Question
In: Finance
Assume you wish to evaluate the risk and return behaviors associated with various combinations of assets...
Assume you wish to evaluate the risk and return behaviors
associated with various combinations of assets V and W under three
assumed degrees of correlation: perfect positive, uncorrelated,
and perfect negative. The following average return and risk values
were calculated for these assets:
Asset Average Return, {r}} Risk (Standard
Deviation), s
V 7.6% 4.7%
W 13.2% 9.4%
a. If the returns of assets V and W are perfectly positively
correlated (correlation coefficient equals plus 1 ), describe the
range of (1) return and (2) risk associated with all possible
portfolio combinations.
(1) Range of expected return: between % and % (Round to one
decimal place.)
(2) Range of the risk: between % and % (Round to one decimal
place.)
b. If the returns of assets V and W are uncorrelated (correlation
coefficient equals 0 ), describe the approximate range of (1)
return and (2) risk associated with all possible portfolio
combinations.
(1) Range of expected return: between % and % (Round to one decimal place.)
(2) Range of the risk: between % and % (Round to one decimal
place.)
c. If the returns of assets V and W are perfectly negatively
correlated (correlation coefficient equals negative 1 ), describe
the range of (1) return and (2) risk associated with all possible
portfolio combinations.
(1) Range of expected return: between % and % (Round to one decimal place.)
(2) Range of the risk: between % and % (Round to one decimal place.)
Solutions
Expert Solution
As per your question you are asked to calculate return and standard deviation of each of the given portfolios separately, which are formed by different combination of Asset V and Asset W.
Return=W1×R1+W2×R2 .
Standard deviation =
| Return | Standard Deviation | |||||||
| Asset V | 7.60% | 4.70% | ||||||
| Asset V | 13.20% | 9.40% | ||||||
| A.perfectly positively correlated (correlation ) | 1 | B.perfectly uncorrelated(correlation )) | 0 | C.perfectly negatively correlated (correlation ) | -1 | |||
| Situation | % in Asset V | % in Asset W | Return | Standard Deviation | Return | Standard Deviation | Return | Standard Deviation |
| 1 | 100% | 0.00% | 7.600% | 4.70% | 7.600% | 4.70% | 7.600% | 4.70% |
| 2 | 99% | 1.00% | 7.656% | 4.75% | 7.656% | 4.65% | 7.656% | 4.56% |
| 3 | 98% | 2.00% | 7.712% | 4.79% | 7.712% | 4.61% | 7.712% | 4.42% |
| 4 | 97% | 3.00% | 7.768% | 4.84% | 7.768% | 4.57% | 7.768% | 4.28% |
| 5 | 96% | 4.00% | 7.824% | 4.89% | 7.824% | 4.53% | 7.824% | 4.14% |
| 6 | 95% | 5.00% | 7.880% | 4.94% | 7.880% | 4.49% | 7.880% | 4.00% |
| 7 | 94% | 6.00% | 7.936% | 4.98% | 7.936% | 4.45% | 7.936% | 3.85% |
| 8 | 93% | 7.00% | 7.992% | 5.03% | 7.992% | 4.42% | 7.992% | 3.71% |
| 9 | 92% | 8.00% | 8.048% | 5.08% | 8.048% | 4.39% | 8.048% | 3.57% |
| 10 | 91% | 9.00% | 8.104% | 5.12% | 8.104% | 4.36% | 8.104% | 3.43% |
| 11 | 90% | 10.00% | 8.160% | 5.17% | 8.160% | 4.33% | 8.160% | 3.29% |
