Gaurav Malhotra
Prof. Guse
Research Proposal
My planned capstone takes another look at the idea of efficiency in the secondary stock market. I
pick efficiency because it is especially compelling in the wake of the 2008 market meltdown, and
even more so since at the epicenter of the crash was the market for complex securities with
(supposedly) very sophisticated participants.
Proposal Question:
I wish to test the efficient market hypothesis as related to the Indian equities market. The
proposed approach is not dissimilar to that of a ‘proof by counter-example’ approach that is often
used in mathematics.
The most basic definition of market efficiency states that past prices cannot and do not predict
future prices, and thus consistent trading profits in excess of the “market”(called alpha) based
solely on past prices are impossible in an efficient market. In general generating alpha is just
another way of saying that the amount of profit is not accounted for by the level of risk taken on
by the strategy. Thus, naturally a portfolio that succeeds in consistently generating positive alpha
“beats the market”. From an econometric perspective what this means is that given an assetpricing model for returns:
R = alpha + β1*ϒ1 + β2*ϒ2 + β3*ϒ3 +…. *
Where the gamma’s are risk factors, R = asset return. The intercept, a, represents “return in
excess of risk factors” and market efficiency demands this to be zero.
My approach to test this claim is to find just one such trading strategy that can consistently
generate alpha. Of course the caveat remains that any such test is a joint-test of efficiency and the
model used to price the assets. However, given that such a strategy exists is a serious challenge
to the market efficiency hypothesis as well as the widely accepted asset pricing models.
*Note: the specification of the model is very import, since the test for efficiency would be a joint
test with the model. I have an entire paper in my literature review dedicated just on this topic and
we will get to it in due course.
Given my research and thoughts at the moment I expect to have about four of those risk factors.
As I will discuss in the literature review, the fourth factor liquidity can be important and even
more importantly, such a model has not been tested ( to my knowledge or that of the papers I
cite) on Indian data yet.
I deliberately choose not to go into the model specification and the strategy specification in this
current paper given that the literature review will provide the reader with a good insight into the
possible options/combinations and moreover, data availability (in the right form) might dictate
my choices.
The data I plan to use is from the commercial COMPUSTAT database found in the WRDS (A
database maintained by the Wharton Business School and UPenn) database that I have access to.
Gaurav Malhotra
Prof. Guse
Research Proposal
The same source also has CRSP data, but unfortunately CRSP does not cover Indian securities. I
have looked at the data available at COMPUSTAT and it seems like they have data for almost
every variable I might be interested in. There might a couple, like the Book value of equity for
these firms that I may not be able to get from here, but overall, I do not think that should be a
cause for any concern. Thus, my data is going to be time-series and will span a decade worth of
trading activity, with the base unit being daily stock prices. I expect to be computing monthly
returns using these prices and having that as my unit for the regression analysis. I shall be
discussing that more in future submissions. Currently, I have data for variables such as date,
closing daily stock price, daily trading volume, shares outstanding, and daily return for approx.
360 firms over 10 years of daily data points (data truncated due to excel limits, the number will
most likely be revised anyway). Talking a little bit more about the data, it is obvious that I will
run into companies that went bankrupt at some point over the course of these ten years and will
have to make appropriate adjustments for that. The huge sample size is critical given that for a
study like this since given the volatility of the variables, a small sample size could have thrown
virtually all the results out of the window.
Literature:
The literature on the topic is vast with as many results as there are views amongst the financial
economists when it comes to market efficiency. However, none of papers in the camp opposing
Jegadeesh and Titman’s “proof” of momentum have made a very convincing stance, and all have
tried to invariably take the route of trying to explain the alpha rationally, where as Jegadeesh &
Co are firmly in the ‘Behavioral finance” camp.
(Jegadeesh and Titman, Returns to Buying Winners and Selling Loser: Implications for Stock
Market Efficiency 1993) : Presented momentum profits as a challenge to market efficiency. They
rank stock based on past 3-12 month returns into deciles, buying the top decile and selling the
lowest. The profits thus generated were (and still are) unexplained by standard asset pricing
models. They also find that these profits reverse after a holding period of a year, thus shedding
light on the phenomenon of “Reversal”. They explain momentum profits using behavioral
finance (specifically under reaction followed by correction) theories. I personal feel this is an
extremely well thought out paper, both theoretically and empirically. The setup is nothing if not
complex, yet the results are so glaring that its hard to miss them in the jumble of various tests
flying all over the place. The only issue here is that they have their test of market efficiency with
the CAPM (capital asset pricing model) , while they could and should have used a multi-factor
model. However, to their credit, the Fama-French model (multi-factor), which took
presecendence over the CAPM, came to be acknowledged right around the time this paper was
released.
