State of Economy Probability of State of Economy Rate of Ret
State of Economy Probability of State of Economy Rate of Return if state occurs
Stock A Stock B Stock C
Boom .15 .37 .47 .27
Good .45 .22 .18 .11
Poor .35 -.04 -.07 -.05
Bust .05 -.18 -.22 -.08
Your portfolio is invested 20% each in stock A and C, and 60% in stock B. Given the analysis above the expected return of your portfolio is _______%, with a portfolio standard deviation of _________%.
Solution
Expected return = 10.96%
Standard dev = 17.26%
| p(x) | return | p*x | p*(x - mean)^2 |
| 0.15 | 41.0% | 0.0615 | 0.0135360 |
| 0.45 | 17.4% | 0.0783 | 0.0018663 |
| 0.35 | -6.0% | -0.021 | 0.0100675 |
| 0.05 | -18.4% | -0.0092 | 0.004310048 |
