Q1) There is a 23.70% probability of a below average economy and a 76.30% probability of an average economy. If there is a below average economy stocks A and B will have returns of -8.00% and 4.90%, respectively. If there is an average economy stocks A and B will have returns of 13.60% and -4.10%, respectively. Compute the standard deviation for stock a and b. |
Expected return = sum of probability * return
standard deviation = [ sum of probability * ( return - expected return )^2 ] ^0.5
Calculation of mean & variance for A | ||||||
Economy | Return (x) | Probability (P) | Px | x - mean | (x - mean)^2 | P(x - mean)^2 |
Below Average | -8 | 0.237 | -1.896 | -16.4808 | 272 | 64.37 |
Average | 13.6 | 0.763 | 10.377 | 5.1192 | 26 | 20.00 |
Mean | 8.481 | Variance | 84.36851136 |
Standard deviation = 84.37^0.5 = 9.19%
Calculation of mean & variance for B | ||||||
Economy | Return (x) | Probability (P) | Px | x - mean | (x - mean)^2 | P(x - mean)^2 |
Below Average | 4.9 | 0.237 | 1.161 | 6.867 | 47 | 11.18 |
Average | -4.1 | 0.763 | -3.128 | -2.133 | 5 | 3.47 |
Mean | -1.97 | Variance | 14.647311 |
Standard deviation = 14.65^0.5 = 3.83%
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