A portfolio manager has a $10 million portfolio, which consists of $1 million in

Question

A portfolio manager has a $10 million portfolio, which consists of $1 million invested in 10 separate stocks. The portfolio beta is 1.2. The risk-free rate is 5% and the market risk premium (rM-rRF) is 6%.

a). What is the portfolio’s required return?

b). The manager sells one of the stocks in her portfolio for $1 million. The stock she sold has a beta of 0.9. She takes the $1 million and uses the money to purchase a new stock that has a beta of 1.6. What is the required return of her portfolio after purchasing this new stock?

Explanation / Answer

a). What is the portfolio’s required return?

Required return= Rf+ Beta(Rm-Rf) where Rf= risk free rate and (Rm-Rf) = market risk premium

Required return = 5% + 1.2(6%) = 12.2%

b) What is the required return of her portfolio after purchasing this new stock?

Beta of the remaing portfolio = 1.2- 0.9(1/10) = 1.11 consisting of 9 stocks

Now 1 more new stock with beta of 1.6 is added.

so new beta- 1.11+1.6(1/10) =1.27

Required return = 5% + 1.27(6%) = 12.62%

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