Consider the following information:
Rate of Return If State Occurs | |||||||||
State of Economy | Probability of State of Economy | Stock A | Stock B | ||||||
Recession | .15 | .06 | −.10 | ||||||
Normal | .56 | .09 | .19 | ||||||
Boom | .29 | .14 | .36 | ||||||
Calculate the expected return for the two stocks. (Do not
round intermediate calculations. Enter your answers as a percent
rounded to 2 decimal places, e.g., 32.16.)
Expected return | |
Stock A | % |
Stock B | % |
Calculate the standard deviation for the two stocks. (Do
not round intermediate calculations. Enter your answers as a
percent rounded to 2 decimal places, e.g.,
32.16.)
Standard deviation | |
Stock A | % |
Stock B | % |
We have the following calculations:
Probability | A | B | A-Mean | (A-Mean)^2 | (B-Mean) | (B-Mean)^2 | Prob Weighted A | prob Weight B |
0.15 | 0.06 | -0.10 | -4.0000% | 0.0016 | -29.6% | 8.7498% | 0.0240% | 1.3125% |
0.56 | 0.09 | 0.19 | -1.0000% | 0.0001 | -0.6% | 0.0034% | 0.0056% | 0.0019% |
0.29 | 0.14 | 0.36 | 4.0000% | 1.6E-03 | 16.4% | 2.6962% | 0.0464% | 0.7819% |
Mean | 10.00% | 19.58% | Variance | 0.08% | 2.10% | |||
SD | 2.76% | 14.48% |
The probability weighted mean is calculated. The each return of the probability state is then deducted from the mean. It is squared and then multiplied by the probability. The sum of all probability weighted difference is summed up to get variance.
Square root of variance gives us standard deviation
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