An equity hedge fund manageer with an equity capital of $50 million sets his portfolio beta to zero in order to be market neutral. He retains a cash cushion of $2 million for unforseen situations (e.g. margin calls and redemption) and utilizes the rest of the equity capital in implementting market neutral strategy.
shares can be borrowed from a prime broker and the short margin ratio requirement m is set at 60% of short sales proceeds. Two mispriced stocks have been identified: A and B. At their current valuation, stock A is expected to yield 19.1% while stock B's expected return is 14.1%.
Suppose CAPM is the correct asset pricing model and the market index's expected return and risk free rate are 10% and 3% respectively. Stock A has a beta of 1.8 while that of stock B is 1.2.
The fund can earn an interest rate of 1% from its $2 million idle cash and the margin deposit with the prime broker. We assume that the hedge fund aims, as usual, to achieve the maximize degree of leverage possible.
Q) Please prove numerically that return of the fund is independent of the return of the market index, wheter ex-ante or ex-post.