Question

The S&P 500 is currently valued at $2,700 and the 1-year Mini Future contract has a price of $2,767. The risk free rate is 2.5% per annum and the S&P 500 dividend yield is 0.5% per annum. You are managing a portfolio that is worth $10 million and has a beta of 1.75. (Remember E-mini S&P 500 Future contracts are 50 x price)

a. What position in futures contracts on the S&P 500 is necessary to hedge the portfolio?

b. 6 months have passed and the S&P 500 is $2,808 and the E-mini future price is now $2,868. What is our portfolio value of your portfolio with the hedge from part a?

Answer 1

Answer a)

To hedge a portfolio we are invested in, we need to go short on index futures. (Note that for a long position, hedge require a equivalent short position)

So, Number of E-Mini contracts to go short on is

N = Beta * Portfolio Value / Value of one E-mini future contract ......................... Equation 1

Beta=1.75

Portfolio Value = $10mn

Value of one future contract = 50*2,767 = 138,350 = .138350 mn

So, N = 1.75 * 10 / 0.138350 = 72.3 ~= 72

We need to sell about 72 E-Mini S&P 500 Contract

Answer b)

Using Equation 1 above:

72 = 1.75 * Value of Portfolio / (2868*50)

Value of portfolio = $5.9 mn