| 25 | 76% | 24.00% | 8.944% | 5.83% | 8.944% | 4.22% | 8.944% | 1.32% |
| 35 | 66% | 34.00% | 9.504% | 6.30% | 9.504% | 4.45% | 9.504% | 0.09% |
| 36 | 65% | 35.00% | 9.560% | 6.35% | 9.560% | 4.49% | 9.560% | 0.24% |
| 37 | 64% | 36.00% | 9.616% | 6.39% | 9.616% | 4.53% | 9.616% | 0.38% |
| 38 | 63% | 37.00% | 9.672% | 6.44% | 9.672% | 4.57% | 9.672% | 0.52% |
| 39 | 62% | 38.00% | 9.728% | 6.49% | 9.728% | 4.61% | 9.728% | 0.66% |
| 40 | 61% | 39.00% | 9.784% | 6.53% | 9.784% | 4.65% | 9.784% | 0.80% |
| 41 | 60% | 40.00% | 9.840% | 6.58% | 9.840% | 4.70% | 9.840% | 0.94% |
| 42 | 59% | 41.00% | 9.896% | 6.63% | 9.896% | 4.75% | 9.896% | 1.08% |
| 47 | 54% | 46.00% | 10.176% | 6.86% | 10.176% | 5.01% | 10.176% | 1.79% |
| 48 | 53% | 47.00% | 10.232% | 6.91% | 10.232% | 5.07% | 10.232% | 1.93% |
| 49 | 52% | 48.00% | 10.288% | 6.96% | 10.288% | 5.13% | 10.288% | 2.07% |
| 50 | 51% | 49.00% | 10.344% | 7.00% | 10.344% | 5.19% | 10.344% | 2.21% |
| 51 | 50% | 50.00% | 10.400% | 7.05% | 10.400% | 5.25% | 10.400% | 2.35% |
| 52 | 49% | 51.00% | 10.456% | 7.10% | 10.456% | 5.32% | 10.456% | 2.49% |
| 53 | 48% | 52.00% | 10.512% | 7.14% | 10.512% | 5.38% | 10.512% | 2.63% |
| 54 | 47% | 53.00% | 10.568% | 7.19% | 10.568% | 5.45% | 10.568% | 2.77% |
| 55 | 46% | 54.00% | 10.624% | 7.24% | 10.624% | 5.52% | 10.624% | 2.91% |
| 56 | 45% | 55.00% | 10.680% | 7.29% | 10.680% | 5.59% | 10.680% | 3.06% |
| 57 | 44% | 56.00% | 10.736% | 7.33% | 10.736% | 5.66% | 10.736% | 3.20% |
| 58 | 43% | 57.00% | 10.792% | 7.38% | 10.792% | 5.73% | 10.792% | 3.34% |
| 59 | 42% | 58.00% | 10.848% | 7.43% | 10.848% | 5.80% | 10.848% | 3.48% |
| 60 | 41% | 59.00% | 10.904% | 7.47% | 10.904% | 5.87% | 10.904% | 3.62% |
| 68 | 33% | 67.00% | 11.352% | 7.85% | 11.352% | 6.49% | 11.352% | 4.75% |
| 69 | 32% | 68.00% | 11.408% | 7.90% | 11.408% | 6.57% | 11.408% | 4.89% |
| 70 | 31% | 69.00% | 11.464% | 7.94% | 11.464% | 6.65% | 11.464% | 5.03% |
| 71 | 30% | 70.00% | 11.520% | 7.99% | 11.520% | 6.73% | 11.520% | 5.17% |
| 85 | 16% | 84.00% | 12.304% | 8.65% | 12.304% | 7.93% | 12.304% | 7.14% |
| 86 | 15% | 85.00% | 12.360% | 8.70% | 12.360% | 8.02% | 12.360% | 7.29% |
| 87 | 14% | 86.00% | 12.416% | 8.74% | 12.416% | 8.11% | 12.416% | 7.43% |
| 88 | 13% | 87.00% | 12.472% | 8.79% | 12.472% | 8.20% | 12.472% | 7.57% |
| 89 | 12% | 88.00% | 12.528% | 8.84% | 12.528% | 8.29% | 12.528% | 7.71% |
| 90 | 11% | 89.00% | 12.584% | 8.88% | 12.584% | 8.38% | 12.584% | 7.85% |
| 100 | 1% | 99.00% | 13.144% | 9.35% | 13.144% | 9.31% | 13.144% | 9.26% |
| 101 | 0% | 100.00% | 13.200% | 9.40% | 13.200% | 9.40% | 13.200% | 9.40% |
| Situation A | Situation B | Situation C | ||||||
| Range | Range | Range | ||||||
| Return | 7.6% to 13.20% | 7.6% to 13.20% | 7.6% to 13.20% | |||||
| Risk | 4.70% to 9.40% | 4.2% to 9.40% | 0.05% to 9.40% | |||||
| Return | Standard Deviation | |||||||
| Asset V | 7.60% | 4.70% | ||||||
| Asset V | 13.20% | 9.40% |
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