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 You have the following historical information for a mutual fund:
Year  Total Return 
2014  16% 
2015  22% 
2016  4% 
2017  20% 
2018  7% 

 Compute the arithmetic mean return for the fund over the 5 years. (3 points)

 Compute your ending wealth for 2018 if you had invested $10,000 in the fund at the beginning of 2014. (3 points)

 Compute the annualized return for the fund over the 5 years. (3 points)

 Cite one 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. (6 points)
[15 total]
Continuing with the same fund data:
Year  Total Return 
2014  16% 
2015  22% 
2016  4% 
2017  20% 
2018  7% 
 The standard deviation of the fund is 4%. If the US Tbill rate is 2%, and investors’ utility functions follow the formula,
U = E( r) – ½ As^{2}
 Suppose one investor has a coefficient of risk aversion of A = 2, while another investor has a coefficient of risk aversion of A=6. Calculate the Certainty Equivalent Rates for this fund for each investor. (4 points)
 Explain why the Certainty Equivalent Rates are different for the two investors in Part (i). Refer to the meaning of Certainty Equivalent (not just the math of the utility function above) in your explanation. (4 points)
 The Downside Risk (Lower Partial Standard Deviation) for the fund is 5%. Explain how this might change an investor’s perception of the riskiness of the fund. (3 points)
[10 total]
 You are considering the following investments 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 (Fund S)  US Bonds (Fund B)  
Expected Return  18%  10% 
Standard Deviation  23%  14% 
Variance  0.0529  0.0196 
r_{S,B}  0.40  
Covariance (S,B)  0.01288 

 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). (7 points)

 Suppose you have a target expected return of 12% for your portfolio.
 Calculate the weights of the Stock/Bond portfolio that satisfies this requirement. (5 points)
 Calculate the standard deviation of your target portfolio Show your work. (8 points)
[20 total]
 Continuing with the stock index fund and bond index fund data, you now have the 3month Tbill available for investment. You have such a stellar credit rating that you can borrow at the Tbill rate (of 2%) if you wish to do so. (NOTE: You don’t need any calculations from Q2 for this question.)
US Stocks  US Bonds  TBill  
Expected Return  18%  10%  2% 
Standard Deviation  23%  14%  
Variance  0.0529  0.0196  
r_{S,B}  0.40  
Covariance (S,B)  0.01288 

 Calculate the weights for stocks and bonds for the Optimal Risky Portfolio. Show your work (if you are using Excel, include a screenshot of your Solver setup). (5 points)

 Calculate:
 the expected return for the Optimal Risky Portfolio;
 the standard deviation for the Optimal Risky Portfolio; and
 the ratio the Optimal Risky Portfolio maximizes (ie, the ratio that makes it the optimal portfolio). (15 points)
[20 total]

 Explain why maximizing this ratio is desirable. (2 points)

 Calculate the weights of the Complete Portfolio that satisfies a target return of 12% for your portfolio. (3 points)
 Calculate the standard deviation of your target complete portfolio. Show your work. (2 points)
 Calculate the RewardtoRisk Ratio of your target complete portfolio. Show your work. (3 points)
[10 total]
 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 (There’s no TBill investment offered in the retirement plan, and this is the only savings vehicle for all three of them). 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.”
 Explain why Professor K is wrong. Ignore any other investments they may have outside this illustration. No calculations are necessary. (5 points)
Illustration for Part a
Asset allocations of US Stock Index and US Bond Index Funds. 
Professor K’s allocation 
Professor H’s allocation 
Professor J’s allocation 
[5 total]
The retirement plan announces that it has added another asset: US TBills. Participants in the plan may lend or borrow at the TBill rate.
Professor J says,
“Now you are both wrong. Since we can now also invest in TBills in our retirement plan, you would both be better off investing some of your wealth in my asset allocation instead of yours.”
 Explain why Professor J is right. Ignore any other investments they may have outside this illustration. No calculations are necessary. (5 points)
Illustration for Part b
Professor H 
Asset allocations with Stock Index and Bond Index Funds, plus TBills. 
Asset allocations with Stock Index and Bond Index Funds. 
Professor J 
TB 
Professor K 
[5 total]
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.”
 Explain why Professor L is right. Ignore any other investments they may have outside this illustration. No calculations are necessary. (5 points)
Asset allocations combining the Stock Index, Bond Index, and International Index Funds, and TBills. 
Illustration for Part c
L 
Asset allocations combining the Stock Index, Bond Index, and International Index Fund. 
Asset allocations with only the Stock Index and Bond Index Funds. 
TB 
K 
J 
H 
[5 total]
 (Note: You don’t need calculations from any other answers for this question.)
Suppose there is an investor with a very high risk tolerance. She could invest 100% of her wealth in a different stock index fund (for example Russell 2000 vs S&P 500 Index funds), with s = 20% and E(r ) = 16%, or she could borrow, and invest in the Optimal Risky Portfolio which has s = 15.5% and E(r ) = 13%. Leverage would give her a higher E(r ) but with the same standard deviation as the stock fund (20%), if she can get a good borrowing rate.
 Assuming she can borrow at the TBill (riskfree) rate of 2%, calculate the weights for the investor to create her Complete Portfolio. (3 points)
 Calculate the Expected Return for this Complete Portfolio, assuming the borrowing rate = 2% (the TBill rate). (2 points)
 Calculate the maximum interest 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, calculate the breakeven borrowing rate. Show your work. If you use Solver in Excel, provide a screenshot and explain your setup. (5 points)
[10 total]