045
TELCO 0.013 0.033 -0.020 0.052 0.035 -0.007 0.024 -0.006 0.024
T ata Chem 0.032 0.072 0.048 0.013 0.007 -0.068 -0.031 -0.076 0.054
ICICI -0.060 -0.009 0.033 0.020 0.041 -0.025 0.104 -0.075 0.053
Grasim 0.012 0.066 0.044 0.052 0.019 -0.034 0.076 -0.116 0.055
Hindalco -0.033 0.014 0.034 0.068 -0.005 0.017 0.016 -0.077 0.049
Ba ja j Auto 0.093 -0.005 0.066 0.006 -0.036 -0.023 -0.121 -0.054 0.058
Cen tury T extiles 0.007 0.012 0.026 0.052 0.037 0.035 0.037 -0.077 0.038
T ata T ea -0.052 -0.003 0.019 0.087 -0.065 -0.050 0.109 -0.040 0.062
Castrol -0.039 0.042 0.014 -0.022 -0.063 -0.039 -0.059 -0.043 0.072
Bro ok e Bond -0.023 -0.047 0.053 0.061 -0.049 -0.029 0.100 -0.007 0.050
HDF C -0.036 0.046 -0.020 0.022 0.008 0.042 0.003 0.070 0.036
A CC 0.074 0.002 0.031 0.036 0.025 -0.017 0.023 0.016 0.030
Nestle 0.059 -0.065 -0.001 0.006 -0.035 -0.039 0.043 -0.069 0.053
GESCO 0.015 -0.012 -0.025 -0.010 -0.034 -0.040 0.101 0.039 0.042
Indian Ra y on -0.129 0.075 0.038 0.061 -0.008 -0.045 0.132 -0.095 0.086
Indo Gulf -0.066 0.030 -0.047 -0.029 -0.046 0.059 -0.020 -0.003 0.038
Co c hin Reneries 0.071 0.001 -0.050 0.023 -0.039 0.032 -0.034 -0.057 0.051
Siemens -0.086 0.079 -0.015 0.024 0.031 -0.021 -0.009 -0.037 0.056
Essar Gujarat 0.036 -0.058 0.039 -0.030 0.066 -0.010 -0.002 0.018 0.038
SCICI 0.126 0.09 0.005 0.034 -0.090 0.003 0.129 -0.024 0.071
GSF C 0.136 -0.014 -0.022 -0.047 -0.036 -0.039 -0.019 -0.081 0.064
Indian Hotels -0.171 0.089 -0.034 0.002 0.004 0.060 -0.031 0.116 0.079
T ata P o w er 0.157 -0.000 0.023 0.055 -0.019 -0.053 -0.004 -0.010 0.055
MICO -0.017 0.064 -0.040 0.012 -0.042 -0.081 0.051 -0.034 0.053
T able 3.6: acf for 30 companies
The t w en t y largest companies sho w no sign of signican t auto-correlation un til at rather long
lags (in this table, at a lag of sev en). Whereas further do wn the list, there app ear rejections of
asymptotic b ounds at lag one. These are all \A" companies whic h ha v e similar c haracteristics of
liquidit y and trading patterns. The size of these companies range from Rs. 104 billion to Rs. 17
billion.
50
In the literature on the u.s. mark ets, the size of the rm has b een found to b e one of the
more inuen tial factors aecting the b eha viour of sto c k returns. This eect has b een do cumen ted
extensiv ely for the u.s. mark ets (Banz 1981, Reingan um 1981, Roll 1981, Bro wn, Kleidon &
Marsh 1983, Stoll & Whaley 1983, Keim 1983, Keim 1986), where the nding is that smaller
rms are consisten tly observ ed to ha v e higher exp ected returns as compared to large rms. The
premise b eing that smaller rms are in some sense \riskier" and the higher returns are just
commensurate with this higher lev el of risk. In the next section, w e fo cus mostly up on the
relationship b et w een size and rejections of mark et eciency . But some simple results ab out the
relationship b et w een size and exp ected returns are also sho wn.
3.2.1.1 Analysis b y Size
The follo wing empirical metho dology is used to examine the size eect on the bse. A t the start
of eac h quarter, all A companies are sorted based on size (i.e. mark et capitalisation). This sorted
list is brok en up in to four quartile p ortfolios: Small, Q2, Q3 and Big. Eac h of these quartile
p ortfolios are held constan t for the duration of the quarter.
7
This pro cess is rep eated at the start of eac h quarter, so that all through, the returns on the
p ortfolio Small reects the impact of size alone, without the confusion caused b y small companies
that switc hed categories. This recalculation also solv es the sligh t turno v er caused b y additions
to A companies etc.
T able 3.7 rep orts the result of this exercise. Eac h quarter sho ws returns on four p ortfolios and
returns on the bse Sensex for a frame of reference. Since the bse Sensex is mostly big companies,
the returns on the bse Sensex often resem ble those of the Big p ortfolio. Ho w ev er the bse Sensex is
7
P ortfolio b etas (not sho wn here) for this set of companies all range from 0.9 to 1.1.
51
v alue-w eigh ted while the quartile p ortfolios are equally-w eigh ted. In addition, there are only 22
companies in the Big p ortfolio whereas the bse Sensex has 30 companies. Hence some deviations
b et w een bse Sensex and Big are to b e exp ected.
The rst line in the table b elo w the Small p ortfolio, framed using the metho dology ab o v e on
30 Marc h 1990, w ould ha v e giv en 23.7% returns o v er the quarter.
Start Small Q2 Q3 Big bse Sensex
Date
30Mar90 23.70 7.60 7.00 6.70 8.90
29Jun90 69.30 56.60 52.70 58.20 67.00
28Sep90 -29.70 76.60 -23.10 -27.10 -26.20
28Dec90 21.00 0.00 15.40 10.20 11.40
29Mar91 1.90 0.00 0.00 0.00 8.70
28Jun91 59.60 45.00 41.70 42.70 47.30
27Sep91 16.40 7.70 7.80 -0.10 2.10
27Dec91 92.20 111.90 89.30 94.50 98.60
27Mar92 -25.50 -22.70 -20.60 -22.80 -18.70
26Jun92 17.40 18.30 6.60 15.00 5.70
25Sep92 0.00 0.00 0.00 -13.80 -19.70
25Dec92 -23.70 -14.90 -10.00 -11.90 -10.50
26Mar93 5.50 5.40 2.50 -3.30 -5.90
25Jun93 36.10 25.20 22.80 28.30 23.50
24Sep93 34.40 27.10 38.90 26.30 22.90
Ov erall 734.70 457.10 458.40 297.20 228.40
The o v erall returns is pro duct of all quarters sho wn.
T able 3.7: Size-Returns(%) analysis of companies by Quartiles
W e can in terpret the ab o v e as b eing preliminary evidence of a size eect on the BSE. P ortfolio
Small yields returns of 734.7% as compared to 328.4% b y the bse Sensex and 297.2% b y Big. So
there do es seem to b e a size eect in the Indian rms similar to that found in the u.s. data.
W e will no w examine there is a similar inuence of size up on the acf of returns. W e calculate
acf for quartiles of the A companies and the 250 companies for eigh t lags. Then w e examine the
n um b er of violations in the asymptotic b ounds for eac h quartile. It is in teresting to apply this
to b oth the A group companies, and to the 250 companies for the follo wing reason. The set of A
52
group companies is relativ ely homogeneous with resp ect to c haracteristics lik e liquidit y , v olumes,
etc. In con trast, the 250 companies are a more heterogeneous set where the range of size is more
disparate than in the case of the A companies alone. If size matters, then w e exp ect to see a
sharp er range of dierences in the p ercen tage of rejections among the quartiles of the second set.
A companies 250 companies
Quartile Num b er of P ercen t Num b er of P ercen t
Rejections Rejections
Big 30 20.7 126 30.5
Q2 36 24.8 107 25.9
Q3 42 29.0 91 22.0
Small 37 25.5 89 21.5
T otal 145 100.0 413 100.0
T able 3.8: Asymptotic V ariance Bounds violations in Size Quartiles
In the case of the \A" companies, w e nd that there is not a v ery large increase of asymptotic
b ound rejections across the quartiles. Ho w ev er, the results are quite remark able in the case of the
250 companies, where rms with ab o v e-median size app ear to ha v e substan tially more rejections
of the n ull as compared with rms of b elo w-median size. This is an anomalous result, in the
sense that w e w ould normally exp ect the b est mark et eciency prop erties to b e upheld for large,
w ell-traded companies.
It is v ery lik ely that this particular relationship b et w een size and mark et eciency is true for
this sample, i.e. the largest 250 corp orations with mark et capitalisation ab o v e $100 million, but
do es not generalise b ey ond. If w e go further do wn to the really small companies, it is v ery lik ely
that size is actually negativ ely correlated with mark et eciency .
8
The results from the serial correlation analysis of returns for the indexes and companies on the
bse seem to suggest some amoun t of mark et ineciency as measured b y statistically signican t
8
W e ha v e, ho w ev er, not explored this issue further due to the paucit y of data.
53
correlation co ecien ts at lag one. P art of this migh t b e due to non-sync hronous trading.
9
There
is some amoun t of a size eect but there is some am biguit y in the the direction of the eect on
the degree of mark et eciency .
3.2.2 Runs T ests
The second common non-parametric test of mark et eciency is the runs test. A run is dened
as the rep eated o ccurrence of the same v alue or category of a v ariable. It is indexed b y t w o
parameters: the t yp e of the run and the length. Price runs can b e P ositiv e (+), No Change ( :)
or of t yp e Negativ e ( ). The length is ho w often a run t yp e happ ens in succession. Th us a series
of four price increases is a p ositiv e run of length four.
The original premise b ehind the test is that a random w alk pro cess for prices implies a xed
distributional form for runs in returns. One of the testable h yp otheses arising from this mo del, as
dened in F ama (1965), is that for long time series of sample size N, the total exp ected n um b er
of runs is distributed as normal with mean,
=
N (N + 1) P
3
i=1
n
2
i
N
and standard deviation
=

