Momentum's beta after a bear market

In the model of Proposition 4.7, take $\bar\beta=1$, $\sigma_\beta=0.4$, $\sigma_e=0.3$ and a two-year market return $R_m=-0.45$. The average loser has $R_i=-0.90$ and the average winner $R_i=+0.20$. (a) Compute the projected betas of losers and winners and the WML beta. (b) If the market then rises 26% over three months (as in March–May 2009), what WML return does the linear beta alone predict? (c) Daniel and Moskowitz report losers +163% and winners +8% over that window. What does the gap between (b) and the reported numbers tell you about the shape of losers' payoffs? Connect to Merton's view of equity as a call option.