Question

1. Consider the following information:

State of Economy	Probability of State of Economy	Rate of Return If State Occurs
		Stock A	Stock B	Stock C
Boom	0.25	14%	15%	33%
Bust	0.75	12%	3%	-6%

What is the expected return and standard deviation of returns on an equally weighted portfolio of these three stocks?

2. Consider the following information:

State of Economy	Probability of State of Economy	Rate of Return If State Occurs
		Stock K	Stock M
Boom	0.10	25%	18%
Growth	0.20	10%	20%
Normal	0.50	15%	4%
Recession	0.20	-12%	0%

1. An individual plans to invest $5,000: $3,000 in Stock K and $2,000 in Stock M. What are the stock weights for this portfolio? (w_K = 60%, w_M = 40%)
2. Using the weights computed in Part a, what is the expected return for the portfolio? (E(R_p) = 8.88%)

c. Using the weights computed in Part a, calculate the variance and standard deviation of the portfolio.

Answer 1

deviation^2x probability state of economy rate of return if state occurs Stock A Stock B Stock C Boom 14% 15% 33% 33% Bust 12% 3% -6% weighted return (weight x return) I weighted sum probability expected return Stock A Stock B Stock C (sum of weighted return) 4.667% 5.000% 11.000% 20.667% | 0.25 5.17% 4.000% 1.000% -2.000% 3.000% 2.25% 7.42% deviation (weighted return- deviation^2 expected return) 13.250% 1.755625% -4.417% 0.195069% 0.004389063 0.00146302 0.75 Weight 33.33% 33.33% 33.33% Variance Standard deviation = variance10.5 0.00585 7.65% Answer: Expected return = Standard deviation 7.42% 7.65%