By S. P. Kothari
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Extra info for Anomalies and Efficient Portfolio Formation
7 percent. In light of our prior belief, this estimate is clearly too high, but how much do we want to discount this estimate? Naturally, the extent to which we will want to lower or shrink the estimated value depends on the confidence we have in our initial belief versus the precision of the statistical estimate. Bayesian analysis provides an appealing framework in which to formalize these ideas and incorporate them in an optimal portfolio decision. Academic work on portfolio optimization has increasingly applied Bayesian methods; the study by Pastor (2000) is the most closely related to the issues considered here.
This uncertainty increases the perceived (or predictive) residual risk of the investment portfolio. If this effect is greater than the effect of uncertainty about the market expected return, the investor should be inclined to tilt the portfolio less aggressively toward the anomaly strategy. 23 Shrinkage implies that the prior for alpha is informative, which means that our analysis with uninformative priors overstates the impact of estimation risk in this case. Also, our conclusions are essentially unchanged if parameter uncertainty regarding the market index parameters is ignored.
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Anomalies and Efficient Portfolio Formation by S. P. Kothari