Homework Answers
First let's look at the following table:
| State | Probability | A | Probability Weighted return | P(X - Expected return of A)^2 | B | Probability Weighted return | P(X - Expected return of B)^2 | P(X - Expected return of A) x (X - Expected return of B) |
| VVW | 0.1 | 60.00% | 6.00% | 2.45% | -60.00% | -6.00% | 5.18% | -4.29% |
| VW | 0.15 | 40.00% | 6.00% | 1.31% | -50.00% | -7.50% | 5.77% | -3.45% |
| W | 0.2 | 20.00% | 4.00% | 0.18% | -15.00% | -3.00% | 1.46% | -0.86% |
| A | 0.25 | 10.00% | 2.50% | 0.00% | 30.00% | 7.50% | 0.81% | 0.02% |
| S | 0.2 | -15.00% | -3.00% | 1.30% | 60.00% | 12.00% | 4.61% | -1.72% |
| VVS | 0.1 | -50.00% | -5.00% | 3.66% | 90.00% | 9.00% | 6.08% | -3.89% |
| Expected return = sum of probability weighted returns | 10.50% | 12.00% | ||||||
| Variance = sum of P(X - Expected return)^2 | 8.90% | 23.91% | ||||||
| Standard Deviation = square root of variance | 29.83% | 48.90% | ||||||
| Covariance = Sum of P (X - Expected return of A) x (X - Expected return of B) | -14.20% | |||||||
| Correlation = Covariance/ Standard deviation of both | -0.9736 | |||||||
Now let's look at the below table for portfolio return and standard deviation for different weights:
Rho
symbol is for the correlation
| Weight B | Weight A | Portfolio Return | Portfolio standard deviation |
| 0.00% | 100.00% | 10.500% | 29.829% |
| 10.00% | 90.00% | 10.650% | 27.287% |
| 20.00% | 80.00% | 10.800% | 25.789% |
| 30.00% | 70.00% | 10.950% | 25.518% |
| 40.00% | 60.00% | 11.100% | 26.512% |
| 50.00% | 50.00% | 11.250% | 28.639% |
| 60.00% | 40.00% | 11.400% | 31.672% |
| 70.00% | 30.00% | 11.550% | 35.379% |
| 80.00% | 20.00% | 11.700% | 39.571% |
| 90.00% | 10.00% | 11.850% | 44.109% |
| 100.00% | 0.00% | 12.000% | 48.898% |
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hi i need help with this question but in details please how do
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clear and when i tried to calculate it myself it resulted
different
note: without using excel
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