A hedge fund expects that proposed elimination of the personal taxation on dividends will be enacted and that this tax reform will benefit particularly stocks paying high dividends. The hedge fund ranks the 500 stocks in the S&P 500 index according to their dividend yield. The 250 stocks with the highest dividend yields are included in the high-dividend portfolio and the 250 stocks with the lowest dividend yields are included in the low-dividend portfolio. The high-dividend portfolio has a beta of 0.7 and the low-dividend portfolio has a beta of 1.3. The risk-free interest rate is 2% and the expected return on the S&P 500 index is 7%. The hedge fund has currently $10 million dollars available to invest in this strategy.
a. Suppose that the hedge fund decides to go long $50 million in the high-dividend portfolio and to go short $40 million in the low-dividend portfolio. What is the beta and the expected return of the hedge fund according to the CAPM? (10 Points)
b. Hedge funds often want to eliminate all systematic risk by pursuing "market-neutral" strategies. Which positions in the two portfolios can the hedge fund enter into with a net investment of $10 million without incurring any systematic risk? Please give the dollar values of the long and short positions in the high- and the low-dividend portfolios. (Hint: A market-neutral portfolio has a beta of zero.) (5 Points)
c. Under what conditions can the hedge fund expect to make abnormal profits from the transaction in (b)? (5 Points)