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Statistics Help

**Question: **An equity hedge fund manager 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 unforeseen situations (e.g. margin calls and redemption) and utilizes the rest of the equity capital in implementing 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 E(RM) and risk free rate RF are 10% and 3% respectively. Stock A has a beta of 1.80 while that of stock B is 1.20.

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.

(a) How should the hedge fund execute its market neutral strategy and what is the expected return of such strategy? Please show the balance sheet of the fund, and compute the expected return and ex-ante alpha of the fund. (10 points) (b) Please prove numerically that return of the fund is independent of the return of the market index, whether ex-ante or ex-post. (8 points)

(c) Please prove theoretically [i.e. in terms of symbols, not numerically as in part (b)] that the realized return of the fund is independent of the realized return of the market index. (12 points)

Please use these symbols in your proof:

αA = ex-ante alpha of stock A αB = ex-ante alpha of stock B βA = beta of stock A βB = beta of stock B εA = unexpected return of stock A εB = unexpected return of stock B eA = unexpected firm-specific return of stock A eB = unexpected firm-specific return of stock B eM = unexpected market index return S = value of stock B shorted E = equity capital of the fund RC = return of cash RM = actual return of the market index

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