Suppose that you are the manager of a hedge fund with a NAV (Net Asset Value) 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 post the short sale proceeds as cash collateral as well as a 20% additional margin requirement. The positions are hedged by buying 8 stocks for $20M each. Your broker finances the long positions and also requires a 20% margin on those.

a. What is the current margin requirement for the entire fund (in dollars)?

b. If the margin requirement for long and short positions changed to 30%, would the current positions remain sustainable (given the funds NAV)?

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%; you earn this rate on your margin deposit (including the short sale proceeds) and the funds free cash (i.e. the part of the NAV that is not being used as margin), and pay this rate on the loan you received from the broker.

- 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)?