A fund manager has a portfolio of assets that is worth $60 million with a beta of 0.75 with respect to the Nasdaq index. Assume that the alpha and expense ratio of the portfolio are both zero. The manager is concerned about the performance of the Nasdaq market over the next three months and plans to use six-month mini futures contracts on the Nasdaq 100 to hedge the risk. The current level of the index is 5914. One contract of mini Nasdaq 100 futures is on $20 times the index. The risk-free rate is r = 0.65% per annum. The dividend yield on the Nasdaq index is y = 1.12% per annum.
(a) What is the theoretical futures price for the six-month mini Nasdaq 100 futures?
(b) If the fund manager ignores the mismatch between the futures maturity and the hedging period and simply uses formula we discussed in class, how many futures contracts (in whole number) will he long or short, intending to eliminate the exposure to the market over the next three months?
(c) How much does the fund manager gain (lose) on his futures position if the market index in three months turns out to be 4731, 5323, 5914, 6505, and 7097? List the profits and losses (P/L) corresponding each index level in a table.
(d) Suppose there are no idiosyncratic shocks to the portfolio returns. (This is true if the portfolio consists only the index and three-month Treasury bills.) Calculate and report the P/L of the portfolio when the index finishes in three months at the five levels listed in question (b). To simplify the calculation, you can approximate the simple k-month dividend yield by yâ‡¥(k/12), i.e., ignore the effect of continuous compounding. Similarly, approximate the k-month simple interest rate by r â‡¥(k/12).
(e) Calculate the fund manager’s P/L and return on the hedged portfolio when the index in three months equals the five levels listed in question (b).
(f) Explain why the hedge is not perfect even when there are no idiosyncratic shocks to the portfolio returns.
This question belongs to Finance and discusses the theoretical futures price for the six-month mini Nasdaq 100 futures.
The answer is in Excel format
Download Full Solution
If you are here for the first time, you can request for a discount coupon, which can knock off upto 20% of the quoted price on any service.