Question

It is July 16. A company has a portfolio of stocks worth $100 million. The beta of the portfolio is 1.2. The company would like to use the December futures contract on a stock index to change the beta of the portfolio to 0.5 during the period July 16 to November 16. The index futures price is 2,000, and each contract is on $250 times the index. (a) What position should the company take

Answer 1

A. The company should take Short position and

140 contract

B. The company should take Long position and 60 contract

B.

Step-by-step explanation:

Calculation for what position that the company should take

Using this formula

Company position=(Beta of the portfolio*Change in beta of the portfolio) *Portfolio of stocks /Index futures price* Each Contract index times

Let plug in the formula

Company position =(1.2-0.5)*$100 million/2,000*250

Company position=0.7*$100 million/500,000

Company position=$70,000,000/500,000

Company position=140 contract

Therefore the position that the company should take will be SHORT position with 140 contract

B. Calculation for the increase in beta of the portfolio from 1.2 to 1.5 and what position tthr company should take in the futures contract and how many contracts

Using this formula

Company position=Increase in beta of the portfolio *Portfolio of stocks /Index futures price* Each Contract index times

Let plug in the formula

Company position =(1.5-1.2)*$100 million/2,000*250

Company position=0.3*$100 million/500,000

Company position=$30,000,000/500,000

Company position=60 contract

Therefore the company should take Long position and 60 contract