Question

A mutual fund manager, Sally Spartan, has a $24.0 million portfolio with a beta of 1.25. The risk-free rate is 3.50%, and the market risk premium is 7.00%. The manager expects to receive an additional $16.0 million which she plans to invest in additional stocks. After investing the additional funds, the total portfolio will equal $40.0 million. Sally wants the final $40 million dollar fund's required and expected return to be 15.0%. What must the average beta of the new stocks be to achieve the target required rate of return.

Answer 1

Formula:
1. Capital Asset pricing model:

As per CAPM model:
Re= Rf+(Rm-Rf)B

Re= required rate of return.
Rf= Risk-free rate. 3.5%
Rm =Market Risk Premium. 7%
B = Beta, systematic risk.

The average beta of the new stocks be to achieve the target required rate of return is "6.34"

Note:
Combined Re= Target Re.

Oldi Re = 3.5+ (7 - 3.5) 1.25 Re= 7.8754 Combined Rec 15y. 15%. 23.5+ (7 - 3-5) Bcom Bcombined - 3.286 Bcombined = weighted 3.206 = 24 x strecage of old & New Beta 1.25 + 16 Bnew 40 4o Bnew at 6.34