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% |
 jeff jeffy answered 1 year agoRelated SolutionsYou have had a portfolio made up of three assets. For each of these three assets,...
You have had a portfolio made up of three assets. For each of
these three assets, pricing data are below:
Price at the end of
Common stock A
Preferred Stock B
Coupon Bond C
year 0
$28
$100
$1,040
year 1
$30
$100
$1,050
year 2
$35
$102
$1,040
year 3
$41
$103
$1,050
year 4 (now)
$44
$105
$1,060
The common stock pays a common
dividend of $2 at the end of each year. The preferred stock pays a...
Comparing Two Population Means with Known Standard Deviations In this problem you do know the population...Comparing Two Population Means with Known Standard
Deviations
In this problem you do know the population standard deviation of
these independent normally distributed populations
The mean for the first set ¯xx¯ 1 = 15.49 with a
standard deviation of σσ 1 = 2.5 There sample size was
13.
The mean for the first set
¯xx¯ 2 = 15.796 with a standard
deviation of σσ 2 = 1.4 There sample size was 18.
Find the test statistic z= Round to 4
places.
Find the...
Indicate if the hypothesis test is for a. independent group means, population standard deviations, and/or variances known...Indicate if the hypothesis test is for
a. independent group means, population
standard deviations, and/or variances known
b. independent group means, population standard
deviations, and/or variances unknown
c. matched or paired samples
d. single mean
e. two proportions
f. single proportion
1. It is believed that 70% of males pass their drivers test
in the first attempt, while 65% of females pass the test in the
first attempt. Of interest is whether the proportions are in fact
equal.
2. A new...
You set up a portfolio made up of five o six funds.Analyse the portfolio you have...You set up a portfolio made up of five o six funds.Analyse the
portfolio you have set up taking into account the risk return
criteria and taking into account the macro economic factors of the
economy .Explain why you prefer managed funds or exchange traded
funds or a mixture of the two.Explain in detail these funds and why
you like these funds.You need to match your asset allocation with
your risk profile.
Consider two assets with means and standard deviations of returns given by arbitrary μ1 and σ1...Consider two assets with means and standard deviations of
returns given by arbitrary μ1 and σ1 > 0 for asset 1, and μ2 and
σ2 > 0 for asset 2. Suppose that correlation of returns is
different from −1, that is ρ12 > −1. Show that there is no
portfolio of these two assets that has risk-free return. Consider
only portfolios with positive weights, i.e., without short
sales.
Portfolio returns and deviations. Consider the following information on a portfolio of three stocks: State of...Portfolio returns and deviations. Consider the following
information on a portfolio of three stocks:
State of
Probability
of
Stock A Rate of return Stock B
ROR Stock C ROR
Economy
State of Economy
Boom
.15
.02
.32
.60
Normal
.60
.10
.12
.20
Bust
.25
.16
-.11
-.35
a. If your portfolio is invested 40 percent each in A and B and
20 percent in C, what is the portfolio's expected return? the
variance? the standard deviation?
b. if...
Explain the assertion that the relationship between the standard deviation on a portfolio and standard deviations...
Explain the assertion that the relationship between the
standard deviation on a portfolio and standard deviations of the
assets in the portfolio is not a simple one.
The standard deviation of a portfolio: Multiple Choice is a weighted average of the standard deviations...The standard deviation of a portfolio:
Multiple Choice
is a weighted average of the standard deviations of the
individual securities held in the portfolio.
is an arithmetic average of the standard deviations of the
individual securities which comprise the portfolio.
can never be less than the standard deviation of the most risky
security in the portfolio.
can be less than the standard deviation of the least risky
security in the portfolio.
must be equal to or greater than the lowest...
Assume a portfolio of assets is made up of two securities, security A and security B....
Assume a portfolio of assets is made up of two securities,
security A and security B. An amount of investment of GHS12,000 is
made in security A and GHS8000 is made in security B. The return
for security A is 30% and the return for security B is 20%. The
standard deviation for security A is 15% whilst the standard
deviation of security B is 10%. The correlation of return of
security A and return of security B is given...
1. Two samples are taken with the following sample means, sizes, and standard deviations ¯x1 =...1. Two samples are taken with the following sample means, sizes,
and standard deviations
¯x1 = 31 ¯x2 = 35
n1= 73 n2= 67
s1= 2 s2 = 5
Estimate the difference in population means using a 99% confidence
level. Use a calculator, and do NOT pool the sample variances.
Round answers to the nearest hundredth.
_____< μ1−μ2 <_____
2. You are conducting a test of independence for the claim that
there is an association between the row variable and...
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
ADVERTISEMENT
|