By S. P. Kothari
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Moreover, this optimal allocation held true for the value stocks even if we injected a healthy dose of conservatism and reduced the alphas by half! The optimal tilt toward strong-momentum stocks with the reduced alpha was about 80 percent. , long in Q5 and short in Q1), but strategies based on these spreads are less relevant from a practical investment perspective. Interestingly, the residual risk of the value spread portfolio was so high that an investor would be better off with an aggressive position in high-BV/ MV stocks than with an optimal spread position.
As earlier, returns are assumed to be jointly normally distributed. The priors for alpha and beta are taken to be uninformative. Because variances are estimated far more precisely than expected return parameters such as alpha, one might, in practice, reasonably have a strong prior about residual variance based on other data. For simplicity, we make the stronger assumption that the residual standard deviation is known. , (α, β) is jointly normally distributed with mean ( αˆ , βˆ ) and variance matrix 2(⑀)(X′ X)–1], where X is the T × 2 matrix of independent variables, including a constant vector (Zellner 1971).
6 percent. 5 percent and because tilting toward the Q1 size portfolio reduces the Sharpe ratio, an investor must short the Q1 portfolio to reach optimality. This shorting improves the Sharpe ratio only marginally, however, so the optimal strategy would essentially be simply to invest in the market portfolio. Consider now a strategy of tilting toward Q5, as shown in the middle sections of Table 2’s Panel A and Panel B. These results suggest that for the 1963–99 period, investors would have gained only slightly by investing in large-cap stocks.
Anomalies and Efficient Portfolio Formation by S. P. Kothari