Question
In: Finance
Given that the risk-free rate is 5%, the expected return on the market portfolio is 20%,...
Given that the risk-free rate is 5%, the expected return on the market portfolio is 20%, and the standard deviation of returns to the market portfolio is 20%, answer the following questions:
a. You have $100,000 to invest. How should you allocate your wealth between the risk free asset and the market portfolio in order to have a 15% expected return?
b. What is the standard deviation of your portfolio in (a)?
c. Now suppose that you want to have a portfolio, which pays 25% expected return. What is the weight in the risk free asset and in the market portfolio?
d. What do these weights mean: What are you doing with the risk free asset and what are you doing with the market portfolio?
e. What is the standard deviation of the portfolio in c?
f. What is your conclusion about the effect of leverage on the risk of the portfolio?
PLEASE SHOW ALL WORK
Solutions
Expert Solution
| a] | Let the weight of the market portfolio be w. | |
| Then, the weight of the risk free asset = 1-w | ||
| Now, the expected return of 0.15 = 0.2*w+0.05*(1-w) | ||
| Solving for w, we have | ||
| 0.15 = 0.2*w+0.05-0.05*w | ||
| 0.15-0.05 = 0.2*w-0.05*w | ||
| 0.1 = 0.15*w | ||
| w = 0.1/0.15 = 66.67% | ||
| So, weight of the market portfolio = 66.67%, and | ||
| weight of the risk free asset = 1-66.67% = 33.33% | ||
| b] | As the SD of the risk free asset is 0 and its correlation | |
| with the market portfolio is also 0, the SD of the new | ||
| portfolio = (weight of the market portfolio^2*SD of the market portfolio^2)^0.5 = weight of the market portfolio*SD of the market portfolioi = 20%*66.67% = | 13.33% | |
| c] | Using similar equation as in [a] | |
| 0.25 = 0.2*w+0.05*(1-w) | ||
| 0.25 = 0.2*w+0.05-0.05*w | ||
| 0.20 = 0.15*w | ||
| w = 0.25/0.15 = 1.67 | ||
| Weight of the risk free asset = 1-1.6667 = -0.6667 | ||
| The weight of the risk free asset = -66.67%. | ||
| d] | It implies that borrowings are made at the risk free | |
| rate of 5% and then the borrowings along with equity | ||
| are invested in the market portfolio. The market | ||
| portfolio will have a weight of 166.67%. | ||
| e] | The SD [as in b] will be 20%*166.67% = | 33.33% |
| f] | Leverage will increase the risk of the portfolio. | |
jeff jeffy answered 5 months agoRelated Solutions
Given that the risk-free rate is 5%, the expected return on the market portfolio is 20%,...
Given that
the risk-free rate is 5%, the expected return on the market
portfolio is 20%, and the standard deviation of returns to the
market portfolio is 20%, answer the following
questions:
You have $100,000 to invest. How should you allocate your
wealth between the risk free asset and the market portfolio in
order to have a 15% expected return?
What is the standard deviation of your portfolio in (a)?
Now suppose that you want to have a portfolio, which...
Given that the risk-free rate is 5%, the expected return on the market portfolio is 20%,...
Given that the risk-free rate is 5%, the expected return on the
market portfolio is 20%, and the standard deviation of returns to
the market portfolio is 20%, answer the following questions:
a. You have $100,000 to invest. How should you allocate your
wealth between the risk free asset and the market portfolio in
order to have a 15% expected return?
b. What is the standard deviation of your portfolio in (a)?
c. Now suppose that you want to have...
Given that the risk-free rate is 5%, the expected return on the market portfolio is 20%,...
Given that
the risk-free rate is 5%, the expected return on the market
portfolio is 20%, and the standard deviation of returns to the
market portfolio is 20%, answer the following
questions:
You have $100,000 to invest. How should you allocate your
wealth between the risk free asset and the market portfolio in
order to have a 15% expected return?
What is the standard deviation of your portfolio in (a)?
Now suppose that you want to have a portfolio, which...
Given that the risk-free rate is 5% and the expected return on the market portfolio is...
