Homework SourseWhat is the expected return and standard deviation of a port
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% |
Solution
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 |