Thus, as would be the hope, the authors delivered by coming back to re-test their findings after
nearly a decade of further research on the topic (below).
(Jegadeesh and Titman, Profitability of Momentum Strategies: An Evaluation of Alternative
Explanations 2001): The authors incorporate the new research in asset pricing and this time test
their data all the way through the 1990’s with both a single fact (CAPM) and a multi-factor(FF)
model. The fact that the momentum profits persist not only into another, entirely new data set
where people where acutely aware of the effect but also with a more power asset pricing model
is a testament to the robustness of their first paper in 1992. However, at the same time, though
proponents of Behavior theories, they critically discuss both the new behavioral theories put
Gaurav Malhotra
Prof. Guse
Research Proposal
forth by others in their original defense as well as the “rational” theories put forth by the likes of
Conrad and Kaul to rationally explain momentum.
As you can guess, this is going to be my trading strategy of choice in my own paper.
(George and Hwang 2004): This paper is a great follow up on the work done by Jegadeesh and
Titman on momentum. It argues that the distance of the current price to the 52-week high is a
much better indicator of future return than a simple ranking by past returns. They find that future
returns forecast using this method do not “reverse”, and thus short-term momentum and longterm reversal are quite separate phenomenon. Thus posing serious questions to contemporary
explanation of momentum (i.e.: under-reaction).
There have been very few studies on momentum in the Indian financial markets, thus making it
the prime candidate for me to test my hypothesis and model on. However, there is one paper that
I was able to find, published in 2004, by Michello and Chowdhur on momentum in the Indian
equities market. The authors do discuss their own lack of knowledge regarding how many
studies that have taken place for this kind of work in India (none according to them).
(Michello and Chowdhury 2006) : In this study, they apply momentum strategies to the Indian
stock market to test their effectiveness. They extend their analysis not only into sub-time frames
( short term, medium term etc) but also include market value and turnover. They use monthly
stock price Index data from DataStream International. After screening for companies with data
points throughout 1991 and 2006, they end up with 254 firms. And this is where I lose some of
their logic, because they use the log difference in the stock index data to calculate the rate of
return on each firm. One I cannot see why would not use direct stock prices in the first place, and
two, if they were disaggregating this stock index price data, unless they had each individual
securities performance within the data file, how would they be able to match their chosen 254
firms with their respective returns? Though I would really like to hope they did (otherwise it
makes zero sense), my experience with market index data suggests that its aggregated, not split
at the security level with corresponding returns/prices, and deconstructing it is a waste of time
and lose of information as compared to directly using the building blocks. So this was one major
thing that I did not like/understand why they do. Next they go onto use this data to for a
momentum portfolio construction. To reflect certain quirks idiosyncratic to the Indian market,
they sort their firms (Note: not a portfolio level) into high and low market value firms, with the
idea being that foreign investment would most like be in more liquid, larger firms and thus
increasing their liquidity even more. I do agree with this particular specification and would likely
test it myself.
Their results are interesting and they find that non-overlapping momentum strategies are not
profitable in India. However, when sorted on turnover and firm size, there are significant
momentum profits in the medium term strategy (6 month ranking period, 6 month holding
period)for high turnover and high market value firms, where as they find significant reversal
with a short term strategy (1 month rank, 1 month hold) for all portfolios ( regardless of turnover
categorization) . They also find their (3,3) strategy to have reversals for low turnover and low
market value firms .
