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. Short 41 contracts b. Short 28 contracts c. Short 34 contracts d. Long 28 contracts e. Long 34 contracts

The answer is option (c) Short 34 contracts

Explanation:

Solution:

Given that

The information about the portfolio is as stated below:

The value of the portfolio = $8.5 million

The beta = 1.3

The future contract of S&P price = $1310

The size of contract = 250

Now,

To hedge the risk completely, the desired beta is = 0

Thus,

The number of contracts is calculated as follows:

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

So,

The number of contracts = (0 - 1.3) * 8500000 / (1310*250) = - 34

Then,

The negative sign means it is going short.

Hence,

A total of 340 contracts must be short.