P
3
i=1
[
P
3
i=1
n
2
i
+ N (N + 1)] 2N (
P
3
i=1
n
3
i
N
3
)
N
2
(N 1)
! 1
2
9
as evinced b y higher co ecien ts in the the case of the Index-250 compared with that of the bse Sensex,
whic h has less sto c ks traded async hronously .
54
where n
i
is the n um b er of runs of t yp e i.
The test for serial dep endence is carried out b y comparing the actual n um b er of runs, A
r
, in
the price series to the exp ected n um b er . The n ull prop osition is :
H
0
: E (r uns) = Ev er since F ama (1965), sev eral pap ers on mark et eciency ha v e emplo y ed the runs tests
in a similar framew ork for v erication of the \w eak form eciency" of mark ets, b oth for the
u.s. and for other coun tries (Sharma & Kennedy 1977, Co op er 1982, Chiat & Finn 1983, W ong
& Kw ong 1984, Y ala w ar 1988, Ko & Lee 1991, Butler & Malaik ah 1992). These t ypically nd
that on most mark ets, the n ull is not rejected.
In this section, runs in the returns of the t w o mark et indexes and then in individual companies,
are studied. The test results for the indexes are displa y ed as Prob V alues are tabulated in T able
3.9.
Y ear No. of bse Sensex Index-250
Observ ations
1979-1994 3113 0.308
1990 199 0.382
1991 206 0.496
1992 188 0.336
1993 213 0.088 0.083
1994 199 0.280 0.127
Mid-1992{1994 560 0.040 0.006
Pre-Scam 339 0.413
Scam 156 0.397
P ost-Scam 549 0.051 0.006
T able 3.9: Prob V alues for H
0
: E (runs) = for bse Sensex and Index-250
55
There seems to b e a clear break in the b eha vioural pattern in 1993 with dierences b et w een
the actual and exp ected n um b er of runs signican t at the 90% condence lev el. This eect seems
to b e accen tuated in the P ost-Scam p erio d with dierences signican t at the 95% condence lev el
for the bse Sensex and at a larger lev el for the Index-250.
10
An in teresting asp ect to runs of b oth series in this p erio d is that the observ ed n um b er of
runs is signican tly less than the exp ected n um b er of runs. This is evidence in supp ort of the
strong negativ e auto-correlations observ ed in the rst lag of b oth the indices and the companies
themselv es.
A further study of the runs can b e done for the indexes. Runs are brok en do wn in to the three
t yp es. Eac h t yp e is then studied for dieren t run lengths. The case of runs of no c hange implies
that prices remained constan t. This migh t arise mainly out institutional reasons
11
and these
t yp es of c hanges will not b e considered in the follo wing analysis. Actual n um b ers are compared
to the exp ected n um b er of runs of eac h sign.
12
The runs of dieren t lengths for the bse Sensex and the Index-250 are tabulated against the
exp ected n um b ers in eac h case b elo w. There are appro ximately 200 daily p oin ts for the bse
10
This seems in accordance with the evidence in the previous section on serial correlations.
11
There exists a lot of no trading da ys and da ys for whic h the mark et remains closed.
12
This is calculated using the follo wing metho dology (F ama 1965, Hogg & Craig 1978): The probabilit y
of the run of a particular sign is the exp ected n um b er of runs of that sign to the total n um b er of runs
exp ected. This dep ends up on the distribution that generates the sign c hanges in the returns. If the signs
of returns are generated b y a Bernoulli pro cess with probabilit y of a p ositiv e c hange b eing P (+), then the
probabilit y of a p ositiv e run is
N P (+)[1 P (+)]
This is the summation of p ositiv e runs of all p ossible lengths (as in a Bernoulli pro cess). P (+) is the
sample probabilit y of a p ositiv e v alue, and N is the sample size. Then, if R is the total n um b er of runs,
the probabilit y of a p ositiv e run of length k is
R
k
(+) = RP (+)
k
[1 P (+)]
The assumption made is that the sample prop ortions of price c hanges are indep enden t and are go o d
estimates of the p opulation estimate of the probabilit y of a run t yp e.
56
Sensex ev ery y ear and the statistical eciency of the follo wing analysis is th us limited. W e use
it mostly for exp ository purp oses and nd it to rev eal in teresting insigh ts.
bse Sensex Index-250
P erio d Length Negativ e P ositiv e Negativ e P ositiv e
Observ ed Exp ected Observ ed Exp ected Observ ed Exp ected Observ ed Exp ected
Pre-Scam
1 42 44.334 31 37.361
2 21 20.068 21 20.339
3 11 9.084 19 11.072
4 3 4.112 4 6.027
5 2 1.861 2 3.281
6 0 0.843 3 1.786
7 2 0.381 0 0.972
8 0 0.173 0 0.529
9 0 0.078 0 0.288
10 0 0.035 1 0.157
Scam
1 19 19.097 14 17.419
2 7 9.240 11 8.991
3 8 4.471 7 4.640
4 1 2.163 2 2.395
5 0 1.047 1 1.236
6 1 0.507 0 0.638
7 0 0.245 0 0.329
8 1 0.119 0 0.170
9 0 0.057 0 0.088
10 0 0.028 1 0.045
P ost-Scam
1 41 58.861 44 54.850 34 53.581 33 50.118
2 30 27.927 23 28.226 24 25.976 23 25.731
3 17 13.250 19 14.525 18 12.593 18 13.211
4 16 6.286 11 7.475 15 6.105 13 6.783
5 4 2.983 11 3.846 5 2.960 7 3.482
6 4 1.415 0 1.979 6 1.435 3 1.788
7 0 0.671 4 1.019 2 0.696 4 0.918
8 0 0.319 1 0.524 0 0.337 1 0.471
9 0 0.163 0 0.242
10 0 0.079 0 0.124
11 0 0.038 0 0.064
12 0 0.019 0 0.033
13 0 0.009 1 0.017
T able 3.10: Run lengths for the indexes classication by Scam Ev ent
57
bse Sensex Index-250
Y ear Length Negativ e P ositiv e Negativ e P ositiv e
Observ ed Exp ected Observ ed Exp ected Observ ed Exp ected Observ ed Exp ected
1990 1 21 23.929 17 22.551
2 13 11.481 13 11.731
3 7 5.509 11 6.102
4 2 2.643 3 3.174
5 1 1.268 1 1.651
6 0 0.608 0 0.859
7 2 0.292 0 0.447
8 0 0.140 0 0.232
9 0 0.067 0 0.121
10 0 0.032 1 0.063
1991 1 29 27.863 20 23.385
2 9 12.640 16 12.662
3 9 5.734 9 6.856
4 2 2.601 1 3.712
5 1 1.180 2 2.010
6 1 0.535 3 1.088
1992 1 18 22.235 20 20.465
2 14 10.464 7 10.725
3 5 4.924 10 5.621
4 2 2.317 3 2.946
5 1 1.090 1 1.544
6 1 0.513 0 0.809
7 0 0.241 1 0.424
8 1 0.114 0 0.222
9 0 0.053 0 0.116
10 0 0.025 1 0.061
1993 1 13 20.792 13 17.387 14 21.408 12 16.329
2 8 9.415 7 9.432 9 9.347 7 9.123
3 6 4.264 4 5.116 6 4.081 4 5.097
4 8 1.931 4 2.775 5 1.782 3 2.847
5 1 0.874 7 1.505 1 0.778 6 1.591
6 2 0.396 0 0.817 3 0.340 2 0.889
7 0 0.179 2 0.443 0 0.148 2 0.497
8 0 0.081 0 0.240 0 0.065 0 0.277
9 0 0.037 0 0.130 0 0.028 0 0.155
10 0 0.017 0 0.071 0 0.012 0 0.087
11 0 0.008 1 0.038 0 0.005 0 0.048
12 0 0.002 0 0.027
13 0 0.001 1 0.015
1994 1 18 22.011 15 19.674 14 21.712 16 22.795
2 9 10.194 11 10.458 8 10.998 9 11.248
3 7 4.722 8 5.559 11 5.571 10 5.550
4 5 2.187 5 2.955 6 2.822 7 2.739
5 1 1.013 1 1.571 2 1.430 0 1.351
6 1 0.469 0 0.835 2 0.724 1 0.667
7 0 0.217 1 0.444 1 0.367 1 0.329
8 0 0.101 1 0.236 0 0.186 1 0.162
T able 3.11: Run Lengths of indexes classied by y ears
The breakup across smaller time-p erio ds sho w similar c haracteristics of the runs pro cess.
Sp ecically ,
58
A t the rst lag of ev ery p erio d, the observ ed n um b er of runs is almost alw a ys less than the
exp ected.
W e tabulated the frequency distribution of the t yp es of runs at the longest run length for
the A companies and the 250 companies data-set. In the A companies, 65% of the longest
run lengths w ere p ositiv e while 52% w ere p ositiv e for the 250 companies.
F or the indexes, the outliers or the longest runs are p ositiv e across all p erio ds.
W e further analysed the runs for the companies b y studying the cross-sectional distribution
of the Prob v alues of the observ ed and the exp ected n um b er of runs, in Figure 3.12. Only t w o
p ercen t of the A companies (three companies) ha v e total runs that are signican tly dieren t from
at the 90% condence in terv al. The n um b er of runs are all less than the exp ected. 75% are
within the 60% in terv al around the mean. Once again, it is found that 83 out of 95 companies
ha v e actual n um b er of runs lesser than exp ected.
59
0.0 0.5 1.0
A companies
0
5
10
15
0.0 0.5 1.0
250 companies
T able 3.12: Cross-sectional distribution of Prob V alues of H
0
: E (runs) = The set of 250 companies ha v e a lot more rejections of the n ull. This is consisten t with the fact
that this set con tains smaller companies than the A group, where more deviations from mark et
eciency are lik ely to b e observ ed.
The results from the runs tests seem to corresp ond to the results found in the serial correlation
tests, with the prep onderance of negativ e runs corresp onding to a larger fraction of negativ e serial
correlations. Similarly , the rejection of the n ull for the exp ected n um b er of runs is w orse in the
case of the Index-250 as compared with the bse Sensex. There is also an implied size eect with
the set of 250 companies ha ving man y more rejections of the n ull than the A companies.
60
3.2.3 Long-term Mean Reversion and V ariance Ratio T ests
The examination of the acf and runs tests ab o v e suggests that on the bse, deviations from
the n ull do exist. But these deviations are substan tially reduced when high trading costs are
accoun ted for.
13
These tests tend to emphasise the b eha viour of the series in the short run.
Indeed, in the early literature, the premise w as that with suc h scan t evidence of deviations in the
short run, eciency in the long run could b e assumed.
In the dissen ting literature, Summers (1986 a) brough t up the issue of eciency from the
p oin t of view that a feasible alternativ e w as that of p ersisten t long-run deviations of price from
fundamen tal v alues. This alternativ e mo del is the mo del of me an-r everting pric es . In this mo del,
prices temp orarily stra y from fundamen tal v alues (short{run p ositiv e correlations), but b ecause
of arbitrage, rev ert to the mean on the longer horizon (negativ e correlations in the longer run).
This sho w ed a pattern of short-run p ositiv e auto-correlations whic h then lead to negativ e auto-
correlations in the long run as w ell. The idea w as dev elop ed more fully in Summers (1986 b) and
P oterba & Summers (1988), who demonstrated that standard statistical tests ha v e little p o w er
to detect p ersisten t deviations b et w een mark et prices and fundamen tal v alues.
Co c hrane (1988) prop osed v ariance-ratio tests, ( vr tests) a non-parametric metho d of testing
for whether time series b eha viour displa y rev ersion to the mean. The basic notion b ehind the
vr test is that under the n ull of white noise, the v ariance of a series aggregated to k p erio ds will
merely b e k times the v ariance of the original series. The ratio of the v ariance of the aggregated
and the original series should b e the factor of aggregation of the data. Th us, if w e dene vr(k)
as
13
The highest auto-correlation at lag one among the companies in T able 3.6 is 0.15, that of the bse
Sensex is 0.11 and of the Index-250 0.33. The round-trip trading cost in the same p erio d w as 2% of the
total v alue of the trade.
61
V R(k ) =
1
k
V ariance(k p erio d returns)
V ariance(Single p erio d returns)
w e exp ect that a graph of vr(k ) against k will giv e a at line at 1, under the n ull. T o the exten t
that vr(k ) stra ys from 1, it suggests deviations from our n ull.
These tests w ere rst dev elop ed for time-series of macro economic v ariables and only later
dev elop ed as tests of eciency for the sto c k mark ets (F ama & F renc h 1988, Lo & MacKinla y
1988, P oterba & Summers 1988). Co c hrane (1988) sho ws that this ratio is close to a linear
com bination of the rst k lags of the acf.
V R(k ) = 1 + 2 1
k 1
k
+ 2 2
k 2
k
+ + 2
k 1
k
Th us, in this denition of the vr, it is a summary statistic that reduces the acf in to a single
n um b er, with linearly declining w eigh ts on the acf. Under the n ull, with a v ery large sample
(T ! 1), the asymptotic distribution of v r (k ) is sho wn to b e normal (Lo & MacKinla y 1988).
The normalised v ariance ratio statistic, z (k ) is dened as
z (k ) =
p
T v r (k )
3k
2(2k 1)(k 1)
1=2
where z (k ) N (0; 1).
62
The vr for the bse Sensex at k = 2; 4; 8; 16; 24 are all signican t at the 5% lev el of signicance,
whic h implies evidence of deviation from mark et eciency .
k 2 4 8 16 24
vr(k) 1.0905 1.110 1.116 1.234 1.385
z(k) 5.051 3.285 2.185 2.971 3.899
T able 3.13: Estimates of vr(k) and normalised statistics
The ca v eat to using the normalised statistic ab o v e is that it only holds for small k and large
samples. And it do es not tak e in to consideration that the data migh t b e heterosk edastic.
14
Alternativ ely , Mon te Carlo metho ds ha v e b een used to infer the distribution of the vr test.
Ric hardson & Sto c k (1990) devised a statistic whic h had a distribution that w as v alid ev en with
non-normal, conditionally heterosk edastic returns and whic h len t itself to Mon te Carlo calculation
v ery w ell.
Mon te Carlo inference w as the basis in Kim, Nelson & Startz (1991) for tests of mean rev ersion
in ann ual returns for the u.s. Their inference pro cedures w ere based up on a tec hnique closely
related to b o otstrapping. Under the n ull, there should b e no time dep endence in the data. In this
case, if the data is scram bled and Mon te Carlo re-sampling is carried out, the resulting sample
should ha v e the same distributional c haracteristics as that of the original series. The asymptotic
distribution of the vr(k) will b e obtained with m ultiple re-sampling of the scram bled data.
14
Lo & MacKinla y (1989) deriv ed a statistic that w as heterosk edasticit y robust. It w as sho wn to create
a substan tial dierence in the implied long run c haracterisitics of mark ets suc h as in Ay adi & Pyun (1994).
63
W e applied this test and inferen tial pro cedure from Kim et al. (1991) to the time series of the
bse Sensex for daily data. As a p oin t p oin t of comparison, w e p erformed a similar exercise for
the s&p500 . W e did this for three p erio ds separately:
April 1979 to Decem b er 1994
Marc h 1985 to Decem b er 1994
Jan uary 1990 to Decem b er 1994
These p erio ds w ere pic k ed out based on their imp ortance in the long-term c hanges that to ok
place on the bse. The y ears of 1985 and 1986 sa w the b eginning of a new p olitical regime in India
that w as also the b eginning of mark et-orien ted p olicies.
15
This trend in b ecoming mark et-orien ted
culminated with the op ening up of the econom y to in ternational mark ets and this pro cess b egan
in 1990. These ev en ts will ha v e had tremendous economic impact and are most lik ely to ha v e
caused long-term eects in the bse Sensex returns.
The solid line depicts the vr at dieren t lags and the other lines demarcate the condence
b ounds at 90%, 95% and 99%. The ratios ha v e b een calculated for lags from 2 to 500. F rom
these gures 3.14, w e can see
that the long-run c haracteristics of the bse Sensex and the s&p500 are v ery dieren t.
substan tial c hanges can b e seen in the vrs from the rst time p erio d to the last.
15
Chapter 1.1
64
50 100150200250300350400450500
1
2
BSE Sensex, 1979--1994
VR
90% CI
95% CI
99% CI
50 100150200250300350400450500
1
2
3
S&P 500
50 100150200250300350400450500
1
2
3
BSE Sensex 1985--1994
VR
90% CI
95% CI
99% CI
50 100150200250300350400450500
1
2
3
S&P500, 1985--1994
50 100 150 200 250 300 350 400
1
2
3
4
5
BSE Sensex, 1990-1994
VR
90% CI
95% CI
99% CI
50 100 150 200 250 300 350 400
1
2
3
4
S&P500, 1990-1994
T able 3.14: Daily vr and b ounds for the bse Sensex and s&p500
65
The sampling w as done for 500 lags of daily data, whic h giv es us a picture for a p erio d of
around t w o and a half y ears. In this time, w e see there is signican t p ositiv e deviations from the
n ull in the rst three mon ths (60 lags) for the bse Sensex whereas the deviations are negativ e
for the s&p500 and not as signican tly large. Th us there seems to b e evidence of strong \mean
a v ersion" on the bse Sensex for the same time as the s&p500 whic h sho ws evidence of \mean
rev ersion".
If w e examine the p erio ds separate of eac h other (ie, P erio d 1 : April 1979 up to Marc h 1985,
P erio d 2 : Marc h 1985 up to Jan 1990, P erio d 3 : Jan 1990 to Dec 1994), then w e see a sligh tly
dieren t picture in Figure 3.15 Here, the con trast b et w een the vr of dieren t p erio ds is m uc h
stronger and seem to p oin t to a case of \w orsening" mark et eciency from the p oin t of view of
risk-a v erting prices on the bse. This result corrob orates the evidence of the serial correlation and
the runs test and b o des ill for the mark et eciency of the bse.
T o get a clearer idea of what the vr means on a longer term basis for the mark ets, w e rep eat
the same exercise as the ab o v e for mon thly data o v er the same p erio ds in Figure 3.16. Here
the bse Sensex has a signican t vr at the rst lag whic h is p ositiv e whereas the s&p500 sho ws
signican tly strong deviations from the n ull in the negativ e direction at m uc h longer lags. This
seems to suggest that the s&p500 is strongly mean-rev erting in comparison to the bse Sensex
whic h seems more of a settled mark et, with v ery little signican t mo v emen t in the long run.
66
50 100150200250300350400450500
1
2
3
4
5
BSE Sensex, 1979--1985
VR
90% CI
95% CI
99% CI
50 100150200250300350400450500
0
2
4
6
BSE Sensex, 1985--1990
VR
90% CI
95% CI
99% CI
50 100 150 200 250 300 350 400
1
2
3
4
5
BSE Sensex, 1990-1994
VR
90% CI
95% CI
99% CI
T able 3.15: Daily v ariance ratios and Mon te Carlo simulated bounds
67
10 20 30 40 50 60
1
2
3
4
Monthly BSE
VR
90% CI
95% CI
99% CI
10 20 30 40 50 60
1
2
3
4
S&P500
6 12 18 24 30 36 42 48 54 60
0
2
4
6
Monthly BSE, 1985--1994
VR
90% CI
95% CI
99% CI
10 20 30 40 50 60
0
2
4
6
S&P500, 1985--1994
6 12 18 24
1
2
3
4
Monthly BSE, 1990--1994
VR
90% CI
95% CI
99% CI
10 20
1
2
3
4
5
S&P500, 1990--1994
T able 3.16: Monthly vr and Monte Carlo simulated b ounds
68
The next stage of analysis con tin ues with the long term p ersp ectiv e on the c haracterisations.
It also in tro duces information v ariables other than that of returns alone. The issues explored
here are:
T esting for seasonalit y in returns,
Da y of the w eek eects.
3.2.4 Seasonality
Tw o kinds of seasonalit y are explored here: seasonalit y o v er mon ths and seasonalit y o v er da y-of-
the-w eek. In this section, the data used is mainly that of the A companies for the Jan uary 1990
to Decem b er 1994 p erio d. The bse Sensex has b een analysed for Jan uary eects for the whole of
the time that it has b een observ ed.
3.2.4.1 The \Jan uary Eect"
Excess returns observ ed on the u.s. index in Jan uary ha v e b een lab eled the \Jan uary ef-
fect". One of the h yp othesis adv anced for explaining found in the United States and in
other coun tries (Reingan um 1981, Gultekin & Gultekin 1983, Jae & W estereld 1985, Kato
& Sc hallheim 1985, Thaler 1987 b) is related to tax-related selling: for the u.s. and most mark ets,
it is alw a ys adv an tageous to sell losing sto c ks in Decem b er in order to reduce the tax pa y out. A
similar eect w as found in the u.k. for April and in Jan uary and June in Japan.
The scal y ear used for taxation in India is April to Marc h. If the h yp othesis of tax-related
selling holds, w e w ould th us exp ect to see an \April eect" in India. The capital gains tax in
India diers from that in the US in one critical w a y: losses on sto c ks can only b e oset against
69
gains in sto c ks (not against other income). The compulsion to sell losing sto c ks at the end of the
y ear is th us m uc h w eak er in India than it is in the US. W e exp ect the \April eect" will b e a
w eak one.
Once again, the statistical precision in measuring seasonalit y o v er mon ths of the y ear is quite
limited compared to other studies that ha v e used far longer time series. W e will measure mon th-
eects using a dumm y v ariable regression.
Mon th Co ecien t Std.Err
Jan 1.001557 .0010943
F eb 1.003056 .0010677
Mar 1.000592 .0010638
Apr 1.001599 .0010859
Ma y 1.000247 .00109
Jun 1.001895 .0010393
Jul 1.002157 .0010638
Aug 1.001671 .0011007
Sep 1.001974 .00109
Oct .9991307 .0010818
No v .9994495 .0010964
Dec 1.001742 .0011441
T able 3.17: Eect of Mon th Dummies on returns of the bse Sensex
This regression uses T = 3155. The sample mean of all daily returns is 1.001263, i.e. mean
daily returns of 0.1263%. T ax-related selling w ould b e presen t in Marc h, and returns in Marc h are
b elo w-a v erage, though not in a statistically signican t w a y . The regression sho ws that the highest
returns of the y ear are obtained in the mon th of F ebruary , the mon th during whic h mark ets a w ait
the F ederal Budget announcemen t (whic h generally tak es place on the last da y of F ebruary).
Ho w ev er, a t w o-tailed test that the F ebruary co ecien t equals 1.001263 has a prob v alue of 0.09.
Th us w e cannot reject the n ull h yp othesis that F ebruary returns ha v e mean 1.001263.
This evidence do es not supp ort the presence of strong mon th eects in India.
70
3.2.4.2 Da y of week eects
Another w ell{do cumen ted anomaly observ ed on man y mark ets all o v er the w orld (Gibb ons &
Hess 1981, Keim 1986, Thaler 1987 a) is the w eek end eect, where excess returns seem to b e
obtainable b y purc hasing at the Th ursda y closing price and selling at the F rida y closing price.
Under the n ull h yp othesis of mark et eciency , w e exp ect returns to ha v e the same distribution
for all da ys of the w eek. This is readily tested using regressions of the form
Returns = a
1
+ a
2
F rida y
where Friday is a dumm y v ariable whic h is true on F rida ys. The exp ected h yp othesis is H
0
:
a
2
= 0.
W e can apply this approac h to the Monday dumm y v ariable also. The bse has a trac k record
of b eing closed on man y w eekda ys, so that the rst trading da y of the w eek ma y sometimes not
b e a Monda y and the last trading da y of the w eek ma y sometimes not b e a F rida y . Hence these
tests are also carried out with resp ect to the dumm y v ariables First trading day of the week
and Last trading day of the week .
W e will rst test daily returns on the bse Sensex, for whic h w e ha v e 3113 observ ations
spanning the p erio d April 1979 to Octob er 1994.
71
Apr 1979 { No v 1994 Jan 1990 { No v 1994
Da y Co ecien t Std. Errors Co ecien t Std. Errors
Mon -0.0010 0.00088 -0.0001 0.00244
T ues 0.0001 0.00056 0.0004 0.00208
W ed -0.0015 0.00076 -0.0030 0.00180
Th ur 0.0002 0.00073 -0.0010 0.00174
F ri 0.0021 0.00077 0.0036 0.00179
Date of
T rading
First 0.0009 0.00078 0.0012 0.00172
Last 0.0017 0.00071 0.0034 0.00173
T able 3.18: Eect of Day Dummies on returns of the bse Sensex
The bse Sensex sho ws Monda y returns that seem consisten t with the n ull; Monda y returns
are not v ery far remo v ed from zero. This b eha viour is consisten t across the new time p erio d
as w ell. On the other hand, the F rida y returns app ear signican tly dieren t from zero. The
eect app ears to ha v e strengthened o v er the curren t p erio d. A w eak er W ednesda y eect, with a
negativ e sign, also seems to exist.
W e turn to in v estigate similar eects in daily returns data for the 92 A group companies.
F ailure of the n ull h yp othesis for a giv en compan y is summarised b y the prob v alue of the t-test
for H
0
. Hence w e summarise the b eha viour of the 92 A group companies b y plotting a histogram
of the 92 co ecien ts.
72
0.00 0.05
Monday
0
20
40
60
80
100
0.00 0.05
Friday
0.00 0.05
First trading weekday
0.00 0.05
Last trading weekday
Figure 3.1: Da y of w eek eects: Coecients
The statistical signicance of these deviations from H
0
are summarised b y plotting a histogram
of the 92 prob v alues obtained from these regressions (lo w v alues imply rejection of the n ull).
0.0 0.5 1.0
Monday
0
1
2
3
0.0 0.5 1.0
Friday
0.0 0.5 1.0
First trading weekday
0.0 0.5 1.0
Last trading weekday
Figure 3.2: Da y of w eek eects: Prob v alues
Once again, there do es not seem to b e a strong dierence b et w een Monda y and the rst
trading da y; or b et w een F rida y and the last trading da y . Returns on Monda y seem to b e broadly
consisten t with H
0
. The distribution of co ecien ts is symmetric around 0, and there are v ery
few companies where the n ull is rejected.
73
In con trast, the F rida y co ecien ts seem to exhibit excess returns. In 81 of the 92 companies,
the F rida y co ecien t is n umerically ab o v e zero. Of these, in 20 cases, H
0
is rejected at the 5%
lev el of signicance.
Ho w ev er, in only four cases is the F rida y co ecien t ab o v e 1%, whic h is the one way trading
cost faced b y small in v estors. As with the companies of the bse Sensex, there is no compan y
where the F rida y co ecien t is ab o v e 2%, to nance arbitrage after pa ying for round{trip trading
costs.
Apart from pure arbitrage, w e can exploit this F rida y eect in p ortfolio managemen t on the
bse. Other things b eing equal, purc hases should b e timed to use the closing price on Th ursda y ,
and sales should b e timed at the closing price on F rida y .
74
3.3 Event Studies
The analysis of the mark et th us far has assumed the minimal information set of the returns v ector
