a. An investor currently holds the following portfolio: Amount Invested 8,000 sh

Question

a.            An investor currently holds the following portfolio:

                                                Amount

                                                Invested

8,000 shares of Stock A        $16,000           Beta = 1.3

15,000 shares of Stock B       $48,000           Beta = 1.8

25,000 shares of Stock C      $96,000           Beta = 2.2

The investor is worried that the beta of his portfolio is too high, so he wants to sell some Stock C and add Stock D which has a beta of 1.0 to his portfolio. If the investor wants his portfolio to have a beta of 1.72, how much Stock C must he replace with Stock D?

Explanation / Answer

The Beta of the portfolio is 1.99(beta of a portfolio is weighted average,weight being the proportion of each investment to the total investment). As per the question requirement we have to bring down the Portfolio beta to 1.72 i.e decrease by 0.27. By selling each Rs.1000 stock of C(having beta of 2.2) and purchasing D from the same amount results in a weighted decrease in the portfolio beta by 0.01375. Therefore Rs.19636.36 of Investment should be transferred from C to D to result in a portfolio beta of 1.72.

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