Question

2. In this problem you will use SP500 index futures to hedge against risks in your stock portfolio. Note that SP500 index is given by $250 times the futures price. We have the following information SP500 spot price = V:500, 1 = 1000 VAL= Value of your portfolio = 5.05M R = 4% Dividend = 1% Beta = 1.5 FI = 1010 a). This is a cross hedge, how much contract should you short? Each SP500 index futures contract needs to be multiplied by 250. b). If the SP500 index is 900 in 3 month and F2-902, Do you have a gain or loss or your overall position? Show steps of your calculation (10 points)

Answer 1

a]

number of contracts to short = (value of portfolio * beta) / (F1 * contract size)

number of contracts to short = ($5.05 million * 1.5) / (1010 * $250) = 30

b]

Loss on stock portfolio = % decrease in SP500 * beginning value of stock portfolio

% decrease in SP500 = (900 - 1010) / 1010 = -10.89%

Loss on stock portfolio = -10.89% * $5.05 million = $549,945

Gain on futures position = number of contracts shorted * (F1 - F2) * contract size = 30 * (1010 - 902) * 250 = $810,000

Overall portfolio gain = $810,000 - $549,945 = $260,055