for the main part. Some of the analysis has used sp ecic time information (as in the seasonalit y
studies), whic h has zero marginal cost of attainmen t. In the next suite of tests, F
t
con tains
information ab out ev en ts in the lifetime of the rm around whic h the b eha viour of its returns are
studied. In this section, the ev en t studied is b onus issues b y rms.
3.3.1 Bonus Issues on the bse
In the US, a sto c k split is a simple ev en t where x shares are replaced b y nx shares. In India, the
ev en t is kno wn as a \pa y out of b on us shares", and there are cosmetic accoun ting c hanges whic h
accompan y it. There is also a notational dierence { what is kno wn in the US as a \t w o for one
split" w ould b e called a \1:1 b on us". In b oth cases, the ev en t is initiated purely b y the rm.
Ev en though it app ears irrational, there exists a v ery strong p erception amongst practitioners
that \b on us issues are v ery go o d news". In a neo classical w orld of rational and w ell-informed
agen ts, sto c k splits w ould b e completely irrelev an t, and at equilibrium, rms should nev er opt
for them. That rms p ersisten tly do announce sto c k splits mak es them v ery in teresting from the
viewp oin t of empirical mark et eciency researc h. Ev en ts of splits oer a unique iden tication
opp ortunit y where mark et imp erfections can b e isolated and analysed.
The rst phase of researc h in to sto c k splits is represen ted b y the classic article b y F ama et al.
(1969), whic h in v en ted the ev en t study metho dology and w as also one of the rst applications of
the CRSP mon thly returns database. The broad conclusion deriv ed using mon thly returns data
has upheld the n ull h yp othesis that mark ets ignore splits. Ho w ev er, the enhanced p o w er obtained
75
in tests whic h use daily data has unco v ered deviations from this p osition. W e ma y summarise
the empirical facts established in the w ork and subsequen t literature (mostly using u.s. mark et
data) as follo ws:
1. Firms whic h split tend to ha v e exp erienced excess returns, as compared with the mark et
index, in the p erio d prior to the announcemen t.
2. The date on whic h the b on us is announced to the public (called the announcemen t date )
is asso ciated with excess returns, of the order of 3%.
3. The date on whic h the b on us is actually distributed to the shareholders (called the XB or
the \ex-b on us" date) is asso ciated with excess returns. These are of the order of 0.5%.
4. The dollar v alue of daily trading v olume de clines follo wing a split.
5. The v olatilit y of the compan y’s sto c k rises b y around 30% follo wing a split (Ohlson &
P enman 1985, Dub ofsky 1991, Dra vid 1987).
6. The n um b er of shareholders rises b y around 30% follo wing the split.
Here, w e analyse the b eha viour of b on us issues for sto c ks in India to see if similar patterns of
price reactions exist. Of the ab o v e, our data resources do not allo w an exploration of (2) and (4)
for the Indian data.
In India, it is t ypical for rms to hold the p er-share dividend constan t when increasing the
n um b er of shares. Th us the b on us announcemen t should ha v e an impact similar to a dividend
increase. Dividend r e ductions in India are rare { most rms attempt to hold the p er-share
dividend constan t ev en in the face of adv erse op erating p erformance, so that a dividend step-up
76
is a p o w erful signal of enhanced dividends in the future. Th us the b on us announcemen t date (lik e
the date of a dividend step-up) should b e asso ciated with strong excess returns.
Practitioners commonly think that b on us issues impro v e the liquidit y , through their impact
up on the pric e . P art of the reasoning ma y in v olv e clien tele eects. F or example, if the minim um
trading lot is 100 shares, then the minim um in v estmen t in a share costing Rs.1000 is Rs.100,000
and this drops to Rs.50,000 after a 1:1 b on us issue. There ma y b e in v estors who w ould tak e
in terest in the sto c k at the lo w er price but not at the higher price. Hence, at the lo w er price there
ma y b e higher liquidit y .
This clien tele eect ma y explain the p ost-split excess v olatilit y observ ed in the US. In the spirit
of Blac k (1987), this ma y b e related to the increased noise trading asso ciated with less-informed
traders who w ere less lik ely to tak e in terest in the high-priced pre-split sto c k.
Ho w ev er, there are other factors at w ork, whic h arise from mark et micro-structure. T raders
sho w a \digit preference", so that quotes are made in m ultiples of Rs.0 :25. Th us, p ost-split quotes
will suer from more discreteness and the bid-ask spread will widen. The reduction in p ost-split
trading v olume also p oin ts to w ards lo w ered liquidit y .
Another imp ortan t researc h question concerns XB-date returns. A simple reason for excess
XB-date returns migh t b e basic measuremen t diculties and the limitations up on mark et e-
ciency imp osed b y transactions costs. These diculties w ould also b e presen t in other studies of
mark et eciency . Th us it b ecomes imp ortan t for us to examine returns in the con text of a simple
\irrelev an t" ev en t lik e the XB-date, in order to get a y ardstic k whic h should b e applied in other
studies. F or example, anomalies observ ed on the ex-date of a dividend pa y out w ould partly b e
a consequence of measuremen t diculties. Studying excess returns asso ciated with b on us issues
77
is useful insofar as it helps us quan tify the role of friction in the trading pro cess in explaining
observ ed anomalies.
3.3.1.1 Data Description
The curren t data-set on the bse companies from 1990 to 1995 includes no data on the b on us
announc ement dates. Hence w e will only fo cus up on the XB-dates.
As is the case with man y other areas of empirical nance, a serious dicult y is created b y
non-sync hronous trading in sto c ks. There are situations where a securit y is not traded for one or
more trading da ys prior to its XB date. In this case, it is hard to in terpret the XB-date returns.
Since E (r
M
) > 0 and the sto c ks correlation with the mark et is close to one on a v erage, this non-
trading prior to the XB-date t ypically imparts an up w ard bias to the XB-date return and to the
residuals used in ev en t studies. In our attempt to understand the eect of frequency of trading
on XB-date b eha viour, w e start with a stringent sample selection based analysis. Later, w e apply
a less r estrictive sample selection criteria and rep eat the analysis. The dierences b et w een the
t w o should help highligh t the non-sync hronous trading eect.
3.3.1.2 More-stringent sample selection
There are 196 XB dates in the data-set uncon taminated b y a XR
16
on the same date, for the
p erio d from 1 Jan 1990 till 1 July 1995.
In the rst stage of analysis, w e apply the stringen t selection criterion: use only those compa-
nies whic h ha v e traded for 55 da ys or more in the preceding three calendar mon ths. This amoun ts
to requiring a trading frequency of around 90% or so, whic h is high b y the standards of the BSE.
16
XR are ex-righ ts issues. A large fraction of Indian companies announce righ ts issues sim ultaneously
with or immediately after (at most a mon th later) a b on us issue announcemen t.
78
This is a harsh restriction, and it lea v es us with a data-set of just 44 XB ev en ts. In practice,
this metho d of sample selection also causes a bias to w ards high mark et capitalisation companies,
whic h generally ha v e higher trading frequencies.
Ev en t study in mean returns
The study uses mark et adjustmen t, i.e. j t
= r
j t
r
M t
, and uses a windo w of 200 da ys in ev en t
time, whic h corresp onds to roughly 11 mon ths of calendar time on a v erage. Eac h p oin t on the
line graph corresp onds to the excess returns for eac h sto c k, cum ulativ e from the b eginning of
the ev en t windo w, a v eraged o v er 44 sto c ks. Eac h p oin t on the bar graph is the excess returns
obtained at a time, a v eraged o v er 44 sto c ks.
T able 3.19: Event study around Bonus Issue for the Restricted Sample
79
Figure 3.19 sho ws abnormal returns of 5 :7% on the XB-date. This is considerably larger than
the XB-date abnormal returns of the order of 0 :5% seen in studies in the US. The standard error
of the mean abnormal return on the ev en t date is 0 :75, and w e reject the n ull h yp othesis that
there are no abnormal returns on the XB-date.
The broad pattern in this graph is a lot lik e ev en t studies around XB-dates for sto c k splits in
the US. Here w e see v ery strong abnormal returns of 60% o v er the h undred da ys that precede the
XB-date. The b on us announcemen t date is somewhere in t < 0 in ev en t time, and the p ositiv e
abnormal returns on the announcemen t date w ould b e part of this buildup prior to the XB-date.
This is similar to studies of sto c k splits for the US. As is the case in the US, there are no abnormal
returns after the XB-date.
Ev en t study in volatilit y
F or a giv en date t in ev en t time, w e fo cus on
RMS
t
=
q
E [(r
j t
r
M t
)
2
]
RMS
t
is a measure of the price c hange on date t in ev en t time. It a v erages the abnormal price
c hanges across all securities. The standard deviation of price c hanges is vulnerable to outliers, and
for companies whic h are infrequen tly traded, daily returns tak e large v alues. The more-stringen t
sample is hence a go o d data-set to use for the ev en t study in v olatilit y .
80
T able 3.20: V olatility of Excess Returns around the Bonus Issue for the Restricted Sample
The dashed line in Figure 3.20 sho ws the non-ev en t a v erage standard deviation of 3 :942%.
There are three spik es in the graph: at date -99 (8 :2%), date -42 (12 :3%) and the ev en t date
(12:33%). The rst t w o of these spik es are caused b y outliers - on date -99 there is a compan y
with returns of 51% in excess of r
M
, and on date -42, there is a compan y with returns of 78 :9%
in excess of r
M
.
Barring these outliers, it is clear that : (a) There is a sharp episo de of excess v olatilit y on the
XB date, and (b) There is no evidence of the excess p ost-split v olatilit y that has b een observ ed
with US data. This graph is a sharp con trast (sa y) with Figure 1 of Ohlson & P enman (1985),
where v olatilit y in the p erio d after the XB-date is appro ximately 30% higher than the preceding
da ys.
Ohlson & P enman (1985) examine sev en p ossible criticisms for their empirical results ab out
excess v olatilit y after the XB-date, and reject all of them. They in terpret the result as an anomaly ,
81
and oer explanations suc h as the clien tele factor and based on the mark et micro-structure eect,
suc h as the digit preference for 1 =8. The clien tele factor should b e applicable on all exc hanges
in the w orld, and the fact that there is no excess v olatilit y on the BSE is evidence against this
explanation. Our results p oin t more to w ards an explanation of excess returns based on the
micro-structure of the mark et.
3.3.1.3 Less-stringent sample selection
W e rep eat this study using a less stringen t sample selection criterion for trading frequency , i.e.
w e accept all securities whic h traded for at least one da y in the calendar mon th prior to the XB
date. This enlarges the data-set from 44 XB dates to 152, and giv es the follo wing results for the
ev en t study around the mean returns:
T able 3.21: Event study around Bonus Issue for the Unrestricted Sample
82
The returns on XB-date seen here are 7 :4%, and the standard error is 0 :586. Th us w e ha v e a
strong rejection of the n ull h yp othesis.
There are t w o dierences that w e see here as compared with the previous graph:
The larger returns on XB-date (7 :4% as compared with 5 :7% ab o v e) are consisten t with
our prior h yp othesis ab out the role of non-trading: to the exten t that this data-set includes
rms that did not trade in the few da ys that immediately preceded the XB date, the returns
on XB date (where all rms trade) includes returns from the previous few dates, and our
estimator is biased up w ards.
As compared with the previous ev en t study results, there app ears to b e some evidence of
over-r e action here: there is a systematic negativ e drift of returns after the XB-date, in
con trast with the previous results, so that the a v erage rm in this data-set loses around
10% o v er the 100 da ys that follo w the XB-date.
As p oin ted out at the start of this section, part of the evidence of o v er-reaction could b e due
to non-sync hronous trading amongst the rms in the sample. Ho w ev er, it is hard to justify
the amoun t of the excess returns observ ed based purely on non-sync hronous trading. This
is lik ely if trading frequency
17
is a pro xy for other v ariables, whic h are related to mark et
eciency , whic h in turn generates and sustains suc h mispricing.
Th us this analysis of XB-date returns lea v es a collection of unansw ered questions:
Wh y agen ts are unable to arbitrage a w a y the seemingly large XB-date abnormal returns
observ ed here, and
17
This is used an indicator of async hronous trading across a set of sto c ks.
83
Wh y less-liquid sto c ks exhibit some kind of o v er-reaction, with prices rising sharply up to
and including the XB-date, and drifting do wn in the half-y ear follo wing the XB-date.
The answ er to the rst question is partly related to transparency and transactions costs. A
lac k of transparency ab out the b on us pro cess implies that there will b e sp eculativ e trading that
could cause these excess returns prior to an XB date. T rading costs are prohibitiv e and there is
the added uncertain t y of whether the rm will actually go through with a sto c k split ev en after
it has b een announced.
18
If the comp etition from alternativ e sto c k exc hanges brings ab out lo w er
trading costs and more ecien t allo cation of issues, there should b e a visible reduction of these
anomalous excess returns.
W e also explored regression mo dels whic h migh t b e able to explain jr
j 0
r
M 0
j= , i.e. the
standardised abnormal return on the XB-date for securit y j , using explanatory v ariables suc h as
size, mem b ership in the A group, the trading frequency in the preceding calendar mon th, the y ear
in whic h the XB-date to ok place, and the cum-b on us price. No statistically robust regularities
w ere observ ed in this exploration. If non-standardised abnormal returns, jr
j 0
r
M 0
j, are used
as left hand side v ariables, then some correlations app ear, but these mostly reect the empirical
relationships of with size, mem b ership in the A group and trading frequency .
3.3.1.4 T rading frequency before and after XB-date
In the absence of v olumes data, trading frequency is the most imp ortan t measure of v olumes
whic h w e ha v e { the ev en t of non-trading on a giv en da y is equiv alen t to zero v olume on that
18
There ha v e b een instance of rms that ha v e announced a sto c k split but not actually follo w ed up with
the split in the follo wing p erio d.
84
da y . The simple empirical regularities ab out trading frequency for our data-set of 154 XB-dates
are summarised as follo ws:
Before XB-date After XB-date
Num b er of companies with 100% trading 38 42
Mean trading frequency 88.00 87.98
trading frequency 16.3 15.8
T able 3.22: T rading F requency around XB dates
A t the lev el of these summary statistics, w e cannot reject the n ull h yp othesis that trading
frequency is unc hanged across the XB-date. W e will attempt to obtain more statistical p o w er in
answ ering this question using the follo wing estimation strategy .
Let v
j t
b e the trading v olume of securit y j on da y t. A commonly used mo del sp ecication
whic h explains the time-series v ariation in v is v
j t
= j
+ j
v
M t
+ , where v
M t
is the total v olume
traded on the exc hange on da y t, and j
is the \v olumes b eta" of the compan y . In our case, w e
do not observ e v
j t
and w e can think of it as b eing a unobserv ed laten t v ariable. W e observ e a
censored v ariable d
j t
= 0 if v
j t
<= 0, and d
j t
= 1 otherwise, i.e. there is a price quotation on
the securit y if and only if the trading v olume w as non-negativ e. A t the lev el of one securit y , this
reasoning lends itself naturally to a probit form ulation.
T o test whether v olumes impro v e after the XB-date, w e will test H
0
: = 0 in v
j t
=
j
+ P ost XB + j
v
M t
+ . W e will p o ol data from our full data-set b y allo wing eac h j
and j
to v ary across companies, and forcing the same . This giv es us a \xed{eects probit" mo del.
Our data in estimating this is limited b y observ ations for the v
M t
series only from Jan uary
1994 on w ard.
85
3.3.2 GDR Study
Another recen t ev en t study helps shed ligh t up on the eciency of the bse. This is the evidence
of price manipulation prior to GDR issues unco v ered in Shah (1995 c).
Euro Issues of Global Dep ository Receipts (GDRs) and Euro Con v ertible Bonds (ECBs)
ha v e b ecome an imp ortan t mec hanism through whic h Indian rms raise resources from capital
mark ets, from No v em b er 1992 on w ard.
19
$3.544 billion w ere raised through the 46 GDR issues
whic h to ok place b et w een No v em b er 1992 and Decem b er 1994, these w ere roughly one{sixth the
size of resources raised in the domestic primary mark et.
In April 1994, Shah (1994) used w eekly returns
20
for 24 issues, with mark et mo del adjustmen t
(using the BSE Sensex as the mark et index) to test whether there w ere un usual price mo v emen ts
in sto c ks around the time of gdr issues. They found evidence of mispricing { the p eak abnormal
returns w ere 9% shortly b efore the pricing date. In addition to this, cum ulativ e abnormal returns
w ere found to go bac k to 0 o v er the eigh t w eeks follo wing the pricing date. Ev en though this w as
a small data-set of only 24 ev en ts, the mispricing w as large enough to pa y atten tion to.
In Ma y 1994, a tec h-rep ort con taining these results w as sen t to 75 individuals on a priv ate
distribution list in the Indian nance industry .
21
The rep ort suggested that price manipulation
migh t b e at w ork b ehind these abnormal price mo v emen ts. If the v aluation of the rm rose as
a consequence of the Euro issue, then the p ositiv e returns should not b e lost in the follo wing
eigh t w eeks. This in terpretation of the evidence is consisten t with the cross-sectional v ariation in
19
GDRs are equit y shares that are sold b y an Indian rm on sto c k exc hanges outside of India to raise
capital from foreign shareholding. ECBs are b onds similarly issued.
20
The pricing date w as kno wn exactly
21
Th us 15 Ma y 1994 is dened as the date at whic h the rst rep ort en tered the information set of agen ts.
86
Cum ulativ e Abnormal Returns car as of date -5 : small rms exhibited m uc h greater mispricing
than large rms.
T o the exten t that these results p oin t to price manipulation as ha ving tak en place, it is
inconsisten t with mark et eciency on the bse. The factors underlying this ma y b e the w eak
micro-structure of trading, and the lac k of a regulatory framew ork to c hec k suc h abuse.
These results, and the suggestion that price manipulation w as in v olv ed, w ere sensational and
got wide notice. It w ould b e fair to assume that most agen ts in v olv ed in an y asp ect of Euro issues
b y Indian companies { ranging from the issuers and facilitators to the purc hasers { knew of the
results of this tec h-rep ort, at least crudely .
Tw en t y six GDR issues ha v e tak en place after 15 Ma y 1994, and Shah (1995 c) sho ws this
graph:
T able 3.23: Abnormal returns from GDR around Pricing Date (%)
87
The metho dology emplo y ed in this latter rep ort uses daily returns instead of the w eekly
returns used earlier, and uses mark et adjustmen t, instead of mark et mo del adjustmen t. Since
the bse Sensex has n umerous diculties the graph ab o v e uses Index-250. Abnormal returns in
the p erio d b efore 15 Ma y 1994 as seen in Shah (1995 c) are m uc h sharp er than those p erceiv ed in
Shah (1994) { the highest abnormal returns seen b efore pricing date is 18 :9% instead of the 9%
rep orted in latter rep ort. This ma yb e partly the eect of w orking with daily returns instead of
w eekly returns : using F rida y-to-F rida y w eekly returns in v olv es a v eraging o v er man y companies
whic h ha v e pricing dates whic h are a few da ys apart, and this a v eraging blun ts the p erceiv ed
a v erage abnormal returns.
The price ramp up for the issues after 15 Ma y 1994 is m uc h more m uted than for the issues
b efore this date. The highest p oin t in the a v erage car graph is at 6 :9%, a reduction of t w elv e
p ercen tage p oin ts. The pre-pricing-date price ram-pup is no w nished around fteen da ys b efore
pricing date, whereas earlier it reac hed its p eak around v e da ys b efore pricing date. The p ost-
pricing-date elimination of the mispricing is no w m uc h faster: earlier it to ok fort y da ys for the
a v erage car to return to zero; in the p erio d after 15 Ma y 1994, the a v erage car reac hes to
essen tially zero on da y 3.
T o quote Shah (1995 c):
This en tire episo de serv es as an illustration of the pr o c ess through whic h mark et
eciency comes ab out { the disco v ery of a mark et ineciency initiates the pro cess
of agen ts learning the sto c hastic en vironmen t from a new angle, and their arbitrage
eorts eliminate the mispricing. Lik e the w ell-publicised recen t researc h in to nas-
daq quotes (Christie & Sc h ultz (1994), Christie, Harris & Sc h ultz (1994)), it is a
88
demonstration of ho w the v ery act of b etter understanding an econom y p opulated
b y optimising agen ts can c hange it.
89
3.4 T ests of insider-information
The previous study of the gdr ev en t can b e considered a test of insider-information, or what F ama
(1991) refers to as the strong-form test of eciency . The h yp othesis b eing that the abnormal
lev els w ere caused b y price manipulation.
This section oers further evidence on strong-form eciency of the bse, in form of traditional
p erformance ev aluation applied to a subset of the closed-end m utual funds op erating in India.
This is w ork done at cmie in the early part of 1993 and completed in 1994.
3.4.1 Mutual F und Performance
T ests of mark et eciency aimed at detecting sp ecic kinds of returns predictabilit y are crucial to
piecing together a detailed and dis-aggregated picture of mark et eciency in the spirit of F ama
(1965), F ama (1970) and Summers (1991). Ho w ev er, they ha v e t w o w eaknesses:
These tests are not generic to all p ossible anomalies: they are limited to rejecting only
sp ecic forms of pricing anomalies.
Practitioners do not appreciate a discussion conducted in terms of issues suc h as the sp ec-
trum of the returns pro cess.
Th us, it seems of v alue to approac h the pro cess of professional p ortfolio managemen t as a
blac k-b o x, and inquire whether this blac k-b o x is able to pro duce excess returns as compared with
easily implemen ted buy{and{hold b enc hmark strategies. One subset of professional p ortfolio
managemen t services where tests of excess returns can b e carried out are the closed-end m utual
funds, b ecause profuse information is a v ailable ab out their p erformance. In this section, w e
ev aluate the p erformance of these funds.
90
These tests could pro vide evidence that professional p ortfolio managers of these funds are
systematically able to pro duce excess returns. Ho w ev er, access to sup erior information leading
to deviations from eciency is only one of the explanations for this b eha viour. An alternativ e
explanation ma y b e that these fund managers face m uc h smaller costs of trading compared with
the individual, and they can b enet from the statistical ineciencies outlined in previous sections.
On the other hand, if the blac k-b o x under examination fails to pro duce excess returns, it
w ould constitute clear evidence against the usefulness of the p ortfolio managemen t pro cess as
curr ently pr actise d to either b eneting from asymmetries of information or from lo w er trading
costs.
Apart from the issue of strong-form eciency , systematic p erformance ev aluation pro cedures
are useful for the follo wing reasons:
A t the simplest, in v estors need to kno w ho w w ell a fund has fared relativ e to other funds.
This has b een done in the industry using crude comparisons of ex{p ost returns. These
comparisons are meaningless unless dieren t lev els of risk adopted are adjusted for.
F or an individual in v estor to correctly visualise ho w his budget set will v ary in the dieren t
states of nature, he m ust kno w more ab out the p olicies adopted b y the fund with resp ect
