By S. P. Kothari
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Table 5 reports the transition probabilities for stocks moving from one quintile portfolio to another in one year. 9 percent probability of being in the same size quintile in the following year. 7 percent. The probability of transition to the “Missing” cell is quite high for stocks in all quintiles and especially so for the stocks in the first quintile. Generally, the transition probabilities for stocks ranked on momentum are roughly the same, regardless of the initial quintile—which is not surprising.
Implementing the Bayesian Analysis. For pedagogical purposes, we initially suppose that alpha is the only unknown parameter. Let α0 be the prior expected value of alpha and σ(α0) be the prior standard deviation. Say α0 equals 0, the value implied if the market index is mean–variance efficient. 023. Of course, the actual alpha is either greater than 4 percent or not, but this probability quantifies our subjective judgment that such large values are implausible. Now, let αˆ denote the given estimate of alpha and se( αˆ )denote its standard error.
This is referred to as the prediction error in standard regression analysis. book Page 49 Thursday, December 19, 2002 11:51 AM Anomalies and Efficient Portfolio Formation where x is the sample mean and s 2x is the variance of the market returns (maximum-likelihood estimates). Whereas x is known in the classical prediction problem, the future market return is yet to be realized when making the asset-allocation decision. Therefore, the relevant predictive residual variance for quintile return y is the average value of the variance in Expression A2 for all possible values of x.
Anomalies and Efficient Portfolio Formation by S. P. Kothari