Question
Problem 8-17 Portfolio beta A mutual fund manager has a $20,000,000 portfolio with a betaof 1.5. The risk free rate is 4.5% and the market risk premium is5.5%. The manager expects to receive an additional$5,000,000, which she plans to invest in a numver of stocks. Afterinvesting the additional funds, she wants the funds requirededreturn to be 13%. What should be the average beta of the new stocksadded to the portfolio? Problem 8-17 Portfolio beta A mutual fund manager has a $20,000,000 portfolio with a betaof 1.5. The risk free rate is 4.5% and the market risk premium is5.5%. The manager expects to receive an additional$5,000,000, which she plans to invest in a numver of stocks. Afterinvesting the additional funds, she wants the funds requirededreturn to be 13%. What should be the average beta of the new stocksadded to the portfolio?
Explanation / Answer
Fund ManagerInvestment $20,000,000 Portfolio Beta 1.5 Risk-free Rate(Rf) 4.50% Market Risk-Premium(MRP) 5.50% Additional Funds received by FundManager $5,000,000 Funds Required Return(RE) 13% Calculating Beta Value(ß): RE = Rf + ß *MRP 0.13 = 0.045 + ß *0.055 0.13 - 0.045 = ß *0.055 0.085 = ß *0.055 ß *0.055 = 0.085 Beta(ß) = 0.085 / 0.055 Beta(ß) = 1.5 Average Beta of the NewPortfolio = ($20,000,000 / $25,000,000) * 1.5 +($5,000,000 / $25,000,000) * 1.5 Average Beta of the NewPortfolio = 0.8 * 1.5 + 0.2 *1.5 Average Beta ofthe New Portfolio (ß) = 1.2 +0.3 = 1.5 Fund ManagerInvestment $20,000,000 Portfolio Beta 1.5 Risk-free Rate(Rf) 4.50% Market Risk-Premium(MRP) 5.50% Additional Funds received by FundManager $5,000,000 Funds Required Return(RE) 13% Calculating Beta Value(ß): RE = Rf + ß *MRP 0.13 = 0.045 + ß *0.055 0.13 - 0.045 = ß *0.055 0.085 = ß *0.055 ß *0.055 = 0.085 Beta(ß) = 0.085 / 0.055 Beta(ß) = 1.5 Average Beta of the NewPortfolio = ($20,000,000 / $25,000,000) * 1.5 +($5,000,000 / $25,000,000) * 1.5 Average Beta of the NewPortfolio = 0.8 * 1.5 + 0.2 *1.5 Average Beta ofthe New Portfolio (ß) = 1.2 +0.3 = 1.5