to issues lik e div ersication, attempts to nd mispriced assets, resp onse to econom y{wide
uctuations, etc.
F or the institution whic h hires professional managers, p erformance ev aluation pro cedures
are essen tial in iden tifying, and rew arding, exceptional p erformance.
91
F or a manager ev aluating alternativ e me chanisms of p ortfolio managemen t, p erformance
ev aluation giv es quan titativ e feedbac k ab out the returns generated b y alternativ e data
sources, alternativ e analytical metho ds, and alternativ e trading strategies.
3.4.1.1 The Ev aluation Strategy
If r
j
are returns on a fund j , r
f
the risk-less rate of return on lending, and r
M
the returns on the
mark et index, the estimation of the mark et mo del w ould b e form ulated as:
(r
j
r
f
) = + j
(r
M
r
f
) + j
(r
M
r
f
) is in terpreted as the risk premium obtained in return for the lev el of systematic risk
j
adopted b y the fund. Under the n ull h yp othesis of the fund manager adding no v alue, the
falsiable prop osition is
H
0
: = 0
This approac h will commen t on the eciency of the bse with resp ect to the information set
and analytical to ols used b y professionals in p ortfolio managemen t, for a giv en lev el of trading
cost they face. In the literature, it is w ell kno wn that ^ is vulnerable to missp ecications in the
mark et index p ortfolio. Our results b elo w use the bse Sensex as the b enc hmark, and nd under-
p erformance b y managed p ortfolios of an extreme degree { this ma y b e relativ ely in vulnerable to
small c hanges in the index p ortfolio.
92
3.4.1.2 The Data Described
The Mutual F unds
The sc hemes analysed in this section are summarised here.
Sc hemes under Ev aluation
Mkt. Cap. (6/4/94)
Sc heme (Rs. billion) Num b er of w eeks
1 Can b on us 1.28 71
2 Canshare 0.47 206
3 Candouble 5.38 139
4 Cangro wth 0.59 201
5 Can triple 4.51 60
6 Canstar-cap 10.29 102
7 Ind Ratna 0.58 140
8 Mastershare 17.54 215
9 Masterplus 91 15.81 81
10 UGS 2000 5.72 87
11 UGS 5000 6.37 87
T otal 68.54
The data-set is w eekly returns, con tin uously comp ounded and not ann ualised. A t b est, w e
ha v e around 200 w eeks of returns, or roughly four y ears.
22
Since man y of the en tran ts in to
the industry are relativ ely y oung, man y sc hemes ha v e few er observ ations. Unlik e m uc h of the
p erformance ev aluation literature to date, w e are not giv en the con v enience of observing all these
sc hemes o v er a common time p erio d: apart from #2, #4 and #8, all the sc hemes are observ ed
from their inception on w ard.
The sc hemes observ ed here ha v e a com bined mark et capitalisation of Rs.68.5 billion. While
this is a go o d data-set in a sampling sense, it is a v ery small data-set as compared with imp ortan t
studies in the US { Jensen’s Ph.D. dissertation (Jensen 1968) studied 115 funds
23
, and Securities
22
The n um b er of observ ations seen in the ab o v e table do not exactly map to the lifespan of the sc heme,
b ecause of missing data whic h is caused b y non-sync hronous trading.
23
56 ha v e data for 20 y ears, and 59 ha v e data for 10 y ears
93
and Exc hanges Commission (1971) uses data from 125 funds for a decade. The r
f
used here is
the bank lending rate.
24
Simple summary statistics ab out these sc hemes are displa y ed in T able 3.24.
Summary Statistics
Sc heme W eeks r
j
r
f
r
M
r
f
E () V ar() E () V ar()
1 Can b on us 71 -1.159 104 0.073 25
2 Canshare 206 0.107 88 0.589 28
3 Candouble 139 -0.096 90 0.535 31
4 Cangro wth 201 -0.320 105 0.605 29
5 Can triple 60 -0.977 107 0.555 25
6 Canstar-cap 102 -0.195 137 0.293 37
7 Ind Ratna 140 0.376 134 0.600 29
8 Mastershare 215 0.511 75 0.514 28
9 Masterplus 91 81 -0.873 52 0.056 23
10 UGS 2000 87 0.260 48 0.228 23
11 UGS 5000 87 0.128 87 0.228 23
T able 3.24: Summary Statistics for the Mutual F unds
In this simplest of comparisons, only #10 has \b eaten the mark et" o v er the comparable
p erio d. The ex{p ost equit y premium has b een p ositiv e for all these time p erio ds, and six sc hemes
out of elev en ha v e generated negativ e returns.
The sc hemes run up enormous lev els of total risk; often three to four times higher than the
total risk of the mark et index. Ev en #10, whic h is three basis p oin ts p er w eek ahead of the
mark et index in ex{p ost returns, requires the consumer to pa y double the total risk as compared
with the mark et index in getting there. Indeed, as illustrated b y T able 3.25, V ar( r
j
r
f
) for man y
of these sc hemes lo oks more lik e the risk of common sto c k rather than the risk of a p ortfolio.
24
This has b een obtained from the Reserv e Bank of India whic h sets the lending and b orro wing rate for
banks. These rates tend to c hange v ery infrequen tly .
94
Securit y Mkt. Cap. V ar( r
j
r
f
) 2
j
V ar( r
M
r
f
)
L ar gest c omp anies in BSE Sensex
Hindustan Lev er 106.74 33 15
Reliance 88.10 98 62
ITC 79.96 55 37
TISCO 67.14 59 40
TELCO 60.22 290 29
L ar gest A c omp anies not in BSE Sensex
Colgate 71.74 32 14
Ba ja j Auto 49.85 38 15
T ata Chemicals 48.56 66 26
Castrol 38.02 79 29
ICICI 37.14 146 48
T able 3.25: Risk of common sto ck: some illustrations (11 April 1994)
This suggests that these m utual funds migh t b e inadequately div ersied, and that they do
not serv e consumers through giving div ersication services at lo w transactions cost.
The Market Index
A market index is crucial to estimation of the mark et mo del, and for the construction of b enc hmark
p ortfolios. There is no mark et index on the bse whic h matc hes the qualities of the mark et indexes
used in researc h in the United States, suc h as the s&p500 and the Wilshire 5000 index.
bse Sensex has wide visibilit y in India and will b e used in the con text of this study . In the
estimation of the mark et mo del, the index has the follo wing w eaknesses, outlined in the earlier
section on semi-strong form testing, of :
It is a p ortfolio of only 30 companies.
There is no algorithm in place for up dating this set of 30 companies. In the en tire history
of the bse Sensex since 1978-79, there has b een only one addition in to the index set.
95
Returns data for the bse Sensex whic h correctly include dividends and righ ts do not exist.
This will generate an upwar d bias on the estimated s and a downwar d bias in the estimated
s; this causes a bias to w ards rejecting the n ull; that m utual funds do not pro duce excess
returns.
25
There are clearly imp ortan t in v estmen t opp ortunities op en to m utual fund managers whic h
are v ery attractiv e as compared with these 30 large companies. F or example, fund managers can
harness the small rm eect (Section 3.2.1.1), the b on us issue eect (Section 3.3.1) and the IPO
under-pricing eect (Shah 1995 b). Giv en the w eak institutional framew ork of underwriting, fund
managers ha v e b een kno wn to purc hase large blo c ks of shares in faltering public oerings at large
discoun ts. Before the ab olition of the CCI, IPOs w ere strongly under-priced; to the exten t that
m utual funds purc hased shares at IPOs b efore 29
th
Ma y 1992, they should ha v e obtained large
excess returns.
Ho w ev er, in the con text of the p erformance ev aluation problem, there is one adv an tage whic h
deriv es from using the bse Sensex. In an en vironmen t where no go o d broad{based mark et index
exists, and no index funds exist, the bse Sensex is con v enien t insofar as it is readily implemen ted
as a p ortfolio. Th us the b enc hmark p ortfolios used in this article are of direct practical relev ance
to an y p ortfolio manager with assets ab o v e Rs.1 million or so.
25
A ttempts to replicate the bse Sensex ha v e rev ealed the p ossibilit y of some computational errors in the
index as published b y the bse. W ork on creating a more comprehensiv e index is curren tly b eing carried
out at CMIE. The Index-250 used in the earlier part of this c hapter w as gleaned from this eort.
96
The Risk-less Asset
There is no mark et{determined short{term risk-less rate of return whic h can b e used o v er the
full time p erio d, i.e. from Jan uary 1990 on w ard. Auctions of 91-da y treasury bills only b egan in
Jan uary 1993.
Hence w e use the (time{v arying) in terest rate paid b y banks on short{term xed dep osits as
the risk-less rate of return. This is only relev an t for risk-less lending. Ho w ev er, to obtain lev erage
b ey ond = 1, a risk-less b orro wing rate of 18% is used.
3.4.1.3 Estimation Results
Alpha
Results of estimating the mark et mo del are summarised in T able 3.26. Standard errors are sho wn
in brac k ets.
97
R
2
1 Can b on us -1.216 0.779 0.147 9.479
(1.13) (0.23)
2 Canshare -0.373 0.815 0.213 8.345
(0.58) (0.11)
3 Candouble -0.523 0.799 0.220 8.403
(0.72) (0.13)
4 Cangro wth -0.966 1.068 0.316 8.489
(0.60) (0.11)
5 Can triple -1.326 0.629 0.094 9.911
(1.29) (0.26)
6 Canstar-cap -0.447 0.862 0.202 10.494
(1.04) (0.17)
7 Ind Ratna -0.360 1.227 0.327 9.535
(0.81) (0.15)
8 Mastershare -0.119 1.226 0.566 5.710
(0.39) (0.07)
9 Masterplus 91 -0.927 0.953 0.402 5.632
(0.63) (0.13)
10 UGS 2000 0.110 0.659 0.212 6.197
(0.67) (0.14)
11 UGS 5000 -0.060 0.822 0.190 8.268
(0.89) (0.18)
V alue w eigh ted a v erage
T able 3.26: Estimation of the market model
There is no fund where the n ull of H
0
: = 0 can b e rejected. All the estimated ^ are
negativ e, other than #10, where ^ = 0:11, and this has little statistical signicance. Most of the
alphas are str ongly negativ e; #5, for example, earns 1 :326% less returns eac h w eek as compared
to that exp ected at = 0:629.
Div ersication using mutual funds?
The residual v ariance seen in T able 3.26 is generally enormous. Analysis of v ariance of ( r
j
r
f
)
for eac h sc heme is presen ted in T able 3.27.
98
Sc heme T otal Risk Of whic h, div ersiable risk
1 Can b on us 104 89
2 Canshare 88 69
3 Candouble 90 70
4 Cangro wth 105 72
5 Can triple 107 97
6 Canstar-cap 137 109
7 Ind Ratna 134 90
8 Mastershare 75 33
9 Masterplus 91 52 31
10 UGS 2000 48 38
11 UGS 5000 83 67
T able 3.27: Analysis of v ariance of ( r
j
r
f
)
This table reinforces the suggestions made in Section 3.4.1.2 to the eect that the total risk
of these sc hemes is unduly high. This rev eals that the excessiv e risk w as not caused b y a high
2
V ar(r
M
r
f
); instead it is more probably caused b y p o or div ersication.
These results are in sharp con trast with the m utual fund industry in the US, where ev en
b efore the adv en t of the CAPM in to industry , Sharp e (1966) found that only 12% of the total
risk of US m utual funds w as div ersiable. A study b y Merill Lync h, cited in Elton & Grub er
(1987) (P age 599) nds that US m utual funds div ersied a w a y all but 10% of the risk.
Sharp e’s Measure
The rational in v estor w ould maximise Sharp e’s measure,
S =
E (r
j
r
f
)
V ar(r
j
r
f
)
99
calculated for their over al l p ortfolio.
26
These sc hemes are all observ ed for dieren t time p erio ds and S for the mark et index will
ha v e to b e calculated separately for eac h of them. When E (r
j
r
f
) < 0, Sharp e’s measure is not
useful for in ter{sc heme comparison.
Sc heme 100 S (r
j
r
f
) 100 S (r
M
r
f
)
1 Can b on us -1.116 0.289
2 Canshare 0.121 2.081
3 Candouble -0.107 1.728
4 Cangro wth -0.305 2.078
5 Can triple -0.917 2.184
6 Canstar-cap -0.142 0.792
7 Ind Ratna 0.280 2.060
8 Mastershare 0.684 1.827
9 Masterplus 91 -1.666 0.243
10 UGS 2000 0.540 0.974
11 UGS 5000 0.153 0.974
T able 3.28: Sharpe’s Measure
F rom the results in T ables 3.28, 3.27 and 3.26, it is arguably clear that these sc hemes will
fare rather p o orly with resp ect to the other measures of p erformance, namely T reynor’s measure
and excess returns obtained o v er risk{equiv alen t b enc hmarks (this could b e done using either or risk).
3.5 In Summary
T o recapitulate the v ariet y of evidence whic h this c hapter has thro wn up and th us try to under-
stand the o v erall picture: the curren t state of h uman kno wledge concerning mark et eciency on
the BSE ma y b e summarised in the follo wing sev en p oin ts :
26
T o the exten t that relativ ely few in v estors dev ote their en tire sa vings in to one sc heme, the usefulness
of this metric is relativ ely limited.
100
1. Auto-correlations , Section 3.2.1
Some predictabilit y of the order of one-da y ahead is often seen. There seems to b e some
size-related regularit y in the pattern of acfs of individual companies, but the pattern of
regularit y is am biguous.
2. Runs test , Section 3.2.2
W e often reject the n ull h yp othesis. Some predictabilit y of the order of one-da y ahead
exists, lending supp ort to the results of the acf tests.
3. V ariance Ratio T ests , Section 3.2.3
The n ull h yp othesis can b e rejected. In addition to this, there is a strong mean a v ersion
trend implied in prices.
4. Seasonalit y , Section 3.2.4
No mon th-eect exists. A sligh t F rida y eect w as found.
5. Sto c k Splits , Section 3.3
Abnormal XB-date pricing w as found.
6. Abnormal pricing prior to GDR issues Section 3.3.2
Abnormal pricing w as found, but after this information en tered the information set of
agen ts, the abnormal pricing w as sharply diminished.
7. Mutual F und P erformance , Section 3.4.1
Mutual funds app ear to b e unable to pro duce excess returns.
101
F rom these results, there seems little doubt that our n ull h yp othesis, of non-forecast-able
returns, can b e rejected at a purely statistic al lev el. The ca v eat is that these result m ust b e
considered in the ligh t of the fact that all these tests w ere conducted assuming homosk edasticit y
of returns. If the data is heterosk edasticit y, then it is quite p ossible that the signicance of
the rejections migh t b e considerably reduced, dep ending up on ho w m uc h heterosk edasticit y is
inheren t in the data stream.
Ev en if the results hold with statistical signicance after accoun ting for the heterosk edasticit y,
the results ma y still b e consisten t with mark et eciency in an e c onomic sense, where w e dene
mark et eciency as the non-existence of arbitrage opp ortunities net of trading costs.
T rading costs on the bse are v ery high. On pap er, brok ers c harge roughly 1% for one-trip
trading. In practice, the costs are m uc h higher. Brok ers are frequen tly inecien t, so that orders
fail to get executed; this is a source of risk from the viewp oin t of an arbitrage strategy . F urther,
the pro cess of trading itself lac ks transparency , so that a brok er can c harge a customer an y price
for a trade: as long as that price lies b et w een the high and the lo w price for the da y , the customer
has no w a y of kno wing whether the brok er actually transacted at the claimed price. Ex-p ost, it
app ears that customers are routinely billed for buy orders at a price close to the da ys high price
and for sell orders at a price close to the da ys lo w price.
F or the database of the 92 A group companies (whic h ha v e the b est liquidit y) o v er the v e
y ears 1990-1994, the a v erage spread of 2 (hig h low )=(hig h + low ) comes to 4 :5%. If brok ers
transact at ( hig h + low )=2 on a v erage, then they w ould earn half this spread (i.e. 2 :25%) on eac h
transaction if buy orders are billed at the high price and sell orders are billed at the lo w price.
A conserv ativ e estimate is that the excess trading cost imp osed b y the lac k of transparency is
at less than half of this, i.e. 1%. The total one-trip trading cost is 2% conserv ativ ely , including
102
the o v ert 1% brok erage fee. T rading costs for companies other than the 92 A group companies,
where the high-lo w spread is greater than 4 :5%, w ould b e higher than this.
If true one-trip trading costs are 2%, then all the ab o v e results of short-term returns pre-
dictabilit y are consisten t with mark et eciency in an economic sense. It is still dicult to
reconcile the observ ed long-run mean a v ersion b eha viour of the vr tests to an y notion of mar-
k et eciency . The same holds for the XB-date mispricing and the pre-Ma y-1994 exp erience of
abnormal returns prior to GDR issues.
The o v erall XB-date mispricing o v er the v e y ears is hard to rationalise. Ho w ev er, when
the v ariation of XB-date mispricing o v er the y ears is analysed, w e nd that the mispricing has
steadily diminished o v er time { in an en vironmen t where the micro-structure of trading has b een
broadly stable, this reduction of XB-date mispricing ma y b e caused b y impro v ed analytical skills
on the part of agen ts. The 45 large companies who did a b on us issue in 1994 had a mean excess
XB-date returns of 5 :13% (the standard deviation of the sampling distribution is 1.26), and the
46 small companies who did the same had mean excess returns of 5 :14% (the standard deviation
of the sampling distribution is 1.60). This ma y not b e a agran t violation of mark et eciency
after taking in to accoun t round-trip arbitrage costs of 4%. It is imp ortan t to recall here that
our estimates of XB-date returns are biased up w ards o wing to lo w trading frequency of man y
securities prior to XB date.
The evidence ab out m utual fund p erformance is consisten t with this view that the exten t
to whic h assets are curren tly mispriced do es not supp ort protable arbitrage in the ligh t of the
curren t micro-structure of trading. The exp erience with gdr mispricing (whic h w as the rst
ev en t study conducted with data from the bse) seems to sho w a mark et whic h do es react in
terms of closing arbitrage opp ortunities.
103
It should b e noted that the XB-date mispricing sho wn here marks the rst analysis of XB-
date b eha viour in the coun try . When this information seeps in to the information set of agen ts,
w e w ould exp ect XB-date mispricing to diminish if it is indeed the case that it can b e exploited
to some exten t as has b een noted in the u.s. mark ets.
Th us the o v erall view of the bse is that of a mark et in whic h some kinds of returns predictabil-
it y exist, through a com bination of w eak micro-structure and w eak nance researc h. Progress in
b oth dimensions will generate impro v emen ts in mark et eciency in the y ears to come.
104
Chapter 4
Heteroskedasticity Models
4.1 Motiv ation
Ev er since arch mo dels w ere in tro duced in to the literature b y Engle (1982), the literature has
unco v ered evidence of heterosk edasticit y in sto c k mark et returns in most OECD coun tries, es-
p ecially the United States (see Bollerslev et al. (1992) for a comprehensiv e literature surv ey).
V ariance of returns at a p oin t in time sho ws strong correlations with prior inno v ations: this has
b een established using arma mo dels estimated for squared returns (as recen tly explored in Gey er
(1994)) and garch mo dels for returns of man y sto c k mark ets in the w orld (a few of the man y
pap ers are Theo dossiou & Lee (1995), Errunza, Hogan, Kini & P admanabhan (1994) and Bo oth,
Martik ainen, Sark ar, Virtanen & Yli-Olli (1994)).
105
4.1.1 Why Heteroskedasticity in Returns Matters
Heterosk edasticit y, if it exists, has n umerous ramications for nancial economics. If the data
generating pro cess underlying returns con tains heterosk edasticit y , then it ma y ha v e to b e ex-
plicitly accoun ted for when addressing a whole host of problems, ranging from tests of mark et
eciency and asset pricing theory to p ortfolio optimisation and the pricing of deriv ativ es.
On the sub ject of the data generating pro cess underlying sto c k mark et returns, evidence
of non-normalit y of con tin uously comp ounded returns in man y coun tries is diminished when
examining residuals from arch mo dels. A t a practical lev el, this impacts on asset pricing theory
and p ortfolio optimisation whic h is aected b y the heterosk edasticit y{ examples of this are Ghosh
(1992), Sc h w ert & Seguin (1990) and Bera, Bubn ys & P ark (1988). A p o w erful imp etus for
v olatilit y mo dels comes from nancial deriv ativ es, where forecasts of v olatilit y are directly used
in pricing algorithms for all deriv ativ e con tracts.
An exploration of what causes heterosk edasticit y brings us bac k to basic questions of mark et
eciency , and the mec hanisms through whic h prices assimilate information. A t the simplest, tests
of mark et eciency whic h assume a homosk edastic data generating pro cess are biased to w ards
rejection of the n ull if heterosk edasticit y is presen t. In one example, F rankfurter & Lamoureux
(1988) sho w that once heterosk edasticit y is accoun ted for, certain kinds of p erceiv ed arbitrage
opp ortunities is explained.
1
W e b egin b y doing a simple univ ariate analysis of the second momen t of the returns data on
the bse Sensex.
1
They apply timing lter rules to mean-v ariance ecien t p ortfolios and nd that the lter rules do not
rev eal arbitrage opp ortunities compared to a buy-and-hold strategy whic h accoun ts for heterosk edasticit y.
106
4.2 Statistical character of the returns vector
A long time-series of returns on the bse Sensex is used widely as a mark et index on the BSE.
Our data-set has 3206 observ ations of daily returns o v er the p erio d from April 1979 to Marc h
1995. The thirt y companies in the BSE Sensex accoun t for only 25% of the mark et capitalisation
of the BSE as of to da y (though this fraction w as around 40% b efore 1992). This co v erage is quite
p o or, but there is no alternativ e mark et index whic h matc hes the span of this time-series. The
BSE Sensex also has one imp ortan t adv an tage as compared to other indexes: while securities on
the BSE often suer from non-sync hronous trading, the thirt y companies in the BSE Sensex are
essen tially imm une to it. This w ould reduce an y spurious auto-correlations that are exp ected
to b e generated b y non-sync hronous trading to a large exten t. W e examine the v olatilit y of the
index as v ariance of daily returns in a y ear for the time p erio d
107
1 6 11 16 21 26 31 36
0.035
0.0
-0.035
-0.2
0.0
0.2
acf of Daily returns: lags 1 to 40
Returns
Returns-Squared
1 6 11 16 21 26 31 36
0.071
0.0
-0.071
-0.2
0.0
0.2
acf of Weekly returns: lags 1 to 40
Returns
Returns Squared
1 6 11 16 21 26 31 36
0.145
0.0
-0.145
-0.2
0.0
0.2
acf of Monthly returns: lags 1 to 40
Returns
Returns Squared
Figure 4.1: Daily acf : lags 1 to 40
The acfs in Figure 4.1 sho w the time series structure of the returns and the squared returns.
The bse Sensex app ears to ha v e strong auto correlations in returns, at least for rst couple of
trading da ys, with signican t co ecien ts in the initial lags of the daily series. In this pap er, with
the fo cus on the v olatilit y , w e examine the squared returns as a measure of daily v ariance.
F rom the acfs, the auto-correlation in the squared returns suggest that there is a clustering
of v ariance. The correlation app ears strongest in daily data with almost ev ery co ecien t of the
108
returns squared series b eing outside the asymptotic b ounds.
2
The correlation is w eak er for the
w eekly squared returns and further reduced for the mon thly series. But all three series sho w
strong rst order correlations in the returns squared series.
The ab o v e c haracteristics of high kurtosis, the v ariance clustering seen in the acf and the
reduction of the correlation across aggregation of the data suggest the arch sp ecication as a
go o d appro ximation to the structure of conditional v ariance of the bse Sensex. Dieb old (1986)
rst sho w ed ho w arch returns cause the three c haracteristics ab o v e.
4.3 arch Models for the bse Sensex
4.3.1 Background
Time series with auto-regressiv e conditional heterosk edasticit y ( arch ), w ere rst mo deled b y
Engle (1982). The simplest arch mo del for a time-series y
t
is written as follo ws:
y
t
= x
0
t
+ t
t
is assumed to b e serially uncorrelated with a conditional v ariance of h
t
, whic h is a func-
tion of the information set at time t, I
t 1
. I
t 1
con tains the set of all realised v alues
y
t 1
; y
t 2
; : : : ; x
t 1
; x
t 2
; : : :. Here x
t 1
; : : : are v ariables that are exogenously determined. They
could include lagged v alues of y
t
as w ell. Engle’s linear arch (q) mo del denes t
as
t
j I
t 1
N (0; h
t
)
2
The b ounds are calculated as 2 =
p
T , whic h amoun ts to 0.04 for the daily data, 0.07 for w eekly data
and 0.15 for the mon thly data.
109
h
t
= 0
+
q
X
i=1
i
2
t i
or
h
t
= 0
+ (L) 2
t
where L is a lag op erator and (L) is the sequence of 1
; : : : ; q
. The mo del assumes that 0
> 0
and i
0 whic h ensures h
t
will b e p ositiv e. Since the v ariance is conditional on the inno v ation
of the previous time p erio ds, large errors of either sign tend to b e follo w ed b y large errors and
lik ewise for small errors. Th us arch mo dels capture the phenomenon of v olatilit y clustering.
Man y of the arch mo dels estimated for nancial data sho w they demand v ery long lag lengths.
