Question

You have a portfolio value of 25,000,000 and what to protect it against market decline using the S&P 500 index. The value of the S&P 500 is at 2578 with a portfolio beta of 1.35. Complete the following: Briefly discuss your results.

1. How many contracts do you need to protect yourself against this market decline? Are you long or short these contracts?

2. Say two months later the portfolio is valued at 25,500,000 and the S&P is at 2500. Calculate the profit/loss on the stock index futures position

3. Calculate the overall profit in dollars and Holding Period Return in percent.

Answer 1

Part (a) Nos. of contracts needed, N = Value of the portfolio / Value of 1 S&P 500 contract x Portfolio beta

Value of 1 S&P 500 contract = $ 50 x index value = $ 50 x 2,578 = $  128,900

Hence, N = 25,000,000 / 128,900 x 1.35 = 261.83 = 262 contracts needed.

Since we are long on the portfolio of stocks, we should short the future contracts.

Part (b)

Profit/loss on the stock index futures position = (F₀ - F₁) x N = $ 50 x (Index value initially - index value now) x 262 = $ 50 x (2,578 - 2,500) x 262 = $  1,021,800 (profit)

Part (c)

Overall profit in dollars = Gain in portfolio value + Gain in future position = (25,500,000 - 25,000,000)+1,021,800 =  1,521,800

Holding period return = Overall profit in dollars / Initial value of the portfolio = 1,521,800 / 25,000,000 = 6.09%