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Q1) There is a 23.70% probability of a below average economy and a 76.30% probability of...

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.
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Answer #1

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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