Question

The Dow Jones is currently valued at $24,000 and the 1-year Dow Jones Mini Future contract has a price of $24,750. Note Dow Jones future contracts are for 5 times the value of the contract price. The risk free rate is 3% per annum and the Dow Jones dividend yield is 0.75% per annum. You are managing a portfolio that is worth $15 million and has a beta of 1.25.A) What position in futures contracts on the S&P 500 is necessary to hedge the portfolio?
B) 6 months have passed and the Dow Jones is now valued at $24,720 and the future price is now $25,100. What is our portfolio value of your portfolio with the hedge from part a?

Answer 1

Answer:

a) 152

b) $15,310,562.50

Explanation:

A) What position in futures contracts on the S & P 500 is it necessary to hedge the portfolio

The position is to short

The number to be shorted  can be calculated using the formula below:

= ( β *  value of portfolio) / (one futures contract size * number of times the value of the contract price)

where ; value of portfolio = $15 million , Beta = 1.25 , one future contract size = $24750,  number of times = 5

= (  1.25 * 15,000,000)   / ( 24,750 * 5)  = 151.5 ≈ 152 contracts

b) What is our portfolio value of your portfolio with the hedge from part a

Given that 6 months has passed

Dow Jones now valued at $24720

Future price now $25,100  

first step : calculate loss from position in part a

= 152 * 5 * ( 24,750 - 25,100 ) = - $266,000

next : calculate Gain on index

=  24,720 - 24,000 / 24,000 = 0.03 = 3.00%

Total gain = Gain on index +  annual dividend / 2

                 = 3% + 0.75 / 2 = 3.375%

where risk free rate ( 6 months ) = gain on index / 2 = 1.5%

Calculate Return with the use of CAPM

= 1.5% + 1.25* ( 3.375% - 1.5% ) = 3.8438%

Hence value of portfolio after 6 months will be calculated as

= Current portfolio value * ( 1 + return )

= 15,576,562.50

Therefore the

Net value = portfolio value - loss from futures position

=$15,310,562.50