Given the following information, what is the standard deviation of Stock "C"?
Rate of Return if State Occurs |
||||
State of Economy |
Probability of |
Stock A |
Stock B |
Stock C |
Boom |
45% |
0.20 |
0.45 |
0.32 |
Bust |
55% |
-0.10 |
-0.35 |
-0.21 |
Asset Weights |
50% |
25% |
25% |
Solution: | |||
Standard deviation of Stock "C" | 26.37% | ||
Working Notes: | |||
Notes: | First of all we compute expected return of stock C returns , then Variance and at last standard deviation. | ||
Expected return of Stock C (Er C) = Sum of ((prob of each state) x (Return of Stock C at each state)) | |||
=45% x 0.32 + 55% x (-0.21) | |||
=0.028500 | |||
2.85% | |||
The variance of this Stock C = Sum of [(Prob. Of each state) x ( Return of the Stock C at each state - Expected return of the Stock C)^2 ] | |||
=45% x (0.32 - 0.02850)^2 + 55% x (-0.21 - 0.02850)^2 | |||
=0.069522750 | |||
0.069522750 | |||
The standard deviation of Stock C = Square root of the variance of Stock C | |||
=(0.069522750)^(1/2) | |||
=0.263671671 | |||
26.37% | |||
Please feel free to ask if anything about above solution in comment section of the question. |
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