Question

The following returns have been estimated for Security T and Security S:

Scenario	Security T	Security S
1	20%	10%
2	13%	-6%
3	15%	20%

Each scenario is equally likely to occur, and you plan to invest 70% in Security T and 30% in Security S. What is the expected return of the portfolio? Round your answer to the nearest tenth of a percent.

Answer 1

Scenario	Security T	Security S
1	20%	10%
2	13%	-6%
3	15%	20%

Each scenario is equally likely to occur means that the probability of occurrence of each scenario is 1/3

Probability of scenario 1 = p₁ = 1/3

Probability of scenario 2 = p₂ = 1/3

Probability of scenario 3 = p₃ = 1/3

Expected return when the probability of occurrence of different scenarios is given is calculated using the formula:

Expected return = E[R] = p₁*R₁ + p₂*R₂ + p₃*R₃

Expected return on Security T = E[R_T] = (1/3)*20% + (1/3)*13% + (1/3)*15% = 16%

Expected return on Security S = E[R_S] = (1/3)*10% + (1/3)*(-6%) + (1/3)*20% = 8%

Portforlio

Weight of Security T in portfolio = W_T = 70%, Expected return on Security T = E[R_T] = 16%

Weight of securty S in portfolio = W_S = 30%, Expected return on Security S = E[R_S] = 8%

Expected return of the portfolio is calculated using the formula:

Expected return of portfolio = E[R_P] = W_T*E[R_T] + W_S*E[R_S] = 70%*16% + 30%*8% = 13.6%

Answer -> Expected return of portfolio = 13.6%