Question

A company has a $20 million portfolio with a beta of 1.2. It would like to use futures contracts on a stock index to hedge its risk. The index futures is currently standing at 1080, and each contract is for delivery of $250 times the index. What is the hedge that minimizes risk? What should the company do if it wants to reduce the beta of the portfolio to 0.6?

Answer 1

Part A:

Number of contracts=
`(1.2*20,000,000)/(270000)`

Number of contracts=88.889≅ 89 contracts.

The hedge that minimizes risk is to short 88 contracts

Part B:

Number of contracts=
`((0.6-1.2)*20,000,000)/(270,000)=-44.44`

Number of contracts≅-44

The company should short 44 futures contracts.

Step-by-step explanation:

Part A:

The formula we are going to use is:

Number of contracts=
`(\beta*Portfolio\ Value)/(Futures\ Value)`

Future Value=Index futures*Multiplier

Future Value=1080*$250

Future Value=$270,000

Number of contracts=
`(1.2*20,000,000)/(270000)`

Number of contracts=88.889≅ 89 contracts.

The hedge that minimizes risk is to short 88 contracts

Part B:

Number of contracts=
`((\beta'-\beta)*Portfolio\ Value)/(Futures\ Value)`

where:

`\beta'` is the new value=0.6

`\beta`=1.2

Future Value=$270,000 (Calculated above)

Number of contracts=
`((0.6-1.2)*20,000,000)/(270,000)=-44.44`

Number of contracts≅-44

The company should short 44 futures contracts