Question 2. Hedging Using Index Futures [20%]

• Assume that you are managing a portfolio tracking the S&P index. The value of your portfolio is $3 million USD. The Beta (b) of your portfolio is currently 2.5.

• Assume that you are going to use Index Futures (with underlying of S&P index) to perform hedging or speculation.

• Answer Question 2 Part A and Part B below based on the following assumptions:

Value of Portfolio ($3 million)	P	$3,000,000
Value of the assets (index) underlying one Index Futures contract (= futures price * contract size)	A	$1000
Beta (b) of Portfolio	b	2.5

Question 2 - Part A [10%]

What position and number of Index Futures contracts are needed to reduce the Beta of the portfolio from 2.5 to 0.75 (i.e., Target Beta (after using futures) = b* = 0.75).

In your answer,

1. Discuss the position (long or short) of Index Futures; and
2. Calculate the number of Index Futures contracts.

[Show your answers, including any formula, steps/calculations, and discussions as clear as possible]

Question 2 - Part B [10%]

What position and number of Index Futures contracts are needed to increase the Beta of the portfolio from 2.5 to 3.25 (i.e., Target Beta (after using futures) = b* = 3.25).

In your answer,

1. Discuss the position (long or short) of Index Futures; and
2. Calculate the number of Index Futures contracts.

[Show your answers, including any formula, steps/calculations, and discussions as clear as possible]