Question

Consider the following information on a portfolio of three stocks:

State of Economy	Probability of State of Economy	Stock A Rate of Return	Stock B Rate of Return	Stock C Rate of Return
Boom	.15	.05	.21	.18
Normal	.80	.08	.15	.07
Recession	.05	.12	-.22	-.02

The portfolio is invested 35 percent in each Stock A and Stock B and 30 percent in Stock C. If the expected T-bill rate is 3.90 percent, what is the expected risk premium on the portfolio? What is the standard deviation of the portfolio?

Answer 1

E(r) = $\sum_{i=1}^{n}$ [Pi x Ri]

E(rA) = [0.15 x 5%] + [0.80 x 8%] + [0.05 x 12%] = 0.75% + 6.40% + 0.60% = 7.75%

E(rB) = [0.15 x 21%] + [0.80 x 15%] + [0.05 x -22%] = 3.15% + 12.00% - 1.10% = 14.05%

E(rC) = [0.15 x 18%] + [0.80 x 7%] + [0.05 x -2%] = 2.70% + 5.60% - 0.10% = 8.20%

E(rP) = [0.35 x 7.75%] + [0.35 x 14.05%] + [0.30 x 8.20%] = 2.71% + 4.92% + 2.46% = 10.09%

E(RP) = E(rP) - rF = 10.09% - 3.90% = 6.19%

$\sigma$P = [$\sum_{i=1}^{n}${Pi x (E(rP) - Ri)²}]^1/2

= [{0.35 x (10.09% - 7.75%)²} + {0.35 x (10.09% - 14.05%)²} + {0.30 x (10.09% - 8.20%)²}]^1/2

= [1.92%² + 5.49%² + 1.07%²]^1/2 = [8.48%²]^1/2 = 2.91%