Berk–Green

(a) Derive the equilibrium size and the revenue-maximising fee in the linear Berk–Green model of Proposition 6B.7.1. (b) Let $\phi = 4\%$, $b = 0.4\%$ per ₹10,000 cr and $f = 1.5\%$. Compute the equilibrium size and the manager's annual fee revenue. (c) A year's realised gross alpha beats expectations by 2 points, and investors' Bayesian weight is $\kappa = 0.25$. Compute the new $\phi$, the new size and the percentage inflow. (d) Suppose instead the manager closes the fund to new money and raises the fee. What fee keeps investors' expected net alpha at zero at the old size? Compute the revenue-maximising fee and size for $\phi = 4\%$. (e) What does the model predict about the persistence of net returns, and what evidence would contradict it?