Anomalies and Efficient Portfolio Formation by S. P. Kothari

By S. P. Kothari

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By an argument similar to that for alpha and residual risk, uncertainty about the market’s true mean return increases the (predictive) risk perceived by the investor and lowers the perceived market Sharpe ratio. Other things being equal, this market effect tends to increase the optimal weight on the tilt portfolio. Recall from our earlier analysis of the BV/MV anomaly that when we ignore parameter uncertainty and assume no short selling, being fully invested in the high-BV/MV quintile is optimal.

Interestingly, the optimal portfolio is fully invested in the highest-BV/MV stocks even after cutting the estimated alpha in half (Shp_opt). One interpretation of the superior performance of the high-BV/MV stocks is that these were distressed stocks that went on to exhibit superior performance ex post in the 1963–99 period. It is also possible that the high average returns reflect ex ante compensation for such risk. Alternatively, these stocks may have been ones that were initially undervalued and subsequently performed better than investors expected.

Even if investors believe that the portfolio parameters are (relatively) constant over time, however, they should consider the potential impact of estimation error on portfolio decisions. Unfortunately, traditional statistical analysis is not well suited to this task. The standard errors reported earlier can be used to derive confidence intervals for, say, alphas, but how should such observations be translated into an investment decision? Intuition for the Bayesian Analysis. Intuitively, if an alpha is not estimated with much precision, the apparent abnormal return (positive alpha) is likely to be a result of chance and, therefore, may not be a good indication of what will happen in the future.

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