In the garch mo del (Bollerslev 1986), a p oten tially long lag structure of 2
t
is replaced b y a
com bination of lagged 2
t
and h
t
. Where the data suggests high v alues of q , this often pro duces
a more parsimonious sp ecication as compared with a simple arch mo del. The conditional
v ariance tak es the form:
h
t
= 0
+
p
X
i=1
i
2
t i
+
q
X
j =1
j
h
t j
or
h
t
= 0
+ (L) 2
t
+ (L)h
t
for a garch (p; q ) mo del. When constrain ts of 0
> 0, i
0 and i
0 are imp osed, h
t
is
strictly p ositiv e. Studies, b oth theoretical (Nelson & Cao 1992) and empirical (F renc h, Sc h w ert
& Stam baugh 1987), ha v e since deriv ed conditions under whic h i
parameters can b e negativ e
and h
t
still b e p ositiv e.
110
The stationarit y prop erties of these mo dels are deriv ed from the unconditional momen ts,
whic h are in turn deriv ed using iterated exp ectations. F or a garch (1,1) pro cess
2
= E ( 2
t
) =
0
1 1
1
The condition 1
+ 1
< 1 ensures stationarit y . Generally , the condition will b e
P
q
i=1
i
+
P
p
j =1
j
< 1
4.3.2 Estimation and Model Selection Criteria
Estimation of garch mo dels is t ypically done using the maxim um lik eliho o d tec hnique, mle.
The standard distributional form used is the normal with the log lik eliho o d b eing
y
t
j I
t 1
N (x
t
; h
t
)
log L( ) =
1
T
T
X
t=1
log L
t
( )
log L
t
( ) = 1
2
log 2 1
2
log h
t
2
t
2h
t
where = (; 0
)
0
. is the conditional mean and are the conditional v ariance parameters. Under
the normal, the information matrix is blo c k diagonal with resp ect to these t w o parameters, whic h
mak es for easier estimation. W eiss (1986) sho ws that qmle
is consisten t as long as the rst t w o
momen ts are sp ecied correctly and assuming that the fourth momen t exists. Giv en the blo c k
diagonal structure of the information matrix, the estimate will b e consisten t as long as the
rst momen t is correctly sp ecied, ev en if h
t
is not. Finite sample prop erties of this estimator
are still in the pro cess of b eing established in the literature, mostly as a result of Mon te Carlo
sim ulations.
111
Other metho ds of garch estimation are the Generalized Metho d of Momen ts (Ric h, Ra ymond
& Butler 1991) and semi-parametric estimation (Engle & Gonzalez-Riv era 1991). These metho ds
are more ecien t estimation tec hniques compared to the mle. Ba y esian tec hniques are also
used in estimating arch mo dels based on the fact that the restrictions on the H
t
can b e easily
incorp orated in to prior distributions.
In this thesis, w e use mle for estimation.
Giv en mle, mo del selection is based on three metrics: the lr statistic, the Ak aik e Information
Criterion, aic, and the Sc h w artz Ba y esian Criterion, sbc. All three statistics are based on the
log lik eliho o d v alue at the estimated parameter v ector. The lr is a ratio of the restricted to the
unrestricted mo del and is distributed as 2
(k ) where k is the n um b er of restricted parameters. W e
estimate mo dels with one restriction imp osed at a time, and th us use the lr test as a comparison
b et w een t w o mo dels, with k = 1.
The aic and sbc are functions of the log lik eliho o d v alues as w ell as the n um b er of free
parameters in estimation. They incorp orate a p enalt y for a larger n um b er of parameters, whic h
giv es us a bias to w ards more parsimonious sp ecications. If a mo del con tains k free parameters,
the aic is 2
log L
T
+ 2
k
T
and the sbc is 2
log L
T
+ log T
k
T
. The aic often leads to o v er-sp ecied
mo dels as compared with the sbc.
Giv en the form of the distribution function and the form of the heterosk edasticit y, the only
v ariable no w is the form of the mean equation.
4.3.3 Specication of the Mean Equation
The form of the mean equation has serious implication for the time series prop erties of the
v ariance. Figure 4.1 sho w ed that there is signican t auto-correlation in b oth the returns and
112
the squared returns. This is a feature do cumen ted in returns in the US (F ama 1965, Amih ud &
Mendelson 1987, McInish & W o o d 1991) and on other sto c k exc hanges as w ell (Co c hran, DeFina
& Mills 1993).
There are mo dels that use mark et micro-structure to explain this excess auto-correlation. F or
instance, Hasbrouc k & Ho (1987) mo deled the auto-correlation as the result of lagged adjustmen t
of limit-order prices. Whereas, Campb ell, Grossman & W ang (1993) mo deled it as arising from
higher returns for risk-taking on the part of mark et mak ers. They mo del an increased v ariance in
returns due to the action of \noise" traders, whic h aect the prot margins of the mark et mak ers.
A more widely emplo y ed mo del for auto-correlation sho ws it to b e a result of non-sync hronous
trading whic h encapsulates the notion that sto c ks in the mark et trade with dieren t frequencies
(Lo & MacKinla y 1990). Th us, the impact of an y particular information sho c k on the mark et
has a lagged eect through its impact on sto c ks that trade at dieren t times.
This implies that ev en on an \ecien t mark et", the eect of an y one sho c k will die out more
slo wly than an ideal one-time c hange in the lev el of the index.
3
In addition, the non-sync hronous
trading auto-correlation eect is a relativ ely short term one, whic h migh t also explain wh y there
is a m uc h reduced acf structure in mon thly data of most sto c k mark ets studied.
Non-sync hronous trading as an explanation of index auto-correlations migh t ha v e b een quite
applicable on the bse, since non-sync hronous trading is rampan t on the bse. Ho w ev er, it is of
limited imp ortance with resp ect to the bse Sensex itself, since the companies in the bse Sensex
trade frequen tly . Rather, these auto-correlations migh t b e the manifestations of the factors listed
at the end of Chapter 2 - high trading costs and lac k of the abilit y to pro cess information.
3
While non-sync hronous trading explains index auto-correlations substan tially , it has b een sho wn to
not completely accoun t for the auto-correlations in the s&p500 500 index (Harris 1989, A tc hison, Butler
& Simonds 1987).
113
Time series mo dels of index returns suggests the arma (2,1) as a go o d sp ecication to c har-
acterise the daily returns data, and the arma (1,1) for w eekly and mon thly returns, under the
assumption of homosk edasticit y . An arma mo del can also b e written as an ar mo del of innite
lags. Since the fo cus is on the v ariance structure of the residuals and the exact sp ecication of
the mean equation is not the issue, the results of the ar estimations for the mean equation are
not included here. Ho w ev er, w e nd that the mean equation t ypically requires short lags, ev en
in the conditional heterosk edasticit y mo dels.
4
Th us, the garch mo del that w e will estimate for the bse Sensex tak es the form :
r
t
= 0
+ L (r
t
) + t
t
N (0; h
t
)
h
t
= 0
+ (L) 2
t
+ (L)h
t
4.3.4 Estimation Results
W e started b y estimating arch (q) mo dels (results not sho wn here) using 22 lagged squared
residuals.
5
The estimations oered strong supp ort for the existence of conditional v ariance. The
optimal lag length c hosen as p er the aic statistic is q = 14 while the sbc statistic w as maximised at
q = 4 for daily data.
6
W e tak e the long lag structure in the v ariance sp ecication as evidence that
the garch sp ecication migh t b e a b etter alternativ e as a mo del for conditional heterosk edasticit y
of the bse Sensex. W e mo v e on to estimating garch mo dels for the bse Sensex. Since our earlier
estimations of the mean equations w ere done without taking heterosk edasticit y in to accoun t, w e
4
W e estimated arma -garch mo dels for the data and found little c hange in the parameters estimated
with c hange in the ar sp ecication of the mean equation. This can b e seen later in T able 4.1.
5
W e elected to start with 22 lags as the largest n um b er of trading da ys in an y mon th in the data.
6
Mo dels estimated for w eekly and mon thly returns of the bse Sensex ga v e q = 4 for w eekly and q = 2
for mon thly .
114
rst test for the presence of longer lags in the mean equation for t w o xed garch sp ecications
{ a garch (1,1) and a garch (4,4) (T able 4.1). W e see that our earlier sp ecication of the mean
equation lags still holds.
garch (1,1) garch (4,4)
Mean Log LR Log LR
T erms Lik eliho o d Statistic aic sbc Lik eliho o d Statistic aic sbc
4 -5819.95 3.643 3.660 -5803.91 3.638 3.663
3 -5821.09 2.28 3.642 3.657 -5806.46 5.10 3.638 3.660
2 -5821.86 1.54 3.641 3.654 -5809.68 6.44 3.638 3.658
1 -5825.30 6.88 3.641 3.652 -5813.44 7.52 3.638 3.657
0 -5839.14 27.68 3.648 3.658 -5872.92 28.96 3.646 3.663
T able 4.1: Selection of mean equation lagged terms
W e estimate garch mo dels for daily data, with the mean equation as an ar(1). Log Lik eli-
ho o d v alues and the test statistics for the v alues of p = 1 : : : 4 and q = 1 : : : 4 are sho wn in T able
4.2.
115
p 1 2 3 4
q
1 -5825.30 (1.84) -5824.38 -5881.07
-5878.45
(1.58) (2.98) ({)
aic 3.593 3.595
sc 3.603 3.606
2 -5824.51 (3.24) -5822.89 (5.78) -5820.00 (0.38) -5819.81
(1.52) (1.42) (2.80) (-1.06)
aic 3.595 3.595 3.595 3.597
sc 3.606 3.609 3.610 3.614
3 -5823.75 (3.14) -5822.18 (7.16) -5818.60 ({) -5869.18
(3.48) (5.92) (5.00) (1.060)
aic 3.596 3.597 3.596 {
sc 3.609 3.612 3.613 {
4 -5822.01 (5.58) -5819.22 (6.24) -5816.10 (5.32) -5813.44
aic 3.597 3.597 3.596 3.596
sc 3.612 3.613 3.615 3.617
(LR) statistics at eac h addition of a parameter b et w een the LogLik eliho o d v alues
aic and sc statistics are en tered b elo w the LogLik eliho o d v alues
( )
estimation did not con v erge
T able 4.2: ar(1)- garch model statistics
The increases in lagged h
t
terms in the v ariance yields least b y w a y of impro ving the Log
Lik eliho o d v alue, in fact, some of the mo dels with the longer lag structure of the lagged h
t
terms
(i.e. higher p), could not b e estimated. In con trast, longer lags in the squared residual (i.e. higher
q ) yields lik eliho o d gains, though these gains are not signican t. The aic and sbc steadily w orsen
with increases in either p or q from a garch (1,1) sp ecication. As for the estimates themselv es,
the co ecien ts on the lagged residual terms ha v e increasing standard errors as the n um b er of
lags increase.
4.3.5 Inference and Analysis
The momen ts of the standardised residuals, based on dieren t garch sp ecications in T able 4.3,
sho w exp ected c hanges in kurtosis. When homosk edasticit y is assumed, there is a pronounced
116
kurtosis whic h c hanges dramatically when using garch (1,1) to sp ecify the v ariance. This is
consisten t with other studies in the literature whic h nd that the evidence for non-normalit y of
returns is diminished when arch eects are accoun ted for.
If the garch mo del is sp ecied correctly , then the residuals standardised b y the conditional
standard deviation, t
=
p
h
t
, should b e a white noise pro cess. The acf of t
=
p
h
t
should also ha v e
smaller co ecien ts than the acf of t
. F rom Figure 4.2, w e nd that the standardised residuals
from the garch (1,1) mo del ha v e acf co ecien ts that are not signican t { they all lie b et w een the
asymptotic b ounds of 2 =
p
T . This is ev en more ob vious in the case of the squared standardised
residuals except for the term at lag v e.
Momen ts of the standardised error, t
=
p
h
t
Num b er
Garc h Mean Standard Sk ewness Excess of
Lags Deviation Kurtosis Observ ations
(0; 0) 0.032 3.034 0.147 6.207 3233
(1; 1) 0.018 1.001 0.355 3.724 3233
T able 4.3: ar(1)- garch : diagnostics
117
1 6 11 16
0.035
0.0
-0.035
ACF of residuals
Residual
Standardized
1 6 11 16
0.035
0.0
-0.035
ACF of Residuals Squared
Residual
Standardised
Figure 4.2: acf of daily residuals: lags 1 to 20
Estimated arch mo dels for the w eekly and mon thly data also sho w that the mo del selection
criteria fa v our the garch (1,1) amongst mo dels with lags up to four in b oth the squared residual
and the v ariance terms. Drost & Nijman (1993) demonstrates that giv en a true garch mo del for
a pro cess at a certain frequency , the mo del for aggregated data is of a higher-order garch form.
In our case, estimations of the daily , w eekly and mon thly mo dels are all seemingly garch (1,1).
P artly , w e realise that statistical p o w er for lo w er frequency data is less than that of higher
118
frequency data. An alternativ e reason is that the simple garch (1,1) migh t b e a missp ecication
of the time series structure for the v olatilit y of daily returns on the bse Sensex.
Daily W eekly Mon thly
P arameters ar(1)-garch (1,1) ar(0)-garch (1,1) ar(0)-garc h(1,1)
0
0.062 0.269 1.327
0.021 0.096 0.569
1
0.099
0.019
0
0.053 0.234 1.661
0.005 0.083 1.256
1
0.099 0.130 0.105
0.008 0.019 0.050
1
0.886 0.861 0.879
0.008 0.021 0.056
1
+ 1
0.985 0.991 0.984
0.011 0.028 0.075
Momen ts of standarised error, t
=
p
h
t
Mean 0.019 0.039 0.054
V ariance 1.001 0.999 1.003
Sk ewness 0.356 0.106 0.459
Excess Kurtosis 3.724 1.324 0.279
Standard errors b elo w the parameter estimates
T able 4.4: garch parameter estimates
T o explore the issue of missp ecication further, w e fo cus on the garch co ecien t estimates,
1
and 1
, in table 4.4. The sum of these co ecien ts denes the p ersistenc e of the v ariance. The
concept of \p ersistence" here is a measure of the n um b er of time p erio ds for whic h the impact of
an y sho c k to v ariance is signican t. F or the mo dels estimated ab o v e, the sum is v ery close to one,
whic h indicates a highly p ersisten t system.
7
F urther, in our estimates, this degree of p ersistence
do es not seem to c hange m uc h across data aggregation.
8
7
A sum of 1.0 implies unconditional v ariance of 1 asymptotically .
8
Lamoureux & Lastrap es (1990 b) dene an in tuitiv ely app ealing notion of the half-life of a sho c k to the
v ariance, whic h is the time p erio d o v er whic h the sho c k diminishes to half it’s original size. The half life
119
The particular issue of p ersistence is addressed in the literature in one of t w o w a ys: one is
that there is indeed long-term p ersistence in the v ariance, c haracterized b y a conditional v ariance
whic h is non-stationary . A non-stationary pro cess implies a system where the eects of a sho c k
are inheren t in the returns pro cess forev er. F rom the p oin t of view of eciency , a mark et is
dened as ecien t if prices on the mark et fully absorbs and in ternalises information in a short
p erio d of time. W e exp ect that information sho c ks to the returns should ha v e a v ery short-term
eect and the p ersistence in v ariance, if an y , is relativ ely small.
An alternativ e explanation is suggested b y Lamoureux & Lastrap es (1990 b), in a mo del that
depicts the p erceiv ed p ersistence as the result of shifts in the lev els of unconditional v ariance.
If not sp ecied, these regime shifts in lev els sho w up as highly p ersisten t garch parameter
estimates, akin to a non-stationary pro cess. These shifts are caused b y economic ev en ts that
aect the b eha viour of the v ariable b eing studied.
The latter mo del has more economic app eal than the non-stationary one, esp ecially in the
con text of a dev eloping coun try
9
, whic h faces man y economic and institutional c hanges that w e
exp ect will ha v e impact on the structural b eha viour of the mark et.
for garch (1,1) is 1 log 2= log ( 1
+ 1
). The half-life for the bse Sensex as measured b y the estimated
parameters is 47 da ys for daily data, 78 w eeks and 44 mon ths. This do es not mak e m uc h sense since it
implies that a sho c k fades a w a y faster with daily data as compared with w eekly or mon thly data.
9
Gey er (1994) found that p ersistence of v ariance as measured b y the sum of the garch parameters
reduced signican tly when a regime shift w as accoun t for in the Vienna Sto c k Exc hange.
120
80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95
daily index levels
March85
Jan93
15Oct87
13Oct89
80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95
-10
-5
0
5
10
returns
March85 Jan93
15Oct87
13Oct89
80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95
0
50
100
150
Squared returns
March85 Jan93
15Oct87
13Oct89
Figure 4.3: Daily data: April 1979 to Marc h 1995
121
4.3.6 Structural changes in the Indian Economy
The idea of shifts in the v ariance in the bse Sensex is particularly app ealing b ecause of the man y
economic c hanges that ha v e happ ened in the last decade to the Indian econom y and sto c k mark et.
Of these, the most in teresting are the follo wing ev en ts:
Ev en ts Pre-1990
In 1984, the new administration of Ra jiv Gandhi initiated a series of p olicy measures whic h
mark the b eginning of India’s turn to w ards mark et-orien ted economic p olicies. While the p olicy
en vironmen t has ev olv ed substan tially o v er the y ears, the early thrust of economic p olicy w as on
eliminating internal en try barriers.
Historically , India had a regime of industrial licensing, where rms had to apply for go v-
ernmen t p ermissions in order to start pro ducing a giv en widget. Industrial licensing w as fully
ab olished in 1991, but from 1984 on w ard, the go v ernmen t made man y c hanges whic h led to li-
censes b eing m uc h more freely a v ailable than b efore. This led to an in v estmen t b o om in the
econom y as rms rushed to en ter industries whic h w ere previously c haracterised b y shortages.
This had t w o implications for nancial mark ets:
Firms often turned to capital mark ets to raise resources in order to nance the new pro jects
that lib eralisation made p ossible. Th us there w as a ma jor increase in the resources raised
from the primary mark et. A t the time, the oer prices of IPOs w ere regulated and v ery
high lev els of IPO under-pricing w ere prev alen t.
Incum b en t rms (whic h includes all the companies in the BSE Sensex p ortfolio) no w faced
a m uc h altered comp etitiv e landscap e. Earlier, the incum b en t rms w ere protected b y
122
en try barriers. In the follo wing y ears, man y industries b ecame ercely comp etitiv e o wing
to en try , and prots (and dividends) b ecame m uc h more v ariable. The impact of news
up on the future prosp ects of the incum b en t compan y w as greater than ev er b efore.
India’s primary mark et
10
is unique b y w orld standards in that ipos are sold directly to la y
in v estors. The enormous gro wth of the ipo mark et coupled with the p olicy-induced high lev els
of IPO under-pricing, serv ed to attract a larger fraction of domestic sa vings in to sto c ks in t w o
w a ys: directly , through selling pap er, and indirectly , b y helping households mak e the transition
from o wning no shares to o wning some shares.
11
W e exp ect that this increase in v olumes in the
mark et also con tributed to the increase in v olatilit y to a small exten t.
12
Resources Raised on Av erage Daily BSE
Y ear Primary Mark et T rading V olume
(Rs. bln) (Rs. mln)
1983-84 9.10 130.3
1984-85 8.58 235.1
1985-86 17.45 371.5
1986-87 25.63 586.1
1987-88 17.77 342.3
T able 4.5: Structural change on the bse
The regime shift is apparen t through a visual examination of the daily data in Figure 4.3,
and w e will explore the prop osition that a distinct c hange in the v olatilit y of returns to ok place
from the rst few mon ths of 1985 on w ard. W e will date the regime shift at 1 Marc h 1985.
10
A detailed recen t study of the ipos and the Indian primary mark et w as conducted b y Shah (1995 b).
11
Although w e do not ha v e long time series data on the p ercen tage of household w ealth in v ested in the
sto c k mark et, w e do kno w that in the p erio d b et w een 1985 and 1987, public issues as a p ercen tage of
sa vings almost doubled, from 4.6% in 1984 to 7.5% in 1986 and 9.5% in 1987.
12
The p ositiv e correlation b et w een relationship b et w een price v ariabilit y and trading v olumes on the us
sto c k mark ets has b een w ell studied, as has b een carefully researc hed in T auc hen & Pitts (1983). Since
then, Lamoureux & Lastrap es (1990 a) has also found v olume to b e a go o d pro xy for information o w that
remo v e arch eects from the conditional v ariance forms of individual sto c ks on the nyse .
123
Ev en ts Post-1990
In the more recen t past, the three outstanding ev en ts whic h ha v e aected the sto c k mark et are
the scam, the op ening up to foreign p ortfolio in v estmen t, and the ban on forw ard trading.
The great scam of 1992 w as an episo de where a sp eculativ e bubble w as created using an illegal
div ersion of funds from the banking system. The scam aects returns data from Septem b er 1991
till the end of Ma y 1992. The bse Sensex exhibits pronounced lo w er v olatilit y from July 1992
on w ard.
F oreign institutional in v estors ha v e gradually started in v esting in India, in resp onse to a
gradual elimination of barriers to foreign capital, from 1992 on w ard. The in tegration of Indian
nancial mark ets in to the w orld has also b een assisted b y large-scale sales of GDRs (global
dep ository receipts) b y Indian rms w orldwide. Both foreign p ortfolio in v estmen t and GDR
issues b y Indian rms b ecame signican t from the middle of 1993 on w ard. Indian in v estors are
still not allo w ed to in v est their w ealth abroad.
Owing to these c hanges, w e exp ect that the Indian sto c k mark ets are slo wly b ecoming in te-
grated with w orldwide sto c k mark ets, as compared with the almost-total isolation that prev ailed
b efore. Kim & Singal (1994) study mon thly returns from the emerging mark ets of nine coun tries
and nd that there is no increase in v olatilit y after the op ening up of the mark et. In this w ork,
to the con trary , the v olatilit y seems to decrease in the p erio d a y ear after op ening up. In an y
case, on the bse Sensex, w e h yp othesize that the rst order eects of increased v olumes and th us,
increased v olatilit y , has tak en a precedence o v er the eects of div ersication so far.
The nal ev en t, the ban on forw ard trading, to ok place on 12 Marc h 1994. The p ost-ban time-
series is to o short for us to analyse in detail. W e migh t exp ect somewhat higher v olatilit y through
the elimination of sp eculativ e traders in the p erio d follo wing 12 Marc h 1994. Shah (1995 a) nds
124
that forw ard trading diminishes rm-lev el unsystematic risk, but this need ha v e no eect on the
total risk of the mark et index, whic h is a w ell div ersied p ortfolio.
Seasonal Eects
In India, the ann ual economic budget is announced on the 28
th
of F ebruary .
13
The budget is a
m uc h-eagerly an ticipated ev en t, wherein whic h sev eral p olicy announcemen ts crucial to industries
and rms are announced. F or instance, a v ariet y of c hanges in domestic tax rates, and customs
taris are announced as part of the budget. Ov er and ab o v e the scal op erations of the go v ern-
men t, the budget sp eec h is commonly used b y the nance minister to announce other imp ortan t
economic p olicy initiativ es. W e w ould th us exp ect a seasonal budget eect in v olatilit y for the
bse, ev en though there is v ery little evidence of signican t mon th-seasonalit y in the returns itself
(Section 3.2.4).
Rumours, prognoses and leaks ab out the budget b egin in the early part of F ebruary and ends
with the announcemen t at the end of F ebruary . The w eeks follo wing the budget w ould reect
mark ets assimilating the news. W e attempt to capture the pre- and p ost-budget announcemen t
eects and mo del the budget p erio d as a com bination of F ebruary and Marc h.
The ab o v e structural economic c hanges to the econom y coupled with the earlier diagnos-
tic evidence against the garch (1,1) sp ecication of v olatilit y motiv ates studying whether the
p ersistence p erceiv ed in the bse Sensex returns are manifestations of shifts in the v ariance.
13
There are some exceptions. It w as announced on the 15
th
of Marc h in 1990 and 1995, and on the 19
th
of July in 1991.
125
4.3.7 Estimation of Shifts in levels of V olatility
The problem with estimating regime-shifts-in-v ariance mo dels is that there has to b e a reasonable
degree of certain t y of when the regime shift to ok place. Recen tly , new tests ha v e b een dev elop ed
to detect regime shifts in v olatilit y (Ch u 1995), and Hamilton & Susmel (1994) in tro duce mo dels
where the probabilit y of the shift of a regime is endogenously determined as a Mark o v pro cess.
In our case, ho w ev er, w e ha v e a fair idea of the dates in v olv ed.
W e mo del the ev en ts using dumm y exogenous v ariables in the v ariance equation, in addition
to the garch v ariables. W e estimate a ar(1)-garch (1,1)-with-dummies mo del:
r
t
= 0
+ 1
r
t 1
+ t
where t
N (0; h
t
)
and
h
t
= 0
+ 1
2
t 1
+ 1
h
t 1
+ k
d
k
where in the mo del for the bse Sensex, the follo wing d
k
are used as:
d
p ost85
= 1, if the observ ation is after F ebruary 1985 and zero otherwise. V olatilit y is m uc h
