hw5_ak - Solution to Problem Set 5 ECN 134 Finance...

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Solution to Problem Set 5 ECN 134 Finance Economics Prof. Farshid Mojaver Part A: Optimal Risky Portfolio 1. a. Even though it seems that gold is dominated by stocks, gold might still be an attractive asset to hold as a part of a portfolio. If the correlation between gold and stocks is sufficiently low, gold will be held as a component in a portfolio, specifically, the optimal tangency portfolio. b. If the correlation between gold and stocks equals +1, then no one would hold gold. The optimal CAL would be comprised of bills and stocks only. Since the set of risk/return combinations of stocks and gold would plot as a straight line with a negative slope (see the following graph), these combinations would be dominated by the stock portfolio. Of course, this situation could not persist. If no one desired gold, its price would fall and its expected rate of return would increase until it became sufficiently attractive to include in a portfolio. 2. The probability distribution is: Probability Rate of Return 0.7 100% 0.3 −50% Mean = [0.7 × 100] + [0.3 × ( - 50)] = 55% Variance = [0.7 × (100 - 55) 2 ] + [0.3 × ( - 50 - 55) 2 ] = 4725 Standard deviation = 4725 1/2 = 68.74% 3. σ P = 30 = y σ = 4 0 y y = 0.75 E(r P ) = 12 + 0.75(30 - 12) = 25.5%
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4. Since we do not have any information about expected returns, we focus exclusively on reducing variability. Stocks A and C have equal standard deviations, but the correlation of Stock B with Stock C (0.10) is less than that of Stock A with Stock B (0.90). Therefore, a portfolio comprised of Stocks B and C will have lower total risk than a portfolio comprised of Stocks A and B. 5. Rearranging the table (converting rows to columns), and computing serial correlation results in the following table: Nominal Rates Small company stocks Large company stocks Long-term government bonds Intermed-term government bonds Treasury bills Inflation 1920s -3.72 18.36 3.98 3.77 3.56 -1.00 1930s 7.28 -1.25 4.60 3.91 0.30 -2.04 1940s 20.63 9.11 3.59 1.70 0.37 5.36 1950s 19.01 19.41 0.25 1.11 1.87 2.22 1960s 13.72 7.84 1.14 3.41 3.89 2.52 1970s 8.75 5.90 6.63 6.11 6.29 7.36 1980s 12.46 17.60 11.50 12.01 9.00 5.10 1990s 13.84 18.20 8.60 7.74 5.02 2.93 Serial Correlation 0.46 -0.22 0.60 0.59 0.63 0.23 For example: to compute serial correlation in decade nominal returns for large- company stocks, we set up the following two columns in an Excel spreadsheet. Then, use the Excel function “CORREL” to calculate the correlation for the data.
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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.

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hw5_ak - Solution to Problem Set 5 ECN 134 Finance...

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