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?

Question

contestada

Respuesta :

ACCESS MORE ACCESS MORE ACCESS MORE ACCESS MORE

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