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SEQ CHAPTER \h \r 1 SEQ CHAPTER \h \r 1Central University of Finance and Economics Chinese Academy of Finance and Development Financial Derivatives Spring 2013 Assignment 2 (Due on April 1) 1. Suppose the current value of the S&P 500 index is 1000, the future value of the dividends over the next six months will be $20 and the T-bill rate is 5%. Suppose the Northwestern endowment has $100,000,000 invested in the S&P 500. a. What will be the futures price for an S&P 500 futures contract which settles in 6 months? b. Suppose the portfolio manager for the endowment thinks that T-bills will outperform the S&P over the next six months. If the contract size for the S&P 500 contract is 250 times the value of the index, what futures position should she take? What rate of return will the manager earn over this period? Draw the manager’s position before and after she puts on the hedge. 2. Consider the following futures prices for Brazilian reals. BRAZILIAN REALS (CME); 100,000 REALS, $ PER REALS OPEN HIGH LOW CLOSE MAR .051450 .052090 .051050 .051130 JUNE .047500 .047500 .047500 .047500 Assume the U.S. risk-free rate is 4.25% and that the T-bill rates in the U.S. and Brazil will be constant over the next six months. Assume the March contract matures in two months. a. What is the risk-free rate in Brazil? b. What is the current dollar/real exchange rate in $/real? c. If the June futures price was .0500, instead of .0475, show how you could earn an arbitrage profit. (Tell me what position you would take and the cash flows). Assume that you can buy or sell fractional amounts. For example, you can buy future for .976 reals. 3. Suppose today is June 1. The spot price of gold is $300/ounce and the annual risk-free rate is 6%. There are no carrying costs associated with holding gold but gold can be leased at a rate of 2% per year. a. What is the price of a gold future with delivery in 6 months? b. Suppose the owner of some gold would like to borrow $30,000 today and in 6 months repay the loan with gold instead of dollars. (This is called a gold-linked note.) i. Suppose the contract calls for the owner of the gold to deliver 100 ounces of gold in six months. What additional cash payment needs to be made at delivery in order for both the owner of the gold and the lender to be willing to enter into the contract? ii. If the gold owner only wanted to delivery 100 ounces of gold at maturity and not make or receive any cash payments at the maturity date of the note, how much could he borrow today? iii. If the owner of the gold wanted to borrow $30,000 today and not make any cash payments at delivery, how many ounce of gold would she have to agree to delivery in six months?