You are trying to decide between two portfolios of securities. You have one port

Question

You are trying to decide between two portfolios of securities. You have one portfolio (Portfolio A) that is comprised of government bonds and stable stocks, and one (Portfolio B) that is made up of volatile stocks. Use the discrete probability distribution tables 3. below to answer the following questions Portfolio A Rate of Retum Probability Rate of Return Probability -2.50% 0.00% 1.25% 4.00% I 1.00% 0.075 0.215 0.35 0.265 0.095 14.75% -6.00% 0.00% 12.00%) 26.00% 0.15 0.25 0.15 0.25 0.2 A) What is the expected rate of return and standard deviation for portfolio A? B) What is the expected rate of return and standard deviation for portfolio B? C) Which portfolio should you choose if you valued high returns over consistent returns? Why? D) Which portfolio should you choose if you value consistent returns over high returns?

Explanation / Answer

A) Expected rate of return for A(E(X)) = -0.0250 * 0.075 + 0 * 0.215 + 0.0125 * 0.35 + 0.04 * 0.265 + 0.11 * 0.095 = 0.02355

E(X2) = (-0.025)^2 * 0.075 + 0^2 * 0.215 + (0.0125)^2 * 0.35 + (0.04)^2 * 0.265 + (0.11)^2 * 0.095 = 0.001675

Variance = (E(X2)) - (E(X ))2

= 0.001675 - 0.000555

= 0.00112

Standard deviation = Sqrt (0.00112) = 0.033466

B) Expected rate of return for B (E(X)) = -0.1475 * 0.15 - 0.06 * 0.25 + 0 * 0.15 + 0.12 * 0.25 + 0.26 * 0.2 = 0.044875

E(X2) = (-0.1475)^2 * 0.15 + (-0.06)^2 * 0.25 + 0^2 * 0.15 + (0.12)^2 * 0.25 + (0.26)^2 * 0.2 = 0.02128

Variance =  (E(X2)) - (E(X ))2

= 0.02128 - 0.00201

= 0.01927

Standard deviation = 0.138816

C) Portfolio B

D) Portfolio A

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