higher in the follo wing p erio d, so the co ecien t should b e p ositiv e and v ery signican t.
d
scam
= 1, if the observ ation is from the scam p erio d, b et w een Septem b er 1991 and July
1992, and zero otherwise. The v olatilit y in this p erio d w as m uc h higher due to the sp ec-
ulativ e bubble; w e exp ect this co ecien t to b e p ositiv e and larger than that obtained for
the p ost-85 dumm y .
d
p ost93
= 1, if the observ ation is after foreign p ortfolio in v estmen t in to India b egan. W e
exp ect the co ecien t will b e negativ e.
126
d
budget
= 1, if the observ ation is from either the mon ths of F ebruary or Marc h, and zero if it
is not. This co ecien t is exp ected to pic k out a higher pre-budget announcemen t v olatilit y
lev el in the data. W e exp ect this co ecien t to b e p ositiv e.
Mo dels with eac h of the ab o v e dummies in the v ariance equation are estimated separately .
If the dummies cause signican t shifts in the v ariance and accoun t for the seeming p ersistence,
w e exp ect that the v alues of the garch parameters and their sum will also decrease. The same
phenomenon should also b e observ ed in the aggregated series.
W e estimate mo dels similar to those used in Section 4.3.4: the ar(1)-garch (1,1) mo del for
daily and ar(0)-garch (1,1) for the w eekly and mon thly series.
127
0
Dumm y 1
1
1
+ 1
Log
Co ecien t Lik eliho o d
h
t
= 0
+ 1
2
t 1
+ 1
h
t 1
Daily 0.053 0.099 0.886 0.985 -5825.30
0.005 0.008 0.008 0.011
W eekly 0.237 0.133 0.858 0.991 -2057.77
0.083 0.020 0.022 0.029
Mon thly 1.767 0.109 0.876 0.985 -708.602
1.166 0.043 0.045 0.062
h
t
= 0
+ 1
2
t 1
+ 1
h
t 1
+ d
post 85
Daily 0.057 0.063 0.097 0.869 0.966 -5814.24
0.006 0.011 0.008 0.009 0.013
W eekly 0.509 1.471 0.143 0.746 0.889 -2044.97
0.166 0.483 0.029 0.053 0.060
Mon thly 4.110 13.904 0.095 0.732 0.827 -703.756
3.574 11.150 0.049 0.162 0.169
h
t
= 0
+ 1
2
t 1
+ 1
h
t 1
+ d
scam
Daily 0.055 0.131 0.098 0.884 0.982 -5821.85
0.006 0.045 0.008 0.008 0.011
W eekly 0.200 1.428 0.103 0.883 0.986 -2057.23
0.070 0.567 0.019 0.021 0.028
Mon thly 3.170 42.780 0.097 0.866 0.965 -706.849
2.264 32.165 0.047 0.049 0.068
h
t
= 0
+ 1
2
t 1
+ 1
h
t 1
+ d
post 93
Daily 0.052 -0.001 0.098 0.887 0.985 -5825.30
0.005 0.008 0.008 0.008 0.011
W eekly 0.258 0.119 0.138 0.851 0.989 -2057.66
0.091 0.267 0.021 0.024 0.032
Mon thly
1.560 -1.182 0.091 0.897 -708.49
h
t
= 0
+ 1
2
t 1
+ 1
h
t 1
+ d
budg et
Daily 0.053 0.004 0.098 0.886 0.985 -5825.26
0.005 0.008 0.008 0.008 0.011
W eekly 0.191 0.298 0.129 0.862 0.991 -2056.98
0.099 0.171 0.020 0.022 0.030
Mon thly 0.000 13.672 0.096 0.877 0.993 -706.458
0.000 6.922 0.040 0.037 0.054
The mo del did not con v erge. Estimates at last iteration are sho wn.
Std. errors b elo w the parameter estimates
T able 4.6: garch with a single dummy in the v ariance equation
128
The P ost 1985 co ecien t is alw a ys p ositiv e and signican t.
The Scam co ecien t is signican t and p ositiv e. It is greater than the P ost 1985 dumm y
only for the daily data.
The P ost 1993 co ecien t is insignican t, and has inconsisten t sign. W e migh t ha v e exp ected
in tegration with foreign mark ets to ha v e a stronger eect on the v olatilit y in the bse Sensex,
but there are t w o diculties: w e ha v e v ery few p oin ts (only t w o y ears of data out of t w en t y)
in this p erio d, and w e ha v e the confounding eect of the ban on forw ard trading in Marc h
1994.
The Budget co ecien t is p ositiv e.
If the regime shifts in v ariance are b eing mistak en for p ersistence in our mo dels without regime
shifts, w e w ould exp ect that explicitly accoun ting for these shifts (ev en in the form of dummies)
will cause a c hange in the sum of the garch co ecien ts, 1
+ 1
. In the estimations ab o v e,
p erceptible c hanges tak es place in the case of the P ost 1985 regime shift only . The p ersistence
is also reduced across data aggregation, when the P ost 1985 dumm y is added. This is further
supp ort for the h yp othesis that the simple garch (1,1) mo del migh t missp ecied.
If the h yp othesis that it is the P ost 1985 shift in unconditional v ariance that causes most of
the heterosk edasticit y in v olatilit y , then estimation of the mo dels using only the P ost-1985 or the
Pre-1985 data in estimation should sho w little sign of heterosk edasticit y.
129
Squared returns from mon thly data in the Pre-1985 p erio d do indeed ha v e m uc h smaller acf
co ecien ts, whic h implies a homosk edastic mon thly series b efore 1985. W e nd that garch mo d-
els are consisten t with homosk edastic mon thly returns in the Pre-1985 p erio d.
14
Heterosk edastic-
it y still exists in the p ost-1985 data, but the mo del estimates for the P ost-1985 data in T able 4.8
are surprising { w e nd that the Budget dumm y remo v es all heterosk edasticit y for the mon thly
data.
14
Estimates for the pre-1985 p erio d are not sho wn here; it can b e seen from Figure 4.3 that there is not
m uc h heterosk edasticit y in the data in this p erio d.
130
0
Dumm y 1
1
1
+ 1
Log
Co ecien t Lik eliho o d
h
t
= 0
+ 1
2
t 1
+ 1
h
t 1
Daily 0.103 0.091 0.882 0.983 -4151.79
0.0136 0.010 0.010 0.014
W eekly 2.033 0.157 0.731 0.888 -1379.92
0.760 0.039 0.066 0.077
Mon thly 47.156 0.137 0.393 0.530 -496.632
46.689 0.083 0.517 0.524
h
t
= 0
+ 1
2
t 1
+ 1
h
t 1
+ d
scam
Daily 0.104 0.122 0.090 0.881 0.971 -4149.55
0.014 0.051 0.011 0.011 0.016
W eekly 2.103 2.581 0.129 0.746 0.875 -1378.41
0.875 1.330 0.044 0.077 0.089
Mon thly 40.740 61.744 0.000 0.696 0.696 -491.000
46.190 74.932 0.000 0.333 0.333
h
t
= 0
+ 1
2
t 1
+ 1
h
t 1
+ d
post 93
Daily 0.125 -0.054 0.089 0.882 0.971 -4147.86
0.017 0.015 0.011 0.011 0.015
W eekly 2.120 -0.353 0.153 0.734 0.884 -1379.72
0.794 0.496 0.046 0.067 0.081
M onthly
41.790 -17.423 0.077 0.556 -495.467
h
t
= 0
+ 1
2
t 1
+ 1
h
t 1
+ d
budg et
Daily 0.084 0.108 0.091 0.884 0.985 -4144.98
0.016 0.025 0.011 0.012 0.016
W eekly 2.081 2.724 0.150 0.710 0.860 -1376.91
0.767 1.111 0.042 0.071 0.082
Mon thly 42.161 64.796 0.073 0.398 0.471 -487.124
34.558 36.018 0.095 0.383 0.395
The mo del did not con v erge. Estimates at last iteration are sho wn.
Std. errors b elo w the parameter estimates
T able 4.7: garch with single dummy in the v ariance, Post 1985
When the mo del is estimated with all the dummies together for the P ost 1985 p erio d, w e
see that the signs of the single-dumm y estimates are the same across single dumm y estimations,
whic h reinforces the results of table 4.7.
131
P arameter estimates of garch mo dels
Daily W eekly Mon thly
P arameters ar(1)-garch (1,1) ar(1)-garch (1,1) ar(1)-garc h(1,1)
0
0.082 0.300 1.680
0.035 0.175 0.914
1
0.149 0.139
0.022 0.099
0
0.108 2.147 93.986
0.021 0.854 14.740
1
0.088 0.135 0.0
0.011 0.043
1
0.879 0.715 0.678
0.013 0.079 0.332
1
+ 1
0.967 0.848 0.678
d
scam
0.109 2.073 66.494
0.050 1.508 73.964
d
post 93
-0.042 -0.199 -7.386
0.017 0.531 10.767
d
budg et
0.107 2.398 12.885
0.027 1.180 26.956
Momen ts for standarised error, t
=
p
h
t
Mean 0.010 0.021 0.016
V ariance 1.000 1.000 1.027
Sk ewness -0.185 -0.066 0.338
Kurtosis 1.088 0.955 -0.241
Std. errors b elo w the parameter estimates
T able 4.8: garch with all the dummies in the v ariance, P ost 1985
The mo del with all four dummies for the daily and the w eekly data sho w marginal c hanges in
the estimated v alues of the co ecien ts when estimated with eac h dumm y separately , except in
the case of the mon thly mo del, where the garch parameters v anish.
The ab o v e result establishes that there is denitely some form of heterosk edasticit y presen t
in the bse Sensex. This heterosk edasticit y follo ws a garch (1,1) pro cess for the daily and the
w eekly data. In the mon thly series, there is no garch pro cess in the v ariance. Instead, there is
132
a strong pattern to the v ariance dened b y a shift in 1985, and a seasonal pattern dened b y the
budget announcemen ts in the data after 1985.
4.4 Complications on the simple arch theme
In the previous section, w e w ork ed within the limits of the linear sp ecication of the conditional
v ariance and unearthed strong evidence of heterosk edasticit y inheren t in the bse Sensex returns.
In this section, w e attempt to explore issues of ramications of this heterosk edasticit y on the
b eha viour of returns itself.
4.4.1 Is volatility on the bse priced?
The n ull h yp othesis long accepted as a basic tenet of mo dern nance is that nondiv ersiable risk
is priced. In the case of the bse Sensex, w e nd that there do es exist heterosk edasticit y, and that
it has seasonal eects. The question is whether the forecastable c hanges in v olatilit y { caused b y
arch eects and caused b y seasonal shifts in v ariance lev els { generate excess returns.
Economic theory suggests that nondiv ersiable risk w ould b e asso ciated with higher returns.
The curren t standard econometric mo del that measures this relationship in the literature is the
garch -in-mean mo del.
4.4.2 garch-in-mean, or garchm Models
This mo del, rst in tro duced in Engle, Lilien & Robins (1987), expresses a linear relationship
b et w een the conditional mean and conditional v ariance, where the latter is garch (p,q). The
mo del is of the form
133
y
t
= x
t
0
+ f (h
t
) + t
Here, the conditional exp ected returns w orks out to b e directly prop ortional to the conditional
v ariance of the error. If the v ariance term ( h
t
) is an indicator of the risk of the sto c k, then the
higher the risk, the higher the exp ected return ough t to b e. f (h
t
) can b e of the form
p
h
t
, log h
t
or h
t
itself dep ending up on the relation b et w een exp ected return and risk. In estimating this
mo del using mle, the blo c k diagonal nature of the information matrix v anishes. The full system
has to b e correctly sp ecied and join tly estimated for consistency of the mle parameters.
4.4.3 Estimation and Analysis of garchm Models
W e estimate an ar(1)-garchm (1,1) mo del for the daily data, dened b elo w as :
r
t
= 0
+ 1
r
t 1
+ h
h
t
+ t
t
= 0
+ 1
2
t 1
+ 1
h
t 1
+
P
4
k =1
k
d
k
This mo del w as estimated using b oth
p
h
t
and h
t
as measures of risk; the estimates are not
m uc h dieren t and w e only sho w results using h
t
.
134
P arameter estimates of garch mo dels
Daily W eekly Mon thly
P arameters ar(1)-garch (1,1) ar(1)-garch (1,1) ar(0)-garc h(1,1)
0
-0.033 -0.041 0.279
0.062 0.266 0.185
1
0.099 0.044
0.019 0.040
h
0.076 0.124 0.190
0.048 0.098 0.229
0
0.062 0.528 3.390
0.006 0.179 4.587
1
0.097 0.130 0.000
0.008 0.031
1
0.865 0.753 0.774
0.010 0.056 0.182
1
+ 1
0.962 0.883 0.774
d
post 85
0.081 1.521 13.653
0.014 0.506 11.330
d
scam
0.140 2.354 46.284
0.059 1.238 41.548
d
post 93
-0.050 -0.358 -5.333
0.017 0.448 5.722
d
budg et
-0.013 -0.114 13.271
0.012 0.253 13.036
Log Lik eliho o d -5807.70 -2040.25 -645.61
Momen ts for standarised error, t
=
p
h
t
Mean 0.009 0.009 0.001
V ariance 1.001 1.004 1.000
Sk ewness 0.368 0.036 0.298
Kurtosis 4.224 1.010 0.034
Std. errors b elo w the parameter estimates
T able 4.9: ar-garch (1,1)-in-mean estimation
The estimation results sho w a w eak relation b et w een the exp ected return and the conditional
v olatilit y . The co ecien ts in all three cases ha v e the p ositiv e sign, but is statistically w eak.
Th us the analysis seems to p oin t out that the v olatilit y on the bse using the garch -in-mean
sp ecication is not priced. Suc h results ha v e also b een found on man y other mark ets in the w orld.
135
This migh t b e b ecause h
t
do es not measure the systematic risk of the sto c k (whic h should b e
priced), but rather only the unsystematic risk (whic h is not).
4.4.3.1 Ev ent Study Analysis
In section 3.2.4, w e examined the issue of seasonalit y in the returns and nd no evidence supp ort-
ing the existence of seasonalit y in the index. No w, motiv ated b y the seasonalit y in the v olatilit y ,
w e explore the issue of the budget-related seasonalit y , with an \ev en t study" analysis using the
mark et index around budget announcemen t dates.
The residuals for the ev en t study are calculated as returns on the mark et index in excess of
the mean returns on non-ev en t dates for the en tire time p erio d of April 1979 to Marc h 1995. The
excess returns are a v eraged o v er 16 ev en ts and accum ulated o v er the ev en t horizon of 40 da ys
prior to and after the ev en t. The resulting cum ulativ e a v erage returns plot (the car) is graphed
in Figure 4.4.
F rom the graph of the car, w e see that there is a signican t buildup in excess returns prior to
the budget announcemen t. The p erio d after the budget announcemen t is not as in teresting in the
story it tells of the returns pro cess as in the story of the squared returns in Figure 4.5. Here, w e
measure v olatilit y at time t in ev en t time b y a v eraging the squared residuals at time t across all
ev en ts. This sho ws a mark ed increase in v olatilit y in the p erio d after the budget announcemen t
as compared to the p erio d b efore the ev en t. If the p oin t in squared returns at the lag of 35 is
discoun ted as an outlier, then there is a v ery sharp increase in the v ariance of returns for the 40
time p erio ds after the budget announcemen t.
136
The ev en t study p oin ts out to increased returns and v olatilit y of returns around the budget
announcemen ts. W e h yp othesize then that the mark et returns do es reect the increased v olatilit y ,
and test the h yp othesis using the garch -in-mean mo del of returns.
-40 -20 0 20 40
-5
0
5
10
Figure 4.4: CAR around budget announcements: April 1979 to March 1995
-50 0 50
0.0000
0.0005
0.0010
Figure 4.5: Squared residuals around budget announcemen ts: April 1979 to March 1995
137
Th us w e ha v e arriv ed at con tradictory results using t w o dieren t metho dologies to analyse
the eect of the budget related shifts in v olatilit y . The ev en t study sho ws an increase in excess
returns in the p erio d b efore and during the shift in v olatilit y , whereas the garchm has v ery
w eakly signican t relationship b et w een con temp oraneous return and risk. This result of w eak
signicance corresp onds to similar univ ariate mo dels estimated for other w orld mark ets.
One reason prop osed to accoun t for this lac k of signicance has its basis in the asset pricing and
p ortfolio managemen t theory in the in ternational con text (Bek aert & Harv ey 1995, Chan, Karolyi
& Stulz 1992). T o the exten t that mark ets are in tegrated
15
, then domestic fund managemen t
b ecomes a sp ecial case of global fund managemen t (Grinold, Rudd & Stefek 1989). The time-series
b eha viour of global p ortfolio factors w ould b e more imp ortan t to explain conditional exp ected
returns on assets in the home mark et. Some of the factors used in these mo dels for asset pricing are
\w orld p ortfolio risk", the U.S. in terest rate spread
16
, currency uctuations, etc.
17
The co v ariance
structure of the index returns of v arious coun tries are t ypically used in order to estimate the risk
of the \w orld p ortfolio".
The recen t literature has concen trated on the former metho d of b etter analysing index re-
turns to estimate co v ariance b y doing estimations sim ultaneously across sev eral time series. This
dev elopmen t is the m ultiv ariate garch mo dels, whic h is used as an alternativ e to the univ ariate
garch -in-mean used earlier.
15
A coun try where the exp ected returns on the mark et are driv en b y its co v ariance with the \w orld
mark ets" rather than b y o wn mark et v ariance is said to b e an \in tegrated mark et". If the exp ected
returns are driv en b y o wn mark et v ariance, then it is said to b e a se gmente d market .
16
This is the dierence b et w een the short and the long term rate.
17
Grinold et al. (1989), and later Roll (1992), to ok curr ency r eturns and lo c al market r eturns to b e
the main dic hotomous factors of returns. Currency returns included the exc hange rate risk and in terest
receiv ed on currency in v estmen t. Lo cal Mark et Returns included asset returns with resp ect to to o wn
mark et, industry sp ecic returns and compan y sp ecic returns.
138
4.4.4 Mutiv ariate Garch ( mvgarch) Models
As opp osed to univ ariate garch mo dels whic h mo del the v olatilit y pro cess of one series in
isolation, m ultiv ariate v ersions in v olv e sim ultaneous estimation of sev eral series and th us in v olv es
the join t estimation of the v ariance co v ariance matrix of their inno v ation terms. A set of t w o
series, y
1t
and y
2t
can b e mo deled th us :
y
1t
= 1t
+ 1t
y
2t
= 2t
+ 2t
where the error terms 1t
and 2t
ha v e unconditional distributions
1t
2t
N
0
0
;
2
1
12
12
2
2
but ha v e conditional distributions as a function of I
t 1
whic h is similar to the information set of
past v alues describ ed earlier in Section 4.3.1
1t
2t
j I
t 1
N
0
0
;
h
1t
h
12t
h
12t
h
2
or more simply written as
y
t
j
I t 1
N ( t
; H
t
)
with t
a (2 1) v ector and H
t
is a (2 2) matrix.
18
More generally , with systems of N time
series v ectors, y
t
, this will b e a system with t
a (N 1) v ector and H
t
a (N N ) matrix. The
18
The distribution of the error term can b e dieren t from that of the normal as in the case of the
univ ariate mo dels.
139
parameterisation of eac h of these matrices is the crux of the mo dels. The problems of a v ery large
parameter set to b e estimated is v ery prominen t in these mo dels. In the simple case of linear
sp ecications, the v ector form of H
t
, lends itself to sp ecication of eac h v ariance and co v ariance
in a simple fashion. Th us, the most general form of sp ecication of a mvgarch (p,q) mo del for a
set of N time series v ectors is
v ech(H
t
) = v ech() +
q
X
i=1
A
i
v ech( t i
0
t i
) +
p
X
j =1
G
j
v ech(H
t j
)
where is an ( N N ) matrix and A
i
and G
i
are (N (N + 1)=2 N (N + 1)=2) matrices. Th us
when N = 2 and p; q = 1, the structure of H
t
is
v ech(H
t
) =
2
6
4
h
1t
h
12t
h
2t
3
7
5
=
2
6
4
11
12
22
3
7
5 +
2
6
4
a
11
a
12
a
13
a
21
a
22
a
23
a
31
a
32
a
33
3
7
5
2
6
4
2
1;t 1
1;t 1
2;t 1
2
2;t 1
3
7
5 +
2
6
4
g
11
g
12
g
13
g
21
g
22
g
23
g
31
g
32
g
33
3
7
5
2
6
4
h
1;t 1
h
12;t 1
h
2;t 1
3
7
5
There are 21 parameters to b e estimated. This translates to
5N
2
2
+
N
2
parameters to b e estimated
for a mo del with N time series and a garch (1,1) structure for the terms of the v ariance co v ariance
matrix. This b ecomes an enormous n um b er of terms to estimate as N increases. The gro wth of
the mvgarch literature has mostly rev olv ed around the issue of creating meaningful economic
restrictions on the A
i
and G
i
while sim ultaneously reducing the parameter space.
When Engle, Granger & Kraft (1986) rst estimated a mvgarch mo del, it w as a biv ariate
arch mo del, with normally distributed errors. In addition, they imp osed a diagonal restriction
on A
i
. This reduced the n um b er of terms to six as opp osed to 12. Or, in the case of garch
140
sp ecications, nine as opp osed to 21, ie, 3 N in the case of N time series v ectors. Giv en this
structure, they deriv e conditions for the p ositiv e deniteness of H
t
as
a
11
0; a
33
0
a
11
a
33
a
2
22
0
But this diagonal sp ecication, kno wn p opularly as the vech mo del, (used in Bollerslev, Engle
& W o olridge (1988)) w as deemed to o restrictiv e, since it is the in teraction terms b et w een 1(t 1)
and 2(t 1)
that capture the degree to whic h the mark ets are correlated through time. This is
esp ecially true for data at higher frequencies lik e daily data. Baba, Engle, Kraft & Kroner (1995)
imp osed a quadratic restriction that had the added adv an tage of ensuring a p ositiv e denite H
t
matrix. This is kno wn p opularly as the bekk mo del and is mo deled as follo ws:
H
t
= +
q
X
i=1
~
A
i
t i
0
t i
~
A
i
+
p
X
j =1
~
G
j
H
t j
~
G
j
where
~
A
i
and
~
G
j
are (N N ) matrices. Here, the n um b er of parameters for N = 2; p = q = 1
system is 11 instead of 21. Another mo del reducing n um b er of parameters further is in Bollerslev
(1990). He uses the assumption of a constan t c orr elation matrix . Then for N = 2 and garch (1,1)
pro cesses for the individual v ariances, H
t
is sp ecied as
H
t
=
"
p
h
1t
0
0
p
h
2t
# "
1 1
# "
p
h
1t
0
0
p
h
2t
#
h
it
= ii
+
P
q
j =1
ij
2
i(t j )
+
P
p
k =1
ik
h
i(t k )
where j j < 1 is the correlation b et w een 1t
and 2t
. The garch parameters still need the
conditions of ij
0; ik
0; ii
> 0 for a p ositiv e denite h
t
.
141
A sp ecication with direct links to economic inuences is the F actor garch , or fgarch mo del.
This mo del is built on the premise that a small subset of factors cause all the v ariables and their
conditional v ariances. Th us if the v ector of time series, y
t
= (y
1
: : : y
n
) can b e represen ted b y
y
t
= F
t
+ t
where t
= ( 1t
; : : : ; nt
), it
(0; ii
) and is an ( N 1) v ector. Then,
V ar (y
t
j I
t 1
) = h
t
0
+ diag ( 11
: : : nn
)
where i
measures the eect of F
t
on eac h y
i
. h
t
has the usual garch (1,1) sp ecication.
4.4.5 Cross-correlation Analysis of the bse and the s&p500
In this thesis, mvgarch mo dels are motiv ated b y the premise that mark ets o v er the w orld are
in tegrated, and the b eha viour of a coun try index returns are inuenced b y not only the v ariance
of the mark et index but the co v ariance of returns with indices of other coun tries. If mark ets are
indeed in tegrated, then the co v ariances of returns of the set of indices serv e as a b etter indicator
of risk faced b y the in v estor { summing b oth coun try and w orld sp ecic economic ev en ts that
aect the returns of the relev an t coun try index. In addition, b ecause of the correlation b et w een
the mark ets, m ultiv ariate mo dels that explicitly tak e co v ariances in to accoun t ha v e b etter p o w er
as tests of the question of heterosk edasticit y b eing priced. Bollerslev et al. (1988) and DeSan tis &
Gerard (1994) nd that v olatilit y is indeed priced in studies on the index when cross-correlations
with other mark et indices are tak en in to accoun t.
142
Here, w e w ork with t w o indexes, the bse Sensex and the s&p500 . W e h yp othesize that if
the t w o mark ets are in tegrated, then the correlation b et w een the t w o mark ets are signican t, and
that this correlation aects the returns on b oth mark ets.
Indian economic p olicy has b een suc h that the Indian mark ets are closed to the w orld econom y .
So w e w ould exp ect the bse Sensex to b e more segmen ted rather than in tegrated with resp ect
to s&p500 . F or example, in Figure 4.3, the returns and squared returns around the 15
th
of Oct,
1987 or Oct, 1989, whic h are da ys of high v olatilit y on the s&p500 , do not mo v e m uc h on the
bse Sensex. In addition, according to the results in the preceding section, for the long-term
mon thly data, the primary source of heterosk edasticit y is the ann ual budget announcemen t. The
eect of the P ost-1993 dumm y , whic h predates foreign p ortfolio in v estmen t in to India, is not v ery
signican t in the v ariance of returns of an y frequency for the bse Sensex.
A t the daily lev el, an examination of the cross-correlation b et w een the returns on the bse
Sensex and the s&p500 ha v e v ery w eak correlations examined at lags from 24 : : : 24. There is
ev en less strength in the correlation of squared returns, whic h seems to supp ort the idea that
there is not m uc h in tegration b et w een the bse Sensex and the s&p500 .
143
-20 -15 -10 -5 0 5 10 15 20
0.037
0.0
-0.037
April 1979 to March 1995
Returns
Returns Squared
-20 -15 -10 -5 0 5 10 15 20
0.047
0.0
-0.047
Post 1985
Returns
Returns Squared
-20 -15 -10 -5 0 5 10 15 20
0.14
0.0
-0.14
Post 1993
Returns
Returns Squared
Figure 4.6: Correlation betw een the bse Sensex and the SP500 in three time periods
144
4.4.6 Estimation and Analysis of mvgarch Models
Of the categories of mo dels listed in the previous section, w e estimate the bekk form with
quadratic garch co ecien ts. This mo del exploits more of the p ossible correlation b et w een
the t w o indexes used than the simple vech form, but is not as data in tensiv e as the fgarch
form. Also, b ecause of the c hanges in p olicy of the Indian Go v ernmen t to w ards lib eralisation in
the recen t past, w e cannot assume that the correlation b et w een the bse and the u.s. mark ets
has remained unc hanged in the time p erio d considered. Th us w e do not consider the constan t
correlation mo del of Bollerslev 1990. But in our estimation using the bekk mo del, w e reduce
the n um b er of parameters estimated b y exploiting the w eak cross-correlation b et w een the t w o
mark ets.
W e rst estimate simple mvgarch mo dels with garch (1,1) form for h
t
and ar(1) form for
the mean equations of b oth indexes. The results sho w that the co ecien ts for the bse Sensex
ha v e not c hanged dramatically from the univ ariate estimations.

