Question

You own a portfolio which is valued at $8.5 million and which has a beta of 1.3. You would like to create a riskless portfolio by hedging with S&P 500 futures contracts. The contract size is $250 times the index level. How many futures contracts do you need to acquire if the current S&P 500 index is 1310?

Select one:

a. Long 34 contracts

b. Short 41 contracts

c. Long 28 contracts

d. Short 34 contracts

e. Short 28 contracts

Answer 1

Given about a portfolio,

Portfolio value = $8.5 million

Beta = 1.3

Future contract of S&P price = $1310

contract size = 250

To hedge the risk completely, desired beta is 0

So, number of contracts is calculated as

Number of contract = (desired beta - portfolio beta)*portfolio value/(future price*contract size)

So, Number of contracts = (0 - 1.3)*8500000/(1310*250) = -34

Negative sign means going short.

So, a total of 340 contracts must be short.

Option d is correct.