8.1. Short selling and capital. Suppose that you are the manager of a dedicated short bias hedge fund with an NAV of $100M. You sell short 10 stocks, with a short position of $20M for each of them. Specifically, you borrow the shares through your broker and sell the shares. You must pass the shortsell proceeds as cash collateral as well as a 20% additional margin requirement. The positions are hedged by buying 8 stocks of $20M each. Your broker also finances the long positions and also requires a 20% margin on those. a. What is the current minimum margin requirement? Correspondingly, what is the current level of free cash? What is the current balance sheet for the hedge fund? b. If the margin requirement for long and short positions changed to 30%, would the current positions remain sustainable? If not, how much would they need to be scaled back? c. Suppose that margin requirements remain at 20% over the next year. Further, the overall stock market performs strongly, yielding a return of 25% for major stock indices. The short positions increase in value by 10% and the long positions by 25%. The risk-free return is 4%, including on your brokerage account and your margin loans (no financing spread). What is the NAV at the end of the year? What is the percentage return of the hedge fund (ignoring transaction costs and other costs)? Did the hedge fund perform well? Specifically, how what was the hedge fund's alpha with respect to the market (assuming that all stocks have a beta of 1)?