Gaurav Malhotra
Prof. Guse
Research Proposal
Thus I believe there are areas on which I can improvise and also add my own approach to
studying moenment in India. It also helps that the study mentioned finds a lot of different results
for time-frames not all that different and give me an opportunity to perhaps explain them ( if I
find them too)
Moving away from the literature on the phenomenon of momentum investing, I feel the Fama
French paper in the early 90’s has a substantial effect on the way not only academics but even
market participants view risk factors. The FF model soon came to be the “base” line used in the
asset management industry (though CAPM is still a checkbox they tick) and then being built
upon in the private sector. Before discussing their paper, it is worth nothing that there are several
other conceivable forms of multi-factor models that explain stock prices, for example and nfactor arbitrage model (APT – Arbitrage Pricing Theory). However, it was they who proved that
risk factors distinct from the market risk influence returns and thus the CAPM beta is not the
catch-all risk factor. It is precisely at this point of them claiming their factors to distinctive is
where people have tried to critique the model.
(Fama and French 1992):
Given that I plan on using the FsF-model as a benchmark for my own analysis it is worth going
over some of the concept behind their “constructed” factors SMB (small minus big – size) and
HML (High minus low – market/book equity value). Again, the actual methodology I don’t get
into since I don’t think it fits the purpose here right now.
In this paper, the authors challenge the validity of the CAPM (capital asset pricing model) as
they showcase another model that does a much better job of explaining stock returns. The CAPM
postulates that the market “Beta” is the only risk factor that matters, while Fama and French
show that there are other factors, like size and book to market ratios that directly affect a stock’s
return as well. The central idea behind their model is the work of numerous other author’s who
proved the relation between size of the firm and its return, and also between “book-to-market”
equity, or “value”. In fact, Fama and French’s tests show that the univariae relationship between
returns and these other factors is consistently stronger than the univariate relationship between
returns and the CAPM beta! It is interesting to note that in order to empirically test the CAPM,
they first run a “first-pass” regression on time-series data, and then run a “second-pass” crosssectional regression based on the average values obtained in the first regression. This second part
is what “tests” the CAPM, as CAPM’s theoretical groundings are in cross-section and consider
only a “unit” time-frame existence for all investor horzions.
The major contribution of Fama and French is proving that these factors mentioned earlier can
viewed as macro-level risk factors which effect portfolio level returns, thus abstracting away
idiosyncratic characteristics and their effect on individual assets to a macro scale. The form the
SMB and HML variables by ranking all US equities , first in order of market value, the in order
of book value, thus giving a matrix : HiSize-High B/M, HiSize-LowB/m, LowSize-High B/M,
LowSize-Low B/M, etc. Then they go long and short within these portfolios to SBM and HML.
Gaurav Malhotra
Prof. Guse
Research Proposal
Bibliography
(Jegadeesh and Titman, Returns to Buying Winners and Selling Loser: Implications for Stock
Market Efficiency 1993)
Fama, Eugene, and Kenneth French. "The Cross Section of Expected Stock Returns." The
Journal of Finance 47, no. 2 (June 1992).
George, and Hwang. "The 52-Week High and Momentum Investing." The Journal of Finance
59, no. 5 (October 2004).
Jegadeesh, and Titman. Profitability of Momentum Strategies: An Evaluation of Alternative
Explanations. Vol. 56. 2 vols. The Journal of Finance, 2001.
Jegadeesh, and Titman. "Returns to Buying Winners and Selling Loser: Implications for
Stock Market Efficiency." The Journal of Finance 48, no. 1 (March 1993).
Asness (1997) shows that momentum is stronger in growth firms than in value firms. Rouwenhorst (1998) documents momentum profits
in international markets. Moskowitz and Grinblatt (1999) document large momentum profits in industry portfolios. Hong, Lim, and Stein
(2000) show that small firms with low analyst coverage display stronger momentum. Lee and Swaminathan (2000) document that
momentum is more prevalent in stocks with high trading volume. Jegadeesh and Titman (2001) show that momentum remains large in
the post-1993 sample. Jiang, Lee, and Zhang (2005) and Zhang (2006) report that momentum profits are higher among firms with higher
information uncertainty using measures such as size, firm age, stock return volatility, and cash flow volatility.
Profitability of Trading Strategies based on Alternative Momentum Measures: Evidences from India
Momentum Profits, Portfolio Characteristics and Asset Pricing Models", Decision, IIM Calcutta, December 2005
Liquidity Proxy: each firm # of analysts and recommendatiosn, then portfolio level?
IS NON OVERLAPPING!! SO DOES THAT MATTER? ALSO THEY DON’T USE FF