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Unformatted text preview: Problem Set 5 (ECN 134) Finance Economics Prof. Farshid Mojaver Optimal Risky Portfolio part 1 1 . Stocks offer an expected rat of return of 18%, with a SD of 22%. Gold offers an expected return of 10% with a SD of 30%. a. In light of the apparent inefficiency of gold with respect to both mean return and volatility, would anyone hold gold? If so, demonstrate graphically why one would do so. b. Given the data above reanswer (a) with the additional assumption that the correlation coefficient between gold and stock equals 1. Draw a graph illustrating why one would or would not hold gold in one’s portfolio. Could this set of assumptions for expected return, SD, and correlation represent equilibrium for the security market? 2 . Suppose you have a project that has 70% chance of doubling your investment in a year and 30% chance of halving your investment in a year. What is the standard deviation of the rate of return on this investment? 3 . Suppose that you have $1 million and the following two opportunities from which to construct a portfolio: (a) Riskfree asset earning 12% per year, (b) Risky asset with expected return 30% per year and standard deviation of 40%. If you construct a portfolio with a standard deviation of 30%, what is the expected rate of return? 4 . Statistics for three stocks A, B, and C, are shown in the following tables. Standard Deviations of Returns Stock A B C Standard Deviation 40% 20% 40% Correlations of Returns Stock A B C A 1.00 0.90 0.50 B 1.00 0.10 C 1.00 Based only on the information provided in the tables, and given a choice between a portfolio made up of equal amounts of stocks A and B or a portfolio made up of equal amounts of stocks B and C, state which portfolio you would recommend. Justify your choice. The following table of compound annual returns by decade applies to Problems 5 & 6. 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s Smallcompany Stocks (%)3.72 7.28 20.63 19.01 13.72 8.75 12.46 13.84 Largecompany Stocks (%) 18.361.25 9.11 19.41 7.84 5.90 17.60 18.20 Longterm Government (%) 3.98 4.60 3.59 0.25 1.14 6.63 11.50 8.60 Intermediateterm Govt (%) 3.77 3.91 1.70 1.11 3.41 6.11 12.01 7.74 Treasury bills (%) 3.56 0.30 0.37 1.87 3.89 6.29 9.00 5.02 Inflation (%)1.002.04 5.36 2.22 2.52 7.36 5.10 2.93 5. Input the data from the table into a spreadsheet. Compute the serial correlation in decade returns for each asset class and for inflation. Also find the correlation between the returns of various asset classes. What do he data indicate? 6 . Convert the asset returns by decade presented in the table into real rates. Repeat the analysis of Problem 1 for the real rates of return. 7 . An investor’s portfolio consists of two assets, one (MSFT) producing computer software, and the other (GOOG) selling internet advertising. Ten years of hypothetical data on returns (in percent) for these two stocks are given below; save these data for use next week also....
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This note was uploaded on 11/02/2009 for the course ECON 134 taught by Professor Mojaver during the Summer '08 term at UC Davis.
 Summer '08
 MOJAVER
 Economics

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