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 Emini S&P 500 Future contracts are 50 x price) What position in futures contracts on the S&P 500 is necessary to hedge the portfolio so our portfolio beta is now 1?

A) Short 54 E-mini S&P 500 future contracts

B) Short 126 E-mini S&P 500 future contracts

C) Short 2,711 E-mini S&P 500 future contracts

D) Long 126 E-mini S&P 500 future contracts

E) Long 2,711 E-mini S&P 500 future contracts

Answer 1

Number on futures contracts N = (target beta - current beta)*(current portfolio value/current value of one future contract)

where target beta = 1; current beta = 1.75

current portfolio value = 10,000,000

current value of one one future contract = current price of one future contract*contract size = 2,767*50 = 138,350

N = (1.75-1)*10,000,000/138,250 = -54.21

Shorting 54 future contracts will hedge the portfolio so that the portfolio beta becomes 1. (Option A)