Question

A fund manager has a portfolio worth $100 million with a beta of 0.88. the manager is concerned about the performance of the market over the next 2 months and plans to use 3-month futurescontracts on the S&P 500 to hedge the risk. The current level of the index is 2600, one contract is on 250 times the index, the risk free rate is 3% per annum, and the dividend yield on the index is 2% per annum.

(a) Calculate the theoretical futures price of a 3-month S&P 500 futures price.

(b) How many futures contracts should the manager buy or sell to hedge the exposure to the market over thenext 2 months?

(c) Calculate the value of the hedged position (stock and futures) if the index in 2 months is 2500.

Answer 1

a.

Futures Price = Spot price * [1+ (rf*– d)(x/365) ]

Where,

rf = Risk free rate

d = Dividend

x = number of days to expiry.

so futures price of a 3-month S&P 500 futures price is

= 2600 x (1 + (3% - 2%)x91/365) = 2606

b. To hedge the exposure of $100mn, numer of contract to be bought = 100,000,000/ 2600 x 250 = 153.8 ~154 futures contract

c. If the value of index drops to 2500 in 2 months, then value of the hedged position is 154 x (2600-2500) = $15,400