FBE441_Homework_2_solutions

FBE441_Homework_2_solutions - USC - MARSHALL SCHOOL OF...

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USC - MARSHALL SCHOOL OF BUSINESS FBE 441 Investments – P. Matos – Spring 2010 Solutions to Homework Assignment #2 Q.1. Consider the following data: Expected Return Standard Deviation Russell Fund 16% 12% Windsor Fund 14% 10% S&P Fund 12% 8% The correlation between the returns on the Russell Fund and the S&P Fund is .7. The rate on T-bills is 6%. Which of the following portfolios would you prefer to hold in combination with T-bills and why? (a) Russell Fund (b) Windsor Fund (c) S&P Fund (d) A portfolio of 60% Russell Fund and 40% S&P Fund. SOLUTION: The answer is D. The reason is that the 60-40 portfolio combination of the Russell Fund and the S&P 500 has the highest Sharpe ratio. In other words, this portfolio gives the best investment opportunity set together with the risk-free Treasury bill. More specifically, when you calculate the Sharpe ratio, that is, the slope of the capital allocation line, (E(R M ) R f )/ M , for each of the three mutual funds as well as the 60-40 combination, you find that the 60-40 combination has the highest slope. Here are the calculations: - Russell Fund: (E(R Russel ) R f )/ Russel = (.16 .06) / .12 = .8333 - Windsor Fund: (E(R Windsor ) R f )/ Windsor = (.14 .06) / .1 = .8 SP500 ) R f )/ SP500 = (.12 .06) / .08 = .75 - Portfolio of .6 in Russell + .4 in S&P 500: We have to calculate E(Rp) and p of this 60:40 portfolio. To do this, we use the formulas for the mean and standard deviation for a two-asset portfolio. Say that asset 1 is the Russell fund and asset 2 is the S&P. First, we calculate E(Rp): E(Rp) = .6E(R 1 ) + .4E(R 2 ) = .6(.16) + .4(.12) = .144 And now we calculate p: p = w 2 1 2 1 + w 2 2 2 2 + 2 w 1 w 2 1 2 1,2 + = (.6) 2 (.12) 2 + (.4) 2 (.08) 2 + 2(.6)(.4)(.7)(.12)(.08) = .0094336 therefore p = .097127
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So for the 60-40 combination we have: (E(R P ) R f )/ P = (.144 .06) / .097127 = .8648 Since .8648 > .8333 > .8 > .5, the slope for the capital allocation line with the 60-40 mutual fund combination is largest Q.2. Consider the data from the lecture notes on the US, UK and Japanese stock market: US UK Japan
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This note was uploaded on 10/11/2011 for the course FBE 441 taught by Professor Callahan during the Fall '07 term at USC.

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FBE441_Homework_2_solutions - USC - MARSHALL SCHOOL OF...

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