What is the expected return and standard deviation of a portfolio which is compr

Question

What is the expected return and standard deviation of a portfolio which is comprised of $4,500 invested in stock S and $3,000 in stock T? Assume the correlation coefficient between the two securities = -.80.

State of Economy

Probability of State

of Economy

Return if State Occurs

Stock S

Return if State Occurs

Stock T

Boom

10%

12%

4%

Normal

65%

9%

6%

Recession

25%

2%

9%

State of Economy

Probability of State

of Economy

Return if State Occurs

Stock S

Return if State Occurs

Stock T

Boom

10%

12%

4%

Normal

65%

9%

6%

Recession

25%

2%

9%

Explanation / Answer

weight of S = 4500/7500 = 0.60

weight of T = 0.40

portfolio return = 0.60*return on S + 0.40*return on T

mean return = 7.15%

Standard deviation = 1.3883%

p(x) return p*x p*(x - mean)^2 0.1 8.8% 0.0088 0.0000272 0.65 7.8% 0.0507 0.0000275 0.25 4.8% 0.012 0.0001381

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