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The market is expected to yield 12% and the risk free rate is 2%. You currently...

The market is expected to yield 12% and the risk free rate is 2%. You currently hold a portfolio with a beta of 0.75 worth $23,600. You want to invest in another portfolio with a beta of 2.9. How much will you have to invest in the new risky asset so that the resulting portfolio will have an expected return of 16%?

answer in $ not in percentage

Solutions

Expert Solution

This question is an application of CAPM and Portfolio management.

By CAPM Equation, Expected return on stock = Risk free rate + Beta * (Expected market return - risk free rate)

So, if you need 16% return on your portfolio, beta of that portfolio should be calculated first.

16% = 2% + Beta * (12% - 2%)

14% = Beta * 10%

Beta = 1.4 --> Beta of new portfolio formed by combining existing portfolio with new portfolio.

Beta of a portfolio is weighted average of its constituents.

This implies,

Portfolio beta = Beta1 * W1 + Beta2 * W2

where W1 and W2 are weights of individual components in portfolio.

1.4 = 0.75 * W1 + 2.9 * W2

But, W1 + W2 = 1 => W1 =1-W2

1.4 = 0.75 * (1 - W2) + 2.9W2

1.4 = 0.75 - 0.75W2 + 2.9W2

W2 = 0.3023

W2 = 30.23%

=> W1 = 69.77%

In order to calculate the amount, lets put the weight in mathematical relation:

7134.23 + 0.3023Amt in portfolio2 = Amt in portfolio 2

Amt in portfolio 2 = 7134.23/0.6977 = $10,225.43

Amt in Portfolio 2 = $10,225.43 --> Answer

jeff jeffy answered 2 years ago
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