When are Contrarian Profits Due to Stock Market Overreaction?

Motivation(s)

The classical definition of random walk is a process with independently and identically distributed increments. The economist’s view of a random walk is a process with uncorrelated but heterogeneously distributed dependent increments. Even though empirical evidence has made apparent that historical stock prices do not follow random walks, several studies still attribute forecastability to the stock market overreaction hypothesis, the notion that investors are subject to waves of optimism and pessimism and therefore create a kind of momentum that causes prices to temporarily swing away from their fundamental values. These theories of overreaction imply price changes must be negatively autocorrelated for some holding period. When in the presence of negative serial correlation, a contrarian portfolio strategy of selling the winners and buying the losers should yield positive expected profits. This causal relationship has been widely accepted, yet no prior studies have questioned whether the profitability of contrarian investment strategies necessarily implies stock market overreaction.

Proposed Solution(s)

The authors claim weekly contrarian portfolio returns are strongly positively autocorrelated due to cross-autocorrelations despite negative autocorrelations in individual stock returns. Positive cross-autocovariances across securities can be understood as a higher return for stock A today implies a higher return for stock B tomorrow on average. Each security’s returns can even be unforecastable using past returns of that security alone. The empirical findings show cross effects are generally positive in sign and have lead-lag structure: the returns of large-capitalization stocks almost always lead those of smaller stocks. Since the empirical results show individual security returns as generally weakly negatively autocorrelated, positive autocorrelation in weekly returns indexes is completely attributable to cross effects.

Evaluation(s)

The authors examine the expected profits of buying losers and selling winners with equally-weighted indexes under various return-generating processes:

  • The Independently and Identically Distributed Benchmark

    • Contrarian strategy reduces to shorting the higher and buying the lower mean return securities.

    • Expected profits are negative as long as there is some cross-sectional variation in expected returns.

  • Stock Market Overreaction and Fads

    • The former necessarily implies the profitability of the portfolio strategy in the absence of cross-autocorrelation while the latter does do not.

  • Trading on White Noise and Lead-Lag Relations

    • Each security can be individually unpredictable as long as the securities are positively cross-correlated at various leads and lags.

  • Lead-lag effects and Nonsynchronous Trading

    • The prices of distinct securities are mistakenly assumed to be sampled simultaneously, which can induce autocorrelation and cross-autocorrelation.

    • Examining the magnitudes of index autocorrelation and cross-autocorrelations generated from thin trading models reveals that news affect more frequently traded stocks first and influences the returns of thinly traded securities with a lag.

  • A Positively Dependent Common Factor, White Noise, and the Bid-Ask Spread Process

    • Empirical evidence invalidates this model as a plausible return-generating mechanism consistent with positive index autocorrelation and negative serial dependence in individual returns.

Analyzing the contrarian arbitrage portfolio, where the weights of securities sum to zero, shows market overreaction as an optional enhancement to profitability. Since the experiments focus on the profits and do not account for risks, this study can only assert that a contrarian strategy is a feasible investment tool; the economic sources of positive cross-autocorrelations across securities have not been identified. Existing research still contests about the profitability of contrarian long-horizon strategies that exploits lower transaction costs.

Future Direction(s)

  • When are stock market fads profitable and with what strategy?

Question(s)

  • Have there been any contrarian strategies that utilizes long-horizon for short-horizon?

  • What is the monthly returns of the simplified contrarian strategy?

Analysis

Less than fifty percent of the expected profits from a contrarian investment rule may be attributed to overreaction; the majority of such profits are due to cross effects among the securities in the form of lead-lag relations. The paper could have been even better had the authors presented the results in a more intuitive fashion; reading a wall of text and figures that replace labels with symbols is quite tiresome. It is surprising that prior research automatically assumed a causal relationship between market overreaction and contrarian profits without any verification. On a similar note, there should have been more justifications behind the use of these specific return-generating processes. Nonetheless, the derivations of the proposed model will be very useful when one needs to reproduce the results.

References

LM90

Andrew W Lo and A Craig MacKinlay. When are contrarian profits due to stock market overreaction? Review of Financial studies, 3(2):175–205, 1990.