11.09 Returns and Standard Deviations Consider the following information: |
Main Page | |||||
State of Economy | Probability of State of Economy | Rate of Return if State Occurs | |||
Stock A | Stock B | Stock C | Portfolio | ||
Boom | 0.25 | 25.00% | 45.00% | 33.00% | |
Good | 0.4 | 9.00% | 10.00% | 15.00% | |
Poor | 0.3 | 3.00% | -10.00% | -5.00% | |
Bust | 0.05 | -5.00% | -25.00% | -9.00% | |
Expected Value | |||||
Variance | |||||
Standard Deviation | |||||
a. Your portfolio is invested 30 percent each in A
and C, and 40 percent in B. What is the expected return of the
portfolio? b. What is the variance of this portfolio? The standard deviation? |
Weight of Stock A = 30%
Weight of Stock B = 40%
Weight of Stock C = 30%
Boom:
Expected Return = 30% * 0.25 + 40% * 0.45 + 30% * 0.33
Expected Return = 0.3540
Good:
Expected Return = 30% * 0.09 + 40% * 0.10 + 30% * 0.15
Expected Return = 0.1120
Poor:
Expected Return = 30% * 0.03 + 40% * (-0.10) + 30% *
(-0.05)
Expected Return = -0.0460
Bust:
Expected Return = 30% * (-0.05) + 40% * (-0.25) + 30% *
(-0.09)
Expected Return = -0.1420
Answer a.
Expected Return of Portfolio = 0.25 * 0.3540 + 0.40 * 0.1120 +
0.30 * (-0.0460) + 0.05 * (-0.1420)
Expected Return of Portfolio = 0.1124 or 11.24%
Answer b.
Variance of Portfolio = 0.25 * (0.3540 - 0.1124)^2 + 0.40 *
(0.1120 - 0.1124)^2 + 0.30 * (-0.0460 - 0.1124)^2 + 0.05 * (-0.1420
- 0.1124)^2
Variance of Portfolio = 0.025356
Standard Deviation of Portfolio = (0.025356)^(1/2)
Standard Deviation of Portfolio = 0.1592 or 15.92%
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