Extreme-group spreads

(a) For $Z \sim N(0,1)$, prove $\mathbb E[Z \mid Z > c] = \varphi(c)/(1 - \Phi(c))$. (b) Compute the top-minus-bottom multiplier of Proposition 6A.3 for deciles, quintiles and terciles. (c) A study reports a 60-day decile spread of 4.2%. Under the linear model of Proposition 6A.3, what drift $\lambda$ per unit SUE does this imply? (d) Why do studies sort into groups rather than regress CAR on SUE? Give one advantage of each approach.