1. You may answer these questions using any format:
a. Write your answers and calculations in the spaces provided Type your answers and calculations in the spaces provided.
2. Do your calculations on Excel using formulas and functions
3. Show all calculations or calculator inputs. If you use Excel, you must use formulas or functions. If you use Solver, include screenshots of your Solver setups. I cannot award partial credit if you just give me numbers.
4. Make sure to state any assumptions that you make in addition to those in the question.
1. You have the following historical information for a mutual fund:
|
Year
|
Total Return
|
|
2013
|
10%
|
|
2014
|
16%
|
|
2015
|
-22%
|
|
2016
|
4%
|
|
2017
|
20%
|
a. Compute the arithmetic mean return for the fund over the 5 years.
b. Computeyour ending wealth for 2017 if you had invested $10,000 in the fund at the beginning of 2013
c. Compute the annualized return for the fund over the 5 years
d. Citeone situation where you would use arithmetic mean and one where you would use annualized return. Explain why the method of calculating average return you chose is appropriate for each case.
Continuing with the same fund data:
Year Total Return
2013 10%
2014 16%
2015 -22%
2016 4%
2017 20%
e. The standard deviation of the fund is 16.6%. If the US T-bill rate is 2%, and investors' utility functions follow the formula,
U = E( r) - ½ Aσ2
i. Calculate the coefficient of risk aversion (A) at which an investor would be indifferent between the fund and the T-bill.
ii. Suppose an investor had a coefficient of risk aversion of A = 4. Calculate the Certainty Equivalent Rate for this fund.
iii. Explain what the Certainty Equivalent Rate represents.
f. The Downside Risk (Lower Partial Standard Deviation) for the fund is 13.8%. Explain how this might change an investor's perception of the riskiness of the fund.
2. You are considering the following investing in a US stock index fund and a US bond index fund. These represent the only 2 investments available to you at this time. You have the following additional information:
|
|
US Stocks
|
US Bonds
|
|
Expected Return
|
25%
|
15%
|
|
Standard Deviation
|
27%
|
20%
|
|
Variance
|
0.0729
|
0.0400
|
|
ρS,B
|
0.70
|
|
Covariance (S,B)
|
0.0378
|
a. Calculate the weights for stocks and bonds for the minimum variance portfolio. Show your work (if you are using Excel, include a screenshot of your Solver setup).
b. Suppose you have a target expected return of 17% for your portfolio.
i. Calculate the weights of the Stock/Bond portfolio that satisfies this requirement.
ii. Calculate the standard deviation of your target portfolio Show your work.
3. Continuing with the stock index fund and bond index fund data, you now have the 3-month T-bill available for investment. You have such a stellar credit rating that you can borrow at the T-bill rate (of 2%) as well. (NOTE: You don't need any calculations from Q2 for this question.)
|
|
US Stocks
|
US Bonds
|
T-Bill
|
|
Expected Return
|
25%
|
15%
|
2%
|
|
Standard Deviation
|
27%
|
20%
|
|
|
Variance
|
0.0729
|
0.0400
|
|
|
ρS,B
|
0.70
|
|
|
Covariance (S,B)
|
0.0378
|
|
a. Calculate the weights for stocks and bonds for the Optimal RiskyPortfolio. Show your work (if you are using Excel, include a screenshot of your Solver setup).
b. Calculate:
i. theexpected return for the Optimal RiskyPortfolio;
ii. the standard deviationfor the Optimal RiskyPortfolio; and
iii. theratio the Optimal RiskyPortfolio maximizes (ie, the ratio that makes it the optimal portfolio).
c. Explain why maximizing this ratio is desirable.
d. Calculate the weights of the CompletePortfolio that satisfies a target return of 17% for your portfolio.
e. Calculate the standard deviation of your target complete portfolio. Show your work.
4. Professors H, J, and K are having a conversation about investments. They all participate in a retirement plan where they can invest in any combination of a US stock index fund and a US bond index fund. They have similar time horizons and net worths, and are all risk averse.
Professor K says,
"Professor H, you are missing out. If you take just a little more risk, you can get as much expected return as Professor J and will be better off."
a. Explain why Professor K is wrong. Ignore any other investments they may have outside this illustration.No calculations are necessary.
Illustration for Part a
The retirement plan announces that it has added another asset: US T-Bills.
Professor J says,
"Now you are both wrong. Since we can now also invest in T-Bills in our retirement plan, you would both be better off investing some of your wealth in my asset allocation."
b. Explain why Professor J is right. Ignore any other investments they may have outside this illustration.No calculations are necessary.
Illustration for Part b
The retirement plan announces that it has added another asset: an International Index Fund.
Professor L comes in and says,
"If you include the new International fund being offered, you can all be better off."
c. Explain why Professor L is right. Ignore any other investments they may have outside this illustration. No calculations are necessary.(5 points)
Illustration for Part c
5. Suppose there is an investor with a very high risk tolerance. She could invest 100% of her wealth in a stock fund with σ= 17% and E(r ) = 15%, or she could borrow, and invest in the Optimal Risky Portfolio which has σ= 12% and E(r ) = 12%. Leverage would give her a higher E(r ) but with the same standard deviation as the stock fund (17%), if she can get a good borrowing rate.
a. Assuming she can borrow at the T-Bill (risk-free) rate of 2%,calculatethe weights for the investor to create herComplete Portfolio.
b. Calculate the Expected Return for this Complete Portfolio.
c. Calculate the maximuminterest rate at which the investor would be willing to borrow before she decided to just invest 100% in the Stock fund (assuming the same weights as you calculated in Part a).
In other words, calculatethe breakeven borrowing rate. Show your work. If you use Solver in Excel, provide a screenshot and explain your setup.
Attachment:- Portfolio-management-work.rar