By S. P. Kothari
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21 For example, the CAPM implies that alpha should be zero when the index is the true market portfolio of all assets. 21 See Pastor for an interesting analysis of the role of a pricing model in forming beliefs. Also see Black and Litterman (1992) and related earlier work by Jobson, Korkie, and Ratti (1979) and Jorion (1985). book Page 28 Thursday, December 19, 2002 11:51 AM Anomalies and Efficient Portfolio Formation Whatever the source of our prior belief, suppose that we judge an annualized alpha bigger than 4 percent to be implausibly large.
18 In the opposite situation, leverage (shorting the riskless asset) would be used to raise the volatility of p∗ to that of the market index. In that case, performance would be overstated insofar as the borrowing rate exceeded the T-bill rate used in the computation. 5) in the absence of short-selling constraints. In the terminology we are using, the Sharpe ratio of the optimal portfolio is (Treynor and Black) Shp_opt = [Shp_mkt 2 + Info 2]1/2. 19 The optimal amount of tilting increases with the magnitude of the Jensen’s alpha and decreases with the residual uncertainty.
Thus, an investment strategy that tries to mimic this factor by forming an optimal tilt with the market index appears to be dominated by other simple tilt strategies. ■ Tilting toward momentum quintiles. A momentum investment strategy has been highly profitable historically, as Table 4 and Figure 3 demonstrate. 4 percent. 9 percent). 7 percent. 0 percent). As with the BV/MV anomaly, the optimal position was to be fully invested in the Q5 stocks. When the alpha is cut in half, the optimal position is about 80 percent invested in the Q5 momentum stocks, although allocations from 60– 100 percent yield similar performance characteristics.