The multiplier for a futures contract on a stock market index is $250. The matur
ID: 2799910 • Letter: T
Question
The multiplier for a futures contract on a stock market index is $250. The maturity of the contract is 1 year, the current level of the index is 1,300, and the risk-free interest rate is 0.5% per month. The dividend yield on the index is 0.2% per month. Suppose that after 1 month, the stock index is at 1,320.
Find the cash flow from the mark-to-market proceeds on the contract. Assume that the parity condition always holds exactly. (Round your answer to 2 decimal places. Omit the "$" sign in your response.)
Find the holding-period return if the initial margin on the contract is $13,000. (Round your answer to 2 decimal places. Omit the "%" sign in your response.)
The multiplier for a futures contract on a stock market index is $250. The maturity of the contract is 1 year, the current level of the index is 1,300, and the risk-free interest rate is 0.5% per month. The dividend yield on the index is 0.2% per month. Suppose that after 1 month, the stock index is at 1,320.
Explanation / Answer
The initial futures price is: Fo = $1300 x (1 + .005-.002)^12 = 1347.58 Initial Future Price = $1300*(1.003^12) Initial Future Price = $1300*1.0366 = $ 1,347.58 after one month, the maturity of the contract will be only 11 months, so the futures price will be F0 = 1320 x (1 + .005-.002)^ 11 = $1364.09 = 1320*(1.003)^11 = 1320*1.0334 $ 1,364.09 Thr Inrease in Future Price = $4364.08 - $1347.58 $ 16.51 The increase in the futures price is 16.51, so the cash flow will be 16.51 x 250 = $4127.5 The rate of return is $4127.5 / $13,000 = 31.75% (a) Cashflow $4127.51 (b) Rate of Return 31.75%