Question
In: Finance
You have a portfolio made up of the following three assets with known means, standard deviations,...
- You have a portfolio made up of the following three assets with
known means, standard deviations, and correlations of monthly
returns:
|
monthly |
return |
Correlation |
Matrix |
|||||
|
Weight |
Asset |
mean |
std dev |
Asset |
Apple |
Amazon |
CVS |
|
|
50% |
Apple |
3.06% |
8.1% |
Apple |
1 |
|||
|
30% |
Amazon |
2.84% |
7.9% |
Amazon |
0.39 |
1 |
||
|
20% |
CVS |
0.42% |
8.4% |
CVS |
0.03 |
0.31 |
1 |
- What is the expected monthly return on this portfolio?
- What is the monthly portfolio standard deviation?
- What is the probability that this portfolio will have a negative return in one month?
- What is the probability that this portfolio will have a return greater than 4% in a month?
- Over one year, what is the probability that the average of the monthly returns for this portfolio will be negative?
Solutions
Expert Solution
| R1 | Expected Return of Apple | 3.06 | % | ||||||
| R2 | Expected Return of Amazon | 2.84 | % | ||||||
| R3 | Expected Return of CVS | 0.42 | % | ||||||
| S1 | Standard Deviation of Apple | 8.1 | % | ||||||
| S2 | Standard Deviation of Amazon | 7.9 | % | ||||||
| S3 | Standard Deviation of CVS | 8.4 | % | ||||||
| Corr(1,2) | Correlation of Apple and Amazon | 0.39 | |||||||
| Corr(1,3) | Correlation of Apple and CVS | 0.03 | |||||||
| Corr(2,3) | Correlation of Amazon and CVS | 0.31 | |||||||
| Covariance(1,2) =Correlation(1,2)*Standard Deviation of 1 * Standard Deviation of 2 | |||||||||
| Cov(1,2)=Corr(1,2)*S1*S2 | Covariance of Apple and Amazon | 24.9561 | %% | ||||||
| Cov(1,3)=Corr(1,3)*S1*S3 | Covariance of Apple and CVS | 2.0412 | %% | ||||||
| Cov(2,3)=Corr(2,3)*S2*S3 | Covariance of Amazon and CVS | 20.5716 | %% | ||||||
| w1 | Weight of Apple in the Portfolio | 0.5 | |||||||
| w2 | Weight of Amazon in the Portfolio | 0.3 | |||||||
| w3 | Weight of CVS in the Portfolio | 0.2 | |||||||
| Expected Portfolio Return =w1*R1+w2*R2+w3*R3 | |||||||||
| Rp=w1*R1+w2*R2+w3*R3 | Expected Portfolio Return = | 2.466 | % | ||||||
| a) | Expected Monthly Return of Portfolio | 2.47% | |||||||
| Portfolio Variance =(w1^2)*(S1^2)+(w2^2)*(S2^2)+(w3^2)*(S3^2)+2*w1*w2^Cov(1,2)+2*w1*w3^Cov(1,3)+2*w2*w3^Cov(2,3) | |||||||||
| Vp | Portfolio Variance | 35.20546 | %% | ||||||
| Sp=SQRT(Vp) | Portfolio Standard Deviation=Square Root (Portfolio Variance) | ||||||||
| Sp=SQRT(Vp) | Portfolio Standard Deviation= | 5.933419 | % | ||||||
| b) | Portfolio Standard Deviation= | 5.9% | |||||||
| c) | Negative Return in one month | ||||||||
| Return Less than Zero | |||||||||
| X< or =0 | |||||||||
| Refering to "Cumulative Area Under Standard Normal Distribution" Table | |||||||||
| D= | (X-Mean)/ Std Deviation=(0-2.47)/5.9= | -0.41864 | |||||||
| For D Value =-0.42 | |||||||||
| N(d)=0.3372 | |||||||||
| Probability of return being Negative | 0.3372 | ||||||||
| Probability of return being Negative | 33.72% | ||||||||
| d) | Return Greater than 4% | ||||||||
| X>or =4% | |||||||||
| Refering to "Cumulative Area Under Standard Normal Distribution" Table | |||||||||
| D= | (X-Mean)/ Std Deviation=(4-2.47)/5.9= | 0.259322 | |||||||
| For D Value =-0.26 | |||||||||
| N(d)=0.6026 | |||||||||
| Probability of return being Less than 4% | 0.6026 | ||||||||
| Probability of return being Greater than 4% |
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