Question

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%)
3. Using the weights computed in Part a, calculate the variance and standard deviation of the portfolio. (σ²_p = 0.7618% , σ_p = 8.73%)

PLEASE show your work by hand (no excel)

Answer 1

(a): wK = 3000/5000 = 60% and wM = 2000/5000 = 40%

(b): Expected return = weighted return of K + weighted return of M

= 0.6*(0.1*25%+0.2*10%+0.5*15%+0.2*-12%) + 0.4*(0.1*18%+0.2*20%+0.5*4%+0.2*0%)

= 5.76%+3.12

= 8.88%

(c): Boom Erp = 0.6*25% + 0.4*18% = 22.2%

Growth Erp = 0.6*10%+0.4*20% = 14%

Normal Erp = 0.6*15%+0.4*4% = 10.6%

Recession Erp = 0.6*-12%+0.4*0% = -7.2%

Variance = 0.1*(22.2%-8.88%)^2 + 0.2*(14%-8.88%)^2 + 0.5*(10.6%-8.88%)^2+0.2*(-7.2%-8.88%)^2

= 0.1774%+0.0524%+0.0148%+0.5171%

= 0.7618

Standard deviation = 0.7618%^(1/2) = 0.873 or 8.73%