Question

It is February 16. A company has a portfolio of stocks worth $100 million. The beta of the portfolio is 1.3. The company would like to use the July futures contract on a stock index to change the beta of the portfolio to 0.5 during the period February 16 to June 16. The index futures price is 2,000, and each contract is on $250 times the index.

a. What position should the company take in the futures contract in order to construct the required adjustment?

b. Suppose that the company changes its mind and decides to decrease the beta of the portfolio from 1.3 to 1.0. What position in futures contracts should it take?

Answer 1

a)

Portfolio beta = weighted average of beta

===> Let's assume weight of index futures as x and the current portfolio as 1-x

===> 1 x + 1.3(1-x) = 0.5

===> 1.3- 0.3 x = 0.5

===> x = 0.8/0.3 = 2.666667

===> 1-x = -1.6667

As they have opposite signs, that implies, the company should short the futures

So, if $100 Million is 1.6667

Then 2.6667 means = (2.6667/1.6667) * $100 million

= $159.9988 Million or $160 Million

Then, as lot size is 250 and futures price is $2000, Contract Value = $0.5 Million

Number of Contracts = 160Million / 0.5 Million = 320 Contracts

b)

=Required Beta

=Portfolio Beta

CMV = Current Market Value of Portfolio

===> (1-1.3)(100Million/0.5Million) = -60 Contracts

So you should short 60 contracts of index futures