Assuming you have $28,100 to invest, how much (in $) do you need to invest in the market fund?

You want to create a portfolio with a beta of 1.5. You want to accomplish this goal by investing in a mutual fund that follows the market and in a stock with a beta of 3.0. Assuming you have $28,100 to invest, how much (in $) do you need to invest in the market fund?

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Expert Solution

Total amount of Investment to make = $28,100

You will invest in a Mutual fund that invest in Market Fund and in Stock

Beta of market fund is 1 (Note- market Beta is always 1)

Stock Beta = 3

Portfolio beta = 1.5

Let the weight of Market fund be X

So, Weight of Stock will be (1-X)

Portfolio Beta = (Weight of Market fund)(Beta of market fund) + (Weight of Stock)(Beta of Stock)

1.5 = X*1 + (1-X)*3

1.5 = X + 3 - 3*X

2*X = 1.5

X = 0.75

So, weight of market fund is 0.75

Amount to be invested in the market fund = $28,100*0.75

Amount to be invested in the market fund = $21,075

jeff jeffy answered 1 year ago

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