Given that the risk-free rate is 5% and the expected return on the
market portfolio is 10%, if bush company's beta is 2, what is Dow's
expected return?
A. 18%
B. 21%
C. 10%
D. 15%
What is the best measure of risk for an asset that is to be
held in isolation (one stock portfolio)?
A. market risk
B. Beta
C. Diversifiable risk
D. Standard deviation
Which is the best measure of risk for choosing an asset which
is...
The risk-free rate is 5%, the expected return on the market portfolio is 14%, and the...
The risk-free rate is 5%, the expected return on the market
portfolio is 14%, and the standard deviation of the return on the
market portfolio is 25%. Consider a portfolio with expected return
of 16% and assume that it is on the efficient frontier. (a) What is
the beta of this portfolio? (b) What is the standard deviation of
its return? (c) What is its correlation with the market return? (d)
Draw the portfolio in two diagrams: one in the...
The risk-free rate of return is 6%, the expected rate of return on the market portfolio...
The risk-free rate of return is 6%, the expected rate of return
on the market portfolio is 15%, and the stock of Xyrong Corporation
has a beta coefficient of 2.3. Xyrong pays out 45% of its earnings
in dividends, and the latest earnings announced were $9.00 per
share. Dividends were just paid and are expected to be paid
annually. You expect that Xyrong will earn an ROE of 18% per year
on all reinvested earnings forever.
a. What is the...
The risk-free rate of return is 10.0%, the expected rate of return on the market portfolio...
The risk-free rate of return is 10.0%, the expected rate of
return on the market portfolio is 17%, and the stock of Xyrong
Corporation has a beta coefficient of 1.6. Xyrong pays out 30% of
its earnings in dividends, and the latest earnings announced were
$15 per share. Dividends were just paid and are expected to be paid
annually. You expect that Xyrong will earn an ROE of 20% per year
on all reinvested earnings forever.
a. What is the...
The risk-free rate of return is 6%, the expected rate of return on the market portfolio...
The risk-free rate of return is 6%, the expected rate of return
on the market portfolio is 14%, and the stock of Xyrong Corporation
has a beta coefficient of 1.3. Xyrong pays out 50% of its earnings
in dividends, and the latest earnings announced were $8.00 per
share. Dividends were just paid and are expected to be paid
annually. You expect that Xyrong will earn an ROE of 15% per year
on all reinvested earnings forever.
a. What is the...
The risk-free rate of return is 9.0%, the expected rate of return on the market portfolio...
The risk-free rate of return is 9.0%, the expected rate of
return on the market portfolio is 14%, and the stock of Xyrong
Corporation has a beta coefficient of 2.0. Xyrong pays out 50% of
its earnings in dividends, and the latest earnings announced were
$20 per share. Dividends were just paid and are expected to be paid
annually. You expect that Xyrong will earn an ROE of 18% per year
on all reinvested earnings forever.
a. What is the...
The risk-free rate of return is 9.0%, the expected rate of return on the market portfolio...
The risk-free rate of return is 9.0%, the expected rate of
return on the market portfolio is 14%, and the stock of Xyrong
Corporation has a beta coefficient of 2.0 resulting in a required
rate of return of 19.00%. Xyrong pays out 50% of its earnings in
dividends, and the latest earnings announced were $20 per share.
Dividends were just paid and are expected to be paid annually. You
expect that Xyrong will earn an ROE of 18% per year...
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- 4) Cost per equivalent unit of direct materials and conversion (4 marks) The cost per equivalent...
- We usually write numbers in decimal form (or base 10), meaning numbers are composed using 10...
- Consider a saturated solution of the salt MX3, which M is a metal cation with a...
- Energyshot is a new energy drink that is about to be introduced into the global market....
- Problem 1: During the month, EKM Enterprise purchased $100,000 in raw material on account, used $150,000...
- An electron is accelerated inside a parallel plate capacitor. The electron leaves the negative plate with...
- There is a region with a constant magnetic field 6.31T . The magnetic field is directed...
ADVERTISEMENT