Question

The Lubin’s Investment Team is considering investing in two securities, A and B, and the relevant information is given below:

State of the economy	Probability	Return on A(%)	Return on B(%)
Trough	0.05	-20%	2%
Recession	0.4	-5%	2%
Expansion	0.5	15%	2%
Peak	0.05	20%	2%

Suppose the Team invested $7000 in security A and $3,000 in security B. Calculate the expected return and standard deviation of the Team’s portfolio.

Answer 1

Total Investment = Investment in Security A + Investment in Security B
Total Investment = $7,000 + $3,000
Total Investment = $10,000

Weight of Security A = Investment in Security A / Total Investment
Weight of Security A = $7,000 / $10,000
Weight of Security A = 0.70

Weight of Security B = Investment in Security B / Total Investment
Weight of Security B = $3,000 / $10,000
Weight of Security B = 0.30

Trough:

Expected Return = 0.70 * (-0.20) + 0.30 * 0.02
Expected Return = -0.1340

Recession:

Expected Return = 0.70 * (-0.05) + 0.30 * 0.02
Expected Return = -0.0290

Expansion:

Expected Return = 0.70 * 0.15 + 0.30 * 0.02
Expected Return = 0.1110

Peak:

Expected Return = 0.70 * 0.20 + 0.30 * 0.02
Expected Return = 0.1460

Expected Return of Portfolio = 0.05 * (-0.1340) + 0.40 * (-0.0290) + 0.50 * 0.1110 + 0.05 * 0.1460
Expected Return of Portfolio = 0.0445 or 4.45%

Variance of Portfolio = 0.05 * (-0.1340 - 0.0445)^2 + 0.40 * (-0.0290 - 0.0445)^2 + 0.50 * (0.1110 - 0.0445)^2 + 0.05 * (0.1460 - 0.0445)^2
Variance of Portfolio = 0.00648025

Standard Deviation of Portfolio = (0.00648025)^(1/2)
Standard Deviation of Portfolio = 0.0805 or 8.05%