a.
Mean return |
13.5 % |
Variance |
4.6675 % |
Explanation:
Stock Fund |
||||||
Scenario |
Probability (a) |
Rate of return (b) |
(c) = (a) x (b) |
Deviation from expected return (d) = (b) - E(R) |
Squared deviation (e) = d2 |
(f) = (a) x (e) |
Severe recession |
0.05 |
-0.41 |
-0.0205 |
-0.5445 |
0.29648025 |
0.014824013 |
Mild recession |
0.20 |
-0.11 |
-0.0220 |
-0.2445 |
0.05978025 |
0.01195605 |
Normal growth |
0.30 |
0.08 |
0.0240 |
-0.0545 |
0.00297025 |
0.000891075 |
Boom |
0.45 |
0.34 |
0.1530 |
0.2055 |
0.04223025 |
0.019003613 |
Expected return E(R) |
0.1345 |
Variance |
0.04667475 |
Expected return or Mean return = 0.1345 or 13.5 %
Variance = 0.04667475 or 4.6675 %
b.
Co-variance |
0.6823% |
Explanation:
Scenario |
Probability (a) |
Stock Fund Rate of Return |
Bond Fund Rate of Return |
Si |
Si- Sm |
Bi |
Bi- Bm |
(Si-Sm) x (Bi-Bm) |
Severe recession |
0.05 |
-0.41 |
-0.18 |
-0.0205 |
-0.155 |
-0.009 |
-0.07 |
0.01085 |
Mild recession |
0.20 |
-0.11 |
0.14 |
-0.022 |
-0.1565 |
0.028 |
-0.033 |
0.0051645 |
Normal growth |
0.30 |
0.08 |
0.05 |
0.024 |
-0.1105 |
0.015 |
-0.046 |
0.005083 |
Boom |
0.45 |
0.34 |
0.06 |
0.153 |
0.0185 |
0.027 |
-0.034 |
-0.000629 |
Mean Sm |
0.1345 |
Mean Bm |
0.061 |
0.0204685 |
||||
0.006822833 |
Covariance = ∑ (Si-Sm) x (Bi-Bm)/ (n -1)
= (0.01085 + 0.0051645 + 0.005083 - 0.000629)/ (4 -1)
= 0.0204685/3 = 0.006822833 or 0.6823 %
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Chapter 6 Q2
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