Question

A mutual fund manager has a $20 million portfolio with a beta of 1.80. The risk-free rate is 7.75%, and the market risk premium is 6.5%. The manager expects to receive an additional $5 million, which she plans to invest in a number of stocks. After investing the additional funds, she wants the fund's required return to be 16%. What should be the average beta of the new stocks added to the portfolio? Negative value, if any, should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

As per CAPM

expected return = risk-free rate + beta * (Market risk premium)

Expected return% = 7.75 + 1.8 * (6.5)

Expected return% = 19.45

Total New portfolio value = Value of Old portfolio + Value of Add. Inv

=20+5

=25

Weight of Old portfolio = Value of Old portfolio/Total New portfolio Value

= 20/25

=0.8

Weight of Add. Inv = Value of Add. Inv/Total New portfolio Value

= 5/25

=0.2

Exp return of New portfolio = Weight of Old portfolio*Exp return of Old portfolio+Weight of Add. Inv*Exp return of Add. Inv

16 = 19.45*0.8+Exp return of Add. Inv*0.2

Exp return of Add. Inv = 2.2

As per CAPM

expected return = risk-free rate + beta * (Market risk premium)

2.2 = 7.75 + Beta * (6.5)

Beta = -0.85