Answer:
a) 152
b) <em>$15,310,562.50</em>
Explanation:
<u>A) What position in futures contracts on the S & P 500 is it necessary to hedge the portfolio</u>
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
<u>b) What is our portfolio value of your portfolio with the hedge from part a</u>
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
=<em>$15,310,562.50</em>
