[Hedge Equity Portfolio] It is July 16. A company has a portfolio of stocks worth $12
million. The beta of the portfolio is 1.5. The company would like to use the CME December
futures contract on the S&P 500 to change the beta of the portfolio to 1.2 during the period
July 16 to November 16. The index futures price is currently 1,000 and each contract is on
$250 times the index.
(a) What position should the company take? (2pts)
(b) On Nov. 1st, the level of S&P 500 is 1200 and the futures price is 1203. What is value of
the position taken in (a) ? (6pts)
(c) Suppose that the company changes its mind and decides to increase the beta of the
portfolio from 1.5 to 1.7. What position in futures contracts should it take? (2pts)
2. [Forward Valuation w/ No Income] A 1-year long forward contract on a non-dividend-
paying stock is entered into when the stock price is $40 and the risk-free rate of interest is
12% per annum with continuous compounding.
What are the forward price and the initial value of the forward contract? (2pts)
Six months later, the price of the stock is $46 and the risk-free interest rate is still
12%. What are the forward price and the value of the forward contract? (2-2pts)
3. [Future Valuation with Dividend Income] A stock index currently stands at 340. The
risk-free interest rate is 9% per annum (with continuous compounding) and the dividend
yield on the index is 5% per annum. What should the futures price for a 4-month contract be?
4. [Future Valuation with Storage Cost] The spot price of silver is $15 per ounce. The
storage costs are $0.24 per ounce per year payable quarterly in advance. Assuming that
interest rates are 10% per annum for all maturities, calculate the futures price of silver for
delivery in 9 months.
5. [Future Evaluation with Varying Interest Rate] An index is 1,200. The three-month
risk-free rate is 3% per annum and the dividend yield over the next three months is 1.2% per
annum. The six-month risk-free rate is 3.5% per annum and the dividend yield over the next
six months is 1% per annum. Estimate the futures price of the index for three-month and six-
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month contracts. All interest rates and dividend yields are continuously compounded.(Hint:
Match the risk-free rate with the dividend yield and corresponding maturity)