r
bse;t
r
s&p500 ;t
!
=
0
@
0:0794
(0:030)
0:0531
(0:015)
1
A
+

r
bse;(t 1)
r
s&p500 ;(t 1)
!
0:0936
(0:020)
0:0622
(0:023)
+

bse;t
s&p500 ;t
!
H
t
=
2
4
0:229
(0:023)
0:006
(0:009)
0:222
(0:027)
3
5
+
~
A
i
"
2
1;t 1
12;t 1
12;t 1
2
2;t 1
#
~
A
i
+
~
G
i
"
h
1;t 1
h
12;t 1
h
12;t 1
h
2;t 1
#
~
G
i
~
A
i
=
2
4
0:3053
(0:019)
0:3133
(0:021)
3
5
h
0:3053
(0:019)
0:3133
(0:021)
i
~
G
i
=
2
4
0:945
(0:007)
0:921
(0:013)
3
5
h
0:945
(0:007)
0:921
(0:013)
i
145
Momen ts for standardised error and error squared
t
=
p
h
t
2
t
=h
t
Mean 0.017 0.974
V ariance 0.974 5.512
Min -10.417 0.000
Max 4.904 68.067
T able 4.10: ar(1)- mvgarch (1,1) diagnostics
The ab o v e results are for the en tire time p erio d from 1979 to Decem b er 1994. The mean Log
Lik eliho o d in this estimation is 3:122. Since the lib eralisation to ok place after 1990, the mark ets
migh t sho w signs of more in tegration after this p oin t in time. So w e also c hec k the estimated
co ecien ts for the p ost-1990 p erio d and nd some c hanges ha v e tak en place but do es not funda-
men tally alter our picture of the bse mark et b eha viour. The mean Log Lik eliho o d in this p erio d
is 3:275.

