Compute the position in futures contracts

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Reference no: EM132012910

Suppose that you manage a portfolio of stocks, the current value of which is $25000. The continuously compounded risk-free rate is 5%.

1. Assume you are fully invested in stock A, whose current price is $100. How many shares of stock A do you currently hold?

2. You wish to temporarily convert your position from stock A to bonds over the next 6 months. In the table below, explain the transactions you undertake to obtain the desired result using the 6-months forward (include in your transactions the purchased shares of stock A you obtained above). In the first column, state each transaction. In the second column, report the associated cost. In the third and fourth columns, report the associated cash-flow if stock A trades at $60 and $120, respectively, in 6 months.

3. Now, suppose your portfolio is only imperfectly correlated with stock A with a correlation coefficient of 0.7. Suppose further that the returns on your portfolio have variance (0.1)², while the returns on stock A have variance (0.2)². Given a 6-months futures contract on stock A with futures price $102 and size 25 times A, you want to hedge your portfolio: compute the position in futures contracts that minimizes the variance of your hedged portfolio. What is the variance of the resulting?

Reference no: EM132012910

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