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?

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

rational decision making is a multi-step process for making choices between alternatives. the process of rational decision making favors logic, objectivity, and analysis over subjectivity and insight. the word “rational” in this context does not mean sane or clear-headed as it does in the colloquial sense.

hope this

the answer is d

brainliest! ?