Suppose that you are the manager of a 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.

1) Suppose that the overall stock market performs strongly, yielding a positive return for major stock indices. The stock of short positions increase in value by 10% and of long positions by 25%. The risk-free return is 3%, including on your brokerage account and your margin loans (no financing spread). What is the NAV at the end of the year?

2)Suppose instead that the stocks that you short sell are on special such that the short proceeds earn a return of 0% instead of 3%. (The additional 20% margin cash for short positions earn the normal risk free rate.) Under this scenario, what is the NAV at the end of the year?

3)Only one of the statements below is true. Select it

a)GARCH models incorporate persistence; EWMA models do not.

b)EWMA models incorporate persistence; GARCH models do not.

c)Both GARCH and EWMA models incorporate persistence.

d)Neither GARCH nor EWMA models incorporate persistence.