Question

- Given the following information, determine the beta coefficient for Stock L that is consistent with equilibrium: = 9.5%; rRF = 2.5%; rM = 11.5%.

- You have been managing a $5 million portfolio that has a beta of 1.05 and a required rate of return of 11.925%. The current risk-free rate is 3%. Assume that you receive another $500,000. If you invest the money in a stock with a beta of 1.35, what will be the required return on your $5.5 million portfolio?

Answer 1

Part 1

Equilibrium rate	9.50%
Rf --> Risk free rate	2.50%
Rm ---> Market rate	11.50%

Equilibrium rate = Risk free rate + Beta x (market rate - risk free rate)

9.5% = 2.5% + Beta x (11.5% - 2.5%)

9.5% - 2.5% = Beta x (11.5% - 2.5%)

7% = Beta x (11.5% - 2.5%)

7% = Beta x (9%)

Beta = 0.78

Part 2

Current portfolio ( in Mn $)	5
Current portfolio beta	1.05
Current portfolio Rate of return	11.925%
Risk free rate	3%
Additional cash (in $)	500000
Additional cash (in Mn $)	0.5
New stock Beta	1.35

Computation of market return

Current portfolio beta	1.05
Current portfolio Rate of return	11.925%
Risk free rate	3%

Required rate of return = Risk free rate + Beta x (market rate - risk free rate)

11.925% = 3% + 1.05 (Rm - 3%)

11.925% - 3% = 1.05 (Rm - 3%)

11.925% - 3% = 1.05 (Rm - 3%)

8.925% = 1.05 (Rm - 3%)

8.5% = (Rm - 3%)

Rm = 8.5%+ 3%

Rm = 11.5%

New portfolio Beta computation

Current portfolio ( in Mn $)	5
Investment in new stock (in Mn $)	0.5
Total investment value (in Mn $)	5.5

Weight of current portfolio	0.9091
Weight of new stock	0.0909

Beta of current portfolio	1.05
Beta of new stock	1.35

Beta of new portfolio

	Weight in new portfolio	Beta	Weighted beta (weight x beta)
Current portfolio	0.9091	1.05	0.95
New stock	0.0909	1.35	0.12
Portfolio beta = Sum of weighted beta	1.08

Computation of Required rate of return of new portfolio ---> 5.5 Mn

Required rate of return = Risk free rate + Beta x (market rate - risk free rate)

Required rate of return = 3% + 1.08 x (11.5% - 3%)

Required rate of return = 12.18%

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