Question

Please show all work and formulas

Please use the following information to answer this question.

State     Probability       A                     B                      C

Boom   .3                     -10%                5%                   0%

Normal            .4                     5                      3                      2                     

Bust     .3                     10                    -5                     2

Find the expected return and variance of the portfolio if an investor spent $5000 on A, $8000 on B and $7000 on C.

Answer 1

Investment in Stock A = $5,000
Investment in Stock B = $8,000
Investment in Stock C = $7,000

Total Investment = Investment in Stock A + Investment in Stock B + Investment in Stock C
Total Investment = $5,000 + $8,000 + $7,000
Total Investment = $20,000

Weight of Stock A = Investment in Stock A / Total Investment
Weight of Stock A = $5,000 / $20,000
Weight of Stock A = 0.25

Weight of Stock B = Investment in Stock B / Total Investment
Weight of Stock B = $8,000 / $20,000
Weight of Stock B = 0.40

Weight of Stock C = Investment in Stock C / Total Investment
Weight of Stock C = $7,000 / $20,000
Weight of Stock C = 0.35

Boom:

Expected Return = 0.25 * (-10%) + 0.40 * 5% + 0.35 * 0%
Expected Return = -0.50%

Normal:

Expected Return = 0.25 * 5% + 0.40 * 3% + 0.35 * 2%
Expected Return = 3.15%

Bust:

Expected Return = 0.25 * 10% + 0.40 * (-5%) + 0.35 * 2%
Expected Return = 1.20%

Expected Return of Portfolio = 0.30 * (-0.50%) + 0.40 * 3.15% + 0.30 * 1.20%
Expected Return of Portfolio = 1.47%

Variance of Portfolio = 0.30 * (-0.0050 - 0.0147)^2 + 0.40 * (0.0315 - 0.0147)^2 + 0.30 * (0.0120 - 0.0147)^2
Variance of Portfolio = 0.000232