State Probability Return on A Return on B Boom .6 0.15 0.08 Bust .4 0.05 0.20 Us

Question

State              Probability          Return on A         Return on B

Boom               .6                           0.15                    0.08

Bust                   .4                           0.05                     0.20

Using the table above,

A) what is the expected return for Stock A?

B) What is the standard deviation for Stock A (Note: Use 7 decimal places to calculate the variance.)?

C) What is the expected return on the portfolio if you invest $7,000 in Stock A and $3,000 in Stock B?

D)  What is the standard deviation of the portfolio if you invest $7,000 in Stock A and $3,000 in Stock B (Note: Use 7 decimal places to calculate the variance.)?

Please show your work

Explanation / Answer

Return on A = (0.6 x 0.15) + (0.4 x 0.05) = 0.11 or 11%
Return on B = (0.6 x 0.08) + (0.4 x 0.2) = 0.128 or 12.80%

Standard Deviation of A = {[(0.15 – 0.11)2 x 0.6] + [(0.05 – 0.11)2 x 0.4]}1/2 = 0.04898
Standard Deviation of B = {[(0.08 – 0.128)2 x 0.6] + [(0.2 – 0.128)2 x 0.4]}1/2 = 0.05878

COVAB = [(0.15 – 0.11) x (0.08 – 0.128) x 0.6] + [(0.05 – 0.11) x (0.2 – 0.128) x 0.4] = -0.00288
COR­AB = COVAB / (Standard Deviation of A x Standard Deviation of B)
= -0.00288 / (0.04898*0.05878) = -1

Return on portfolio = (0.7 x 0.11) + (0.3 x 0.128) = 11.54%
Standard Deviation of Portfolio = (0.048982 x 0.72) + (0.058782 x 0.32) + (2*0.7*0.3*0.04898*0.05878*-1) = 0.000278

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