Question

Use a risk-free rate of 3% and a market return of 7%. If your $500,000 portfolio has a beta of 1.1, should you add $50,000 of a stock with a beta of 1.8 and an expected return of 11.0%?

• . Depends on the market conditions

• B. Yes

• C. No

• D. Not enough information to answer

Answer 1

We will first find the weighted beta of portfolio after the investment is made. Then we shall find the expected return from CAPM formula. We shall compare this expected return with our return of 11%.

Current Portfolio Value	500000		New investment	50000
Current Portfolio Beta	1.1		New Investment beta	1.8
Portfolio value after investment	550000
Weighted Beta of new Portfolio Weight of old portfolio*beta of portfolio + Weight of new investment*beta of investment
= (500000/550000)*1.1 + (50000/550000)*1.8	1.163636
Capital Asset Price Modeling
Expected Return = Rf + Bi(Rm - Rf)
Expected Return = 3% + 1.16(7% - 3%)
Expected Return = 7.64%

Clearly the expected return is coming out to be 7.64% but expected return given in question is 11%. Therefore, we should not invest in the new stock.

Hence, the correct option is C. No

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