Question

A) Listed below is the probability distribution of the rates of return associated with 2 stocks, RST corporation and ABC Inc. If an investor were to put in $40,000 in RST and $60,000 in ABC, calculate his portfolio's expected return and standard deviation.

State of Economy	Probability	RST Corp.	ABC Inc.
Weak	30%	-5%	20%
Normal	40%	10%	5%
Boom	30%	20%	-5%

B) If treasury securities are currently yielding 3%, the expected market risk premium is 7%, RST's beta is 1.3, and ABC's beta is 0.8, is the portfolio appropriately valued? Explain your answer.

Answer 1

A)

		Rate of Return if State Occurs
State of	Probability of
Economy	State of Economy (p)	RST Corp.	ABC Inc.	Expected return of each state of economy rE	Expected return of each state of economy * p	(rE-rp)	(rE-rp)^2	Variance calculation = p*(rE-rp)^2
Weak	0.30	-5.0%	20.0%	10.000%	3.00%	2.70%	0.07%	0.02%
Normal	0.40	10.0%	5.0%	7.00%	2.80%	-0.30%	0.00%	0.00%
Boom	0.30	20.00%	-5.0%	5.00%	1.50%	-2.30%	0.05%	0.02%
Expected return on each stock (average)		8.50%	6.50%
Weight of stocks in portfolio		40.00%	60.00%
Expected return of portfolio (Sum) rp					7.30%
Variance of portfolio (sum)								0.04%
Standard Deviation of portfolio = (variance)^(1/2)								1.95%

B) If treasury securities are currently yielding 3%, the expected market risk premium is 7%, RST's beta is 1.3, and ABC's beta is 0.8, is the portfolio appropriately valued? Explain your answer.

Required rate of return of portfolio, re = risk-free rate + beta * Market Risk Premium

Beta of portfolio = 0.4 * 1.3 + 0.6 * 0.8 = 1

Required rate of return of portfolio = 3% + 1*7% = 10%

But the expected of portfolio is 7.30%; it means that the portfolio is not appropriately valued