FM11_Ch_05_Tool_Kit - Michael C Ehrhardt Model Ch 05 Tool...

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983ee486f2b383ac35dd7b729bba9bf726517f7e.xls Model Michael C. Ehrhardt Page 1 01/20/2014 Ch 05 Tool Kit 5/2/2003 