Question

You are a manger of the Lowell Fund and manage a portfolio of $21 million. Your portfolio has a beta of 1.2 and required return of 12 percent. You receive $4 million additional to invest in the portfolio, and you invest it in a stock with a beta of 1.6. The risk-free rate is 5 percent. What is the required return on the new portfolio? (Hint: Calculate weighted average beta after new capital investment.)

Answer 1

E(R) = R_F + (R_M - R_F) Beta

where,

E(R) = Expected return from a portfolio

R_M = Market rate of return

R_F = Risk free return

E(R) = R_F + (R_M - R_F) Beta

12% = 5% + (R_M - 5%) x 1.2

12% - 5% = (R_M - 5%) x 1.2

R_M - 5% = 7%/1.2

R_M = 5.83% + 5%

R_M = 10.83%

Calculation of weighted beta

	Investment	Weight of investment (i)	Beta (ii)	Weighted beta (i) x (ii)
Old portfolio	$21 million	21/25 = 0.84	1.2	0.84 x 1.2 = 1.008
New stock	$4 million	4/25 = 0.16	1.6	0.16 x 1.6 = 0.256
	$25 million			Total = 1.264

Hence, beta of the new portfolio is 1.264

Calculation of required return on the new portfolio

E(R) = R_F + (R_M - R_F) Beta

= 5% + (10.83% - 5%) x 1.264

= 5% + (5.83 x 1.264)

= 5% + 7.37%

= 12.37%

Hence, required return on the new portfolio will be 12.37%