Aqr Case Report

AQR Case Report

Q1: The idea of momentum effect is that the winner will keep winning and loser will keep losing. This effect preserves after the paper published while size and value effect diminish. The key point behind this phenomenon can be divide into two parts on a bias of whether market is efficient:

1. Market is efficient

If the market is efficient, according to Markowitz’s mean-covariance efficient theory and Sharpe’s CAPM, only market risk will be rewarded. Since SMB and HML are using information on balance sheet, they are not undiversifiable market risk, thus will not be compensated. So if the market is efficient, these coefficient would be 0, that’s the reason why after paper published, the effect diminishes, because this information result in the market’s more efficient performance.

However, under momentum effect, the more profitable stocks on average, are the high beta stocks. Of course these stocks will outperform market, this does not contradict the market efficiency. Moreover, if the market is not efficient, low beta stocks on average can on average outperform the high beta stocks because of a high alpha, but the more the market is efficient, the less likely this may occur. That's the reason why after the paper published, this effect preserves.

2. Market is not efficient

If the market is efficient, Fama-French model (The Cross-Section of Expected Stock Returns, The Journal of Finance 1992) is a good supplementary to CAPM, thus SMB and HML is valid, and thus we can use these two factors to seek for abnormal return. However, this phenomenon also appeared on S&P500 membership stocks (William E.Jacques; The S&P500 Membership Anomaly, or Would You Join This Club? Financial Analysts Journal, Vol 44, No.6; 1988) In this paper, one key point for denying the arbitrage opportunity on S&P500’s abnormal return is that S&P500 membership does not change regularly. Thus for a short time interval, you can either sell the stocks to realize...