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?

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zainsubhani zainsubhani · Answer 1 · 2020-02-19T04:48:27+01:00

Answer:

Part A:

Number of contracts=[tex]\frac{1.2*20,000,000}{270000}[/tex]

Number of contracts=88.889≅ 89 contracts.

The hedge that minimizes risk is to short 88 contracts

Part B:

Number of contracts=[tex]\frac{(0.6-1.2)*20,000,000}{270,000}=-44.44[/tex]

Number of contracts≅-44

The company should short 44 futures contracts.

Explanation:

Part A:

The formula we are going to use is:

Number of contracts=[tex]\frac{\beta*Portfolio\ Value}{Futures\ Value}[/tex]

Future Value=Index futures*Multiplier

Future Value=1080*$250

Future Value=$270,000

Number of contracts=[tex]\frac{1.2*20,000,000}{270000}[/tex]

Number of contracts=88.889≅ 89 contracts.

The hedge that minimizes risk is to short 88 contracts

Part B:

Number of contracts=[tex]\frac{(\beta'-\beta)*Portfolio\ Value}{Futures\ Value}[/tex]

where:

[tex]\beta'[/tex] is the new value=0.6

[tex]\beta[/tex]=1.2

Future Value=$270,000 (Calculated above)

Number of contracts=[tex]\frac{(0.6-1.2)*20,000,000}{270,000}=-44.44[/tex]

Number of contracts≅-44

The company should short 44 futures contracts