r
bse;t
r
s&p500 ;t
!
=
0
@
0:1866
(0:070)
0:0029
(0:021)
1
A
+

r
bse;(t 1)
r
s&p500 ;(t 1)
!
0:1186
(0:038)
0:0040
(0:025)
+

bse;t
s&p500 ;t
!
H
t
=
2
4
0:346
(0:066)
0:002
(0:011)
0:056
(0:017)
3
5
+
~
A
"
2
1;t 1
12;t 1
12;t 1
2
2;t 1
#
~
A +
~
G
"
h
1;t 1
h
12;t 1
h
12;t 1
h
2;t 1
#
~
G
~
A =
2
4
0:316
(0:031)
0:138
(0:022)
3
5
2
4
0:316
(0:031)
0:138
(0:022)
3
5
~
G =
2
4
0:939
(0:011)
0:987
(0:004)
3
5
h
0:939
(0:011)
0:987
(0:004)
i
146
Momen ts for standarised error and error squared
t
=
p
h
t
2
t
=h
t
Mean 0.016 0.978
V ariance 0.979 3.391
Min -3.908 0.000
Max 4.581 20.981
T able 4.11: ar(1)- mvgarch (1,1) diagnostics: Post 1990
In terms of the statistics on the standardised errors, the mvgarch seems a b etter t in the
p ost-1990 p erio d than b efore. This migh t b e tak en for evidence that the degree of in tegration
has increased since 1990, but the evidence is in no w a y conclusiv e. Th us, the premise of lac k
of in tegration b et w een India and the u.s. mark ets seen in the univ ariate analysis, is seemingly
justied.
The results of the simple mvgarch mo del sho w that the correlation b et w een the t w o mark ets
is v ery lo w and insignican t from 0. W e test this b y estimating t w o mvgarch -in-mean mo dels
using b oth mark ets. In one case, w e use the coun try’s o wn v ariance in the returns equation:
r
bse ;t
= 0
+ 1
r
bse ;t 1
+ 1
H
bse ;t
. In the second case, w e use the other coun try’s v ariance in
the returns equation as w ell: r
bse ;t
= 0
+ 1
r
bse ;t 1
+ 1
H
bse ;t
+ 2
H
snp ;t
. Our h yp othesis is
that if the Indian mark et is in tegrated with the \w orld mark et", then the 2
will b e signican t
in the Indian returns while 1
will not b e signican t.
Our results sho w that the second mo del has a b etter p erformance (in terms of b etter sbc
than that for the rst mo del. Ho w ev er, w e nd that in neither co ecien t on the v olatilit y for the
mean equation for the Indian mark et is signican tly dieren t from zero in either equation. This
holds when w e use either H
t
or
p
H
t
as the v olatilit y estimate.
147
Our previous results in T able 4.9 sho w that daily data is more noisy than mon thly data,
and that there is a higher probabilit y of missp ecication in the daily data mo del compared with
mo dels using mon thly data. Therefore, w e test whether v olatilit y is priced using mon thly data.
Ho w ev er, these estimates w ere not signican tly dieren t from the results using daily data either.
W e also estimated these mo dels using data only from the p ost 1990 p erio d, to test for the
eects of the economic reforms. W e nd that the signicance of the co ecien t w orsens in the
p ost-1990 p erio d compared to the o v erall data p erio d.
19
Therefore, w e conclude that the Indian sto c k mark ets do not sho w evidence of b eing in tegrated
with the w orld sto c k mark ets, where w e use the u.s. sto c k mark ets as a pro xy for the w orld sto c k
mark et.
4.5 In Summary
This c hapter has concen trated on issues of the second momen t of the returns of the bse Sensex.
1. Simple arch and garch mo dels, Section 4.3.4.
Daily and w eekly returns on the bse exhibit strong arch eects. The simple ar(1)-
garch (1,1) mo del seems to b e a go o d mo del for daily returns, and ar(0)-garch (1,1) is a
go o d mo del of for w eekly and mon thly returns.
2. Regimes and Seasonalit y 4.3.7
19
This result has resonance with those found for the degree of in tegration b et w een the Indian and
the w orld mark et in Bek aert & Harv ey (1995). Their results sho w that the Indian mark et had a higher
probabilit y of in tegration with w orld mark ets till 1985 whic h dropp ed o in the later p erio d. W e do not
ha v e an y historic or economic reasoning to supp ort this puzzling evidence.
148
There app ears to b e a regime shift on 1 Marc h 1985, with m uc h higher v olatilit y in
the p erio d after this date. This regime shift is lik ely to b e related to the economic
lib eralisation program whic h b egan with the Ra jiv Gandhi administration in 1984.
The ann ual federal budget announcemen t, t ypically on 28 F ebruary , is asso ciated
with excess v olatilit y in the mark et index, esp ecially in the mon th after the budget
announcemen t.
The scam of 1992 is asso ciated with increased v olatilit y .
While relativ ely little data is a v ailable after the recen t p olicy initiativ es (op ening up
to foreigners in 1992, and banning forw ard trading in early 1994), there app ears to
b e no ma jor c hange in the time series prop erties of returns in the follo wing p erio d.
The regime shift and the seasonalit y in v olatilit y are apparen t in all of daily , w eekly
and mon thly returns. Ho w ev er, in the case of mon thly returns, after con trolling
for the regime shift and seasonalit y , the p ersistence in the series seems essen tially
homosk edastic.
In the case of daily and w eekly returns, there is evidence of p ersistence ev en after
con trolling for the regime shift and seasonalit y .
3. Risk-Returns Relationships
garch -in-mean mo dels suggest that forecastable uctuations in v olatilit y of the mark et
index do not app ear to b e priced. This is b orne out ev en after ha ving considered an
in tegrated mark et system, whic h the bse Sensex do es not sho w signs of b eing in tegrated
with the u.s. mark et. The mvgarch mo del estimations supp ort the simple univ ariate
correlation analysis sho wing v ery little correlation b et w een the Indian and the u.s. mark ets.
149
Chapter 5
Epilogue
The c onscious motivation for cr e ating a c apital market is to pr ovide the me ans for
nancial tr ansactions. However, an obje ctive c onse quenc e of this action is to cr e ate
a ow of information that is essential for al l agent’s de cision-making, including that
of those agents who only r ar ely tr ansact in the market.
{ unkno wn
Part of the genius of nancial markets is that, when ther e is a r e al demand for a
metho d to enhanc e sp e culative opp ortunities, the market wil l sur ely pr ovide it.
{ Burton Malkiel in Random W alk Do wn W all Street
Given p ast suc c esses of the eciency hyp othesis against some alternatives, it is pr ob-
ably a bit harsh to char acterize its ac c eptanc e as "as shar e d act of faith". Perhaps
some agnosticism would b e he althy, but atheism is pr ematur e.
{ Rob ert Stam baugh in resp onse to Does the Stock Market Ra tionall y Reflect Fund ament al
V alues? b y La wrence Summers
150
5.1 Synopsis
The ab o v e quotations capture in part the essence of the issues that this thesis attempts to address.
Capital mark ets { in particular, the bse { ha v e b een ph ysically presen t in India for a while. Y et,
the gro wth of the bse as the w orking mec hanism of resource allo cation has b een v ery slo w in all the
time since its conception. The mark et has had a v ery dieren t a v our of institutional structure
and in v estor constituency compared with other mark ets w orldwide. The lev els of information
and the information pro cessing mec hanisms a v ailable to the a v erage in v estor on the mark et is far
b ehind that found in \dev elop ed mark ets".
Of these mark ets, the u.s. mark ets seem to stand as the b enc hmark that generates a rela-
tiv ely ecien t allo cation of resources. Giv en the bses v ery dieren t institutional structure with
resp ect to the u.s. mark ets, giv en an index that, b y theoretical standards, suers considerably in
comparison to those on the nyse , do es the bse serv e as one that allo cates resources ecien tly?
In this thesis, all the c haracteristics of the bse, from the p oin t of view of index returns, rev eal,
at face v alue, a m yriad of statistical evidence, summarized in Section 3.5, con tradicting mark et
eciency . The tests of returns predictabilit y con vincingly reject the h yp othesis of the pro cess
b eing white noise in either the short term { the acf or the runs tests { or the long term analysis
{ the vr tests.
While the magnitude of the rejection migh t b e lessened b y taking heterosk edasticit y in to
consideration, it is highly improbable that a time v arying inno v ation or sho c k completely explains
a w a y the observ ed large deviations a w a y from white noise prop erties of bse Sensex returns. In
Chapter 4, w e do nd strong evidence of heterosk edasticit y for the bse Sensex, although at the
lev el of long in terv al data, these seem b est represen ted as t w o discrete shifts in lev els of v olatilit y
151
rather than a con tin uous time v ariation (Section 4.3.7). W e then c hec k ed for dep endencies of
return on the heterosk edasticit y and nd no strong evidence of an y suc h relationship (Section
4.4.1), ev en in a m ultiv ariate framew ork.
This notion of existing mark et ineciency is strengthened giv en the evidence of the greater
information-set based ev en t studies, lik e the Bon us Issue ev en ts of Section 3.3, whic h seem to sho w
abnormally high lev els of prots. And the most damaging evidence comes in the t w o studies on
gdrs done outside of this researc h w ork, where the mark et is sho wn to correct { at a far later
stage, with a public rev elation of the fact { mispricing of instrumen ts that p ersisted for long
lengths of time with no explicable underlying economic motiv ation.
Economically , the high lev els of transactions costs, in terms of those men tioned in summary in
Chapter 2 { high trading costs, p o or information a v ailabilit y leading to high costs of information
accum ulation, dated tec hniques of information pro cessing { will accoun t for some of the p erceiv ed
ineciency . But surely not all of it.
Some fraction of this certainly relates to obsolete institutional infrastructure, some to con-
cen trated con trol of the trading pro cess and concen trated mark et p o w er. But, it is this author’s
opinion that these factors con tribute less to the problem of p ersisten t arbitrage opp ortunities
than the bac kw ard tec hniques of information pro cessing and analysis presen t to the in v esting
comm unit y on the bse and India in general. This b elief is inferred from the p o or p erformance
b eha viour of the m utual funds in the third and most information-in tensiv e tests. Mutual F unds
are institutions that ha v e mark et p o w er, face relativ ely lo w er trading costs due to large orders
and access to a larger information set with resp ect to rms. Despite this apparen t freedom
from the institutional disadv an tages faced b y an individual in v estor, their p erformance is p o or
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(Section 3.4.1.3 and T able 3.27); con trary to that exp ected if faced with suc h ob vious arbitrage
opp ortunities.
With these observ ations in mind, w e stand facing the follo wing set of alternativ e h yp othesis
regarding the curren t state of eciency on the bse :
The mark et is truly inecien t and the primary barrier to ecien t p erformance is the lac k
of sophisticated mo dels and to ols for information analysis. This explanation has additional
merit in the face of the fact that India is a coun try that is lo w on b oth nancial and
h uman capital in order to o v ercome the lo w abilit y to analyse information ecien tly . This
is further exacerbated b y lac k of curren t tec hnology . If this is true, then the follo wing is
the testable prop osition: that a rapid ino w of capital and tec hnology should b e a remedy
to the problem. The implication is that in a relativ ely short space of time, suc h as the next
t w o to three y ears at most, all these ineciencies do cumen ted in the w ork of this thesis
will v anish.
The alternativ e is that the mark et is truly ecien t, but the curren t suite of tests only
addresses a limited denition of eciency .
Th us, one reason for the p o or results migh t b e the limitation of the data examined in this
thesis { increasing the span of the information set b y including compan y lev el information
w ould b e an order of magnitude increase in the p o w er of the tests. Or giv en the t yp e of
tests, the time series is to o short for the tests to ha v e m uc h p o w er to distinguish an ecien t
mark et from an inecien t one.
A second reason migh t b e the form of the h yp otheses themselv es. The h yp othesis b eing
tested are deriv ed from a set of macro-assumptions, whic h migh t inheren tly b e a bad
153
appro ximation to what migh t actually exist on the Indian sto c k exc hange. The tests and
h yp othesis migh t p erform b etter under non-linear sp ecications rather than the linear ones
to whic h w e restrict the researc h in this thesis. That a reform ulation of the h yp othesis and
mo dels of asset pricing migh t b e called for is b est evinced b y the ev en t study around the
budget announcemen ts and its aect on rst and second momen ts of returns (Figures 4.4
and 4.5).
F or this second n ull, there are no readily formed testable h yp othesis. T o quote Summers
(1986b),
The w eakness of the empirical evidence v erifying the h yp othesis that securities
mark ets are ecien t in assessing fundamen tal v alues w ould not b e b othersome if
the h yp othesis rested on rm theoretical foundations, and if there w ere no con-
trary empirical evidence. Unfortunately , neither of these conditions is satised
in practice.
It w ould seem that to test this alternativ e w ould call for a b etter form ulation of the de-
nition and the theory of eciency of mark ets.
Both these alternativ es are p ertinen t within the curren t con text - this thesis oers a snapshot
of mark et eciency at a p oin t in time. So, ev en if the rst alternativ e is true, it is true of the
bse of to da y . In fact, as the testable h yp othesis p oin ts out, with the institution of b etter h uman
capital in terms of nance theories and analysis, the mark et should see a collapse of the particular
ineciencies that w e see to da y . In that sense, the concept of mark et eciency is a dynamic one
- a mark et is alw a ys mo ving to w ards eciency , as information is rev ealed in the econom y .
154
5.2 F uture research
A gap in the thesis w ork as it w as done and presen ted w as the relativ ely shallo w en umeration
and do cumen tation of the institutions of the securities mark ets. A t the time, mark et micro-
structure w as a relativ ely nascen t eld. There w as little ac kno wledgmen t of the imp ortance of
mark et institutions in driving the incen tiv es and b eha viour of mark et participan ts. Tw o decades
later, an y analysis of mark et outcomes explicitly ac kno wledge and incorp orate the role of the
institutions. Without robust institutions, mark ets fail to deliv er robust p erformance.
In the conceptual framew ork of Douglass C. North, institutions ev olv e to enable friction-less
transactions. Mark et failures in the nancial mark ets, whic h are asso ciated with malfunctioning
institutions, include inecien t prices, p o or liquidit y , systemic crises and unfair treatmen t of
consumers. Households feel safe participating in nancial mark ets that do not suer from failures.
This, in turn, increases the o ws of capital through nancial in termediation and the liquidit y of
the mark et.
Indian equit y mark et ha v e seen signican t ev olution since the w ork of this thesis. This
ev olution can b e separated in to three broad phases.
Phase 1: Institutional dev elopmen t
A common problem of the older mark et micro-structure w as the organisational structure
of the exc hanges themselv es. As of the early 1990s, the exc hange w as an asso ciation of
p ersons, whic h comprised a small comm unit y of securities rms, whose emplo y ees w ere the
only ones p ermitted on to the exc hange o or. T rading w as done b y op en outcry , and there
w as no transparency ab out trade prices or v olumes. There w as little risk managemen t b y
w a y of pro cesses to collect and manage the obligations of coun ter-parties, and disputes on
155
the transaction w ere handled in ternally . The p erio dicit y of trade settlemen t w as uncertain
and left to the traders on the o or. Closing prices and traded v olumes w ere p osted b y the
exc hange, with no v alidation outside of the closed comm unit y of the brok ers.
Despite a clear iden tication of the problems, the p olitical p o w er of the bse w as considerable
and they w ere able to blo c k prop osed c hanges. The turning p oin t w as the balance of
pa ymen ts crisis and IMF program of 1991. India needed to nance the curren t accoun t
decit at the time, through foreign capital o ws in to the securities mark ets. But these w ere
hamp ered b y the malfunctioning of the bse. The nal stra w w as the sto c k mark et scam of
1991 (Section 2.3.4).
As a consequence of b oth these compulsions, a series of far-reac hing reforms w as put in to
motion. A new securities regulator, the SEBI, w as created in 1992, analogous to the
creation of the US SEC in 1934 (Section 2.4.1). SEBI initiated regulations that dealt
with consumer protection, micro-pruden tial regulation and systemic risk regulation. The
Ministry of Finance and SEBI devised a far-reac hing reform to address the problem of the
monop oly-lik e p o w ers of the bse: the creation of a new exc hange, the nse (Section 2.4.2.
nse w as in tended to comp ete with bse, giving greater c hoice to consumers who till then
had no c hoice but trade on the bse. nse w as also set up with new concepts of go v ernance
at its core. In particular, it w ould devise trading rules that catered to the b est in terests
of users rather than securities rms, and it w ould b e impartial in the enforcemen t of these
rules.
nse started electronic trading (Section 2.3.5) whic h impro v ed legibilit y in the ey es of the
State and consumers when compared with the opacit y of o or trading. The transparency
of information ab out in tra-da y prices and liquidit y has b een unpreceden ted. The nse w as
156
one of the rst exc hanges in the w orld that released the b est top v e limit orders with b oth
price and quan tit y , on the buy and sell side for securities, to all traders as w ell as on their
w ebsite. This allo w ed in v estors to calculate the price of a future transaction with more
precision than compared to ev en the NYSE whic h published only the bid-ask prices.
Along with new trading mec hanisms, the reform w as solving the problem of settlemen t
of transactions. Ph ysical share certicates had t w o problems: time tak en in the ph ysical
transfer of shares, as w ell as b eing more vulnerable to coun terfeiting. The nse built the
‘National Securities Dep ository Ltd.’ (NSDL), where shares w ere dematerialised, and held
in electronic accoun ts on b ehalf of their o wners. This eliminated frictions in the settlemen t
pro cess and enabling equit y mark et transactions to b e settled on a T+2 basis.
In parallel to the domestic mark et reforms and an increased participation from domestic
in v estors, there w as a pro cess of capital accoun t decon trol starting from 1992, through
whic h foreign in v estors started coming in to the equit y mark et. F oreign in v estors made
greater demands of the new domestic institutions. Their participation brough t in greater
business activit y and liquidit y in to the mark et.
In resp onse to these reforms, there w as a dramatic c hange in the b oth the size and qualit y
of the equit y mark ets in India (Thomas 2005). T rading at nse started in No v em b er 1994
and b y Octob er 1995, nse b ecame the largest exc hange trading equit y in India (Shah &
Thomas 2000). In the rst quarter of 2017, the W orld F ederation of Exc hanges statistics
ranks the nse as the 4th largest exc hange in the w orld b y n um b er of transactions in equit y .
1
1
The tables can b e found at h ttp://www.w orld-exc hanges.org/
157
A k ey insigh t of institutional economics is the impact of sound institutions up on the costs
of transacting. The Indian equit y mark et obtained signican t impro v emen ts in liquidit y
as a consequence of the reforms. Shah & Thomas (1997) organised the sub-comp onen ts
of transactions costs in equit y mark et trading and nds that the costs of trading dropp ed
from 5% in 1993 to 0.38%. The k ey table there is :
New Y ork
India Sto c k Exc hange
Cost Comp onen t 1993 1997 2004 1997
(Before nse ) (After nse )
T rading 3.75 0.65 0.35 1.23
Brok erage 3 0.5 0.25 1
Mark et Impact Cost 0.75 0.15 0.1 0.23
Clearing
Coun ter-part y Risk Presen t In P art 0 0
Settlemen t 1.25 1.5 0.03 0.05
Bac k Oce 0.75 0.75 0.03 0.05
Bad P ap er Risk 0.5 0.75 0 0
T otal 5 2.15 0.38 1.28
T able 5.1: T ransactions costs in India’s equity mark et (percent)
Corwin & Sc h ultz (2012) prop osed a new metho dology for measuring the bid-oer spread
using limited information sets from historical data-sets. As an example of their metho ds,
they applied these to ols to the Indian exp erience. They found that the mean spread dropp ed
from 5% in 1994 to 1.5% in 1995.
2
Phase 2 Lev eraged trading
2
Also see https://ajayshahblog.blogspot.in/2012/04/new-insights-into-events-on-indian.
html
158
Access to lev eraged trading facilitates a more rapid mo v emen t of information in to prices.
The traditional metho d for lev eraged trading w as the b ad la system at the bsewhic h had
dev elop ed without sound micro-pruden tial to ols needed to enable safe trading on the ex-
c hange (Section 2.3.2). b ad la led to recurring pa ymen t crises whic h often led to long p erio ds
where the exc hange had to b e k ept closed while the crisis w as resolv ed.
Globally , lev eraged trading is done separately from sp ot trading through deriv ativ es. Sp ot
and deriv ativ es mark ets are connected b y arbitrage, through whic h there is an information
o w from the deriv ativ es price to the underlying sp ot mark et. Ho w ev er, deriv ativ es trading
required tec hnical researc h, b oth in constructing pro ducts that w ould attract mark et liquid-
it y as w ell as risk managemen t systems at clearing corp orations to manage coun ter-part y
risk.
A new mark et index w as dev elop ed where the index constituen ts w ere selected based on
mark et capitalisation and liquidit y measured from the new electronic limit order b o oks
for the rst time (Shah & Thomas 1998), the new nse50 (\Nift y") index. The nse set
up the National Securities Clearing Corp oration (NSCC), whic h w as a k ey institutional
dev elopmen t to facilitate reliabilit y of transactions. A clearing corp oration in terp oses itself
b et w een the buy er L and the seller S so that a transaction L $ S is replaced b y L $
C C $ S . If either L or S defaults, the clearing corp oration mak es go o d the obligations.
Without this, trading is restricted to trusted p ersons. The in ternal implemen tation of the
clearing corp oration used adv ances in the econometrics of forecasting risk in the form of
V alue at Risk or V aR forecasts. The w ork of this Ph.D. thesis on v olatilit y mo deling w as
used b y the NSCC in 1999 to carry out real-time measuremen t of the risk of ev ery mark et
159
participan t. Adv ances in mo del selection for v olatilit y forecasts to calculate v alue at risk
w ere used in the mo deling pro cess (Sarma, Shah & Thomas 2003).
Since the separation in to sp ot and deriv ativ es mark ets, and the op erationalisation of the
NSCC in 1998, the equit y sp ot mark ets ha v e not sh ut do wn trading for ev en a single da y .
The nse index futures and options mark ets ha v e b een in the top ten exc hanges b y n um b er
of transactions for the last ten y ears. Deriv ativ es trading in Indian underlyings ha v e spread
b ey ond India to the global nancial system. Nift y and rup ee deriv ativ es are no w traded,
b oth o v er-the-coun ter and on exc hange, at n umerous lo cations all o v er the w orld including
SGX in Singap ore and CME in Chicago.
Phase 3 Algorithmic trading
The ev olution of the use of tec hnology naturally suggested automation of trading decisions,
where a h uman trader writes an algorithm to trade. This new w orld of ‘algorithmic trading’
{ some of whic h is ‘high frequency trading’ { has b een a ma jor force reshaping the global
nancial mark ets o v er the last 20 y ears.
In India also, algorithmic trading has b ecome imp ortan t, with b oth the bse and the nse
launc hing ‘co-lo cation’ through whic h nancial rms could place their computers at a lo-
cation within the exc hange. Aggarw al & Thomas (2014) analyse the eect of the shift
of trading to algorithmic trading b y exploiting cross-sectional v ariation in the in tensit y
of algorithmic trading across dieren t securities. The share of algorithmic trading grew
sharply for the shares of some rms but not for others. Matc hing tec hniques are used to
create a quasi-exp erimen t with a treatmen t and a con trol. The analysis rev eals that n u-
merous mark et qualit y measures impro v ed sharply when algorithmic trading grew. What
160
is imp ortan t is that the impro v emen t in mark et qualit y is seen in small sto c ks. T ypically ,
trading in terest and activit y is concen trated on larger sto c ks in a mark et, with a sharp
fall o in liquidit y for smaller sto c ks. This increases the cost of capital for smaller rms.
The impro v emen t in liquidit y as a consequence of algorithmic trading th us has imp ortan t
implications for smaller rms whic h are then able to obtain liquidit y at a lo w er ob jectiv e
size threshold.
Eac h of these phases ha v e led to imp ortan t new researc h questions and agenda ab out the
nancial mark ets in India. The separation of the deriv ativ es and sp ot mark ets is another area
leading to researc h questions. Do es price disco v ery tak e place as exp ected b et w een sp ot and
deriv ativ es? A w ell established literature on this literature rev eals a puzzle: in theory , deriv ativ es
are exp ected to lead sp ot prices, but this can only b e established for index futures. In other
mark ets, sp ot lead deriv ativ es. Aggarw al & Thomas (2011) suggests that one answ er lies in
previous studies rep orting only the a v erage b eha viour. Deriv ativ es prices lead sp ot prices, when
they are more liquid than the sp ot mark et, or during p erio ds of high in tensit y information o ws.
In suc h instances, deriv ativ es prices dominate sp ot prices.
The eect of liquidit y on prices and in v estmen t c hoices is also b etter researc hed in an en viron-
men t when there is greater transparency of data ab out liquidit y . Gro v er & Thomas (2012) sho ws
that mark et liquidit y adjusted options prices oer a b etter estimate of the implied v olatilit y of
the underlying sto c k than closing prices.
Lastly , there are questions ab out the eect of new institutions. One of the biggest questions
has to do with the success of the nse. In the in ternational exp erience, once liquidit y is estab-
lished at one exc hange, a second exc hange is seldom successful b ecause the exc hange is a natural
monop oly with net w ork eects. Orders tend to go where other orders go. The nse had a lo w
161
c hance of success, and y et it succeeded in b ecoming the largest equit y exc hange with a lev el of
liquidit y man y times larger than the previous regime. A k ey insigh t app ears to b e that the o v erall
transactions cost is comp osed of impact cost (where there is a net w ork eect) and other costs
(where there is no net w ork eect). bse w as v ery w eak on the latter, and nse made enormous
gains whic h enabled an early order o w to nse. Another k ey insigh t lies in the use of tec hnology
to lo w er en try barriers. The bse w as a closed club while nse ran an op en en try system where
new securities rms could come ab out. This tapp ed in to a class of p ersons who w ere k een to b e
in this business but had b een historically blo c k ed o b y the bse. Ho w ev er, what w ere the factors
that made it w ork is a researc h problem that is y et to b e solv ed.
162
Reference List
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170

Abstract (if available)

Abstract This thesis studies stock markets in India. Here, the behaviour of the Indian markets is analysed using the returns on an index calculated for the period from April 1979 to March 1995. This series characterises market behaviour across a reasonably long time period in which there have been a vast number of policy and structural changes in the economic climate in India. In the course of this period, the Indian investor has seen the birth of an IPO market which offered him viable investment alternatives. The Indian economy has been opened up to the international economy by the removal of barriers to the inflow of foreign capital and investment. In this thesis, we aim to document the statistical behaviour of the Bombay Stock Exchange (BSE), the largest and most active stock market in India, and analyse the economic implications thereof.

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Creator Thomas, Susan (author)

Core Title An empirical characterisation of the Bombay Stock Exchange

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Economics

Publication Date 06/20/2017

Defense Date 06/20/2017

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag efficient market tests,Indian equity,OAI-PMH Harvest,political economy and equity markets,regime shifts in volatility,volatility models

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Aizenman, Joshua (committee chair), Hsiao, Cheng (committee member), Nugent, Jeff (committee member), Wise, Carol (committee member)

Creator Email susant@igidr.ac.in

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-388634

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