Question

a. The expected rate of return for portfolio A is:

The standard deviation of portfolio A is:

b. The expected rate of return for portfolio B is:

The standard deviation for portfolio B is:

(Computing the expected rate of return and risk) After a tumultuous period in the stock market, Logan Morgan is considering an investment in one of two portfolios. Given the information that follows, which investment is better, based on risk (as measured by the standard deviation) and return as measured by the expected rate of return? Portfolio B Portfolio A Return Probability 0.15 0.50 0.35 -3% 18% Probability 0.05 0.32 0.42 0.21 Return 4% 8% 26% 10% 16%

Answer 1

Portfolio A

Probability	Return of A
0.15	-3%
0.5	18%
0.35	26%

Expected return is calculated using the formula:

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

Expected return of A = E[R_A] = 0.15*(-3%) + 0.5*18% + 0.35*26% = 17.65%

Varaicnce is calculated using the formula:

Variance = σ² = p₁*(R₁-E[R])² + p₂*(R₂-E[R])²+p₃*(R₃-E[R])²

Varaicne of A = σ_A² = 0.15*(-3%-17.65%)²+0.5*(18%-17.65%)²+0.35*(26%-17.65%)² = 0.00884275

Standard deviation is square root of variance

Standard deviation of A = σ_A = 0.00884275^1/2 = 0.0940358974009394 = 9.40358974009394%

Portfolio B

Probability	Return of B
0.05	4%
0.32	8%
0.42	10%
0.21	16%

Expected return is calculated using the formula:

Expected Return = E[R] = p₁*R₁ + p₂*R₂ + p₃*R₃+p₄*R₄

Expected return of B = E[R_B] = 0.05*4% + 0.32*8% + 0.42*10% + 0.21*16% = 10.32%

Varaicnce is calculated using the formula:

Variance = σ² = p₁*(R₁-E[R])² + p₂*(R₂-E[R])²+p₃*(R₃-E[R])²+p₃*(R₃-E[R])²

Varaicne of B = σ_B² = 0.05*(4%-10.32%)²+0.32*(8%-10.32%)²+0.42*(10%-10.32%)²+0.21*(16%-10.32%)² = 0.00105376

Standard deviation is square root of variance

Standard deviation of B = σ_B = 0.00105376^1/2 = 0.0324616697044376 = 3.24616697044376%

Answers

a. The expected rate of return for portfolio A is: 17.65%

The standard deviation of portfolio A is: 9.40358974009394%

b. The expected rate of return for portfolio B is: 10.32%

The standard deviation for portfolio B is: 3.24616697044376%