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Consider the following information: State of the Economy Probability of State of the Economy Return on A % Return on B % Boom 0
Consider the following information:
|
State of the Economy |
Probability of State of the Economy |
Return on A % |
Return on B % |
|
Boom |
0.40 |
10 |
4 |
|
Growth |
0.20 |
-4 |
0 |
|
Normal |
0.20 |
24 |
16 |
|
Recession |
0.20 |
16 |
20 |
a) What is the expected return for A? For B?
b) What is the standard deviation for A? For B?
c) What is the expected return on a portfolio of A and B that is 30% invested in A and the remainder in B?
Expert Solution
Part A:
Expetced Return:
Avg Ret = Sum [ Prob * ret ]
Stock A:
| Scenario | Prob | Ret | Prob * Ret |
| Boom | 0.4 | 10.00% | 4.00% |
| Growth | 0.2 | -4.00% | -0.80% |
| Normal | 0.2 | 24.00% | 4.80% |
| Recision | 0.2 | 16.00% | 3.20% |
| Expected Ret | 11.20% |
STock B:
| Scenario | Prob | Ret | Prob * Ret |
| Boom | 0.4 | 4.00% | 1.60% |
| Growth | 0.2 | 0.00% | 0.00% |
| Normal | 0.2 | 16.00% | 3.20% |
| Recision | 0.2 | 20.00% | 4.00% |
| Expected Ret | 8.80% |
Part B:
SD:
It spcifies the risk of Stock
SD = SQRT [ SUm [ Prob * (X-AVgX)^2 ] ]
STock A:
| State | Prob | Ret (X) | (X-AvgX) | (X-AvgX)^2 | Prob * (X-Avg X)^2 |
| Boom | 0.4000 | 10.00% | -1.20% | 0.000144 | 0.00006 |
| Growth | 0.2000 | -4.00% | -15.20% | 0.023104 | 0.00462 |
| Normal | 0.2000 | 24.00% | 12.80% | 0.016384 | 0.00328 |
| Recsion | 0.2000 | 16.00% | 4.80% | 0.002304 | 0.00046 |
| Sum[ Prob * ( X-AvgX)^2 ) ] | 0.00842 | ||||
| SD = SQRT [ [ Sum[ Prob * ( X-AvgX)^2 ) ] ] ] | 0.09174 |
I.e SD is 9.17 %
STock B:
| State | Prob | Ret (X) | (X-AvgX) | (X-AvgX)^2 | Prob * (X-Avg X)^2 |
| Boom | 0.4000 | 4.00% | -4.80% | 0.002304 | 0.00092 |
| Growth | 0.2000 | 0.00% | -8.80% | 0.007744 | 0.00155 |
| Normal | 0.2000 | 16.00% | 7.20% | 0.005184 | 0.00104 |
| Recsion | 0.2000 | 20.00% | 11.20% | 0.012544 | 0.00251 |
| Sum[ Prob * ( X-AvgX)^2 ) ] | 0.00602 | ||||
| SD = SQRT [ [ Sum[ Prob * ( X-AvgX)^2 ) ] ] ] | 0.07756 |
I.e SD is 7.76 %
Part C:
Portfolio Ret is weighted Avg ret of securities in portfolio.
| Stock | Weight | Ret | WTd Ret |
| A | 0.30 | 0.1120 | 0.0336 |
| B | 0.70 | 0.0880 | 0.0616 |
| Portfolio Ret Return | 0.0952 |
Portfolio Ret is 0.0952 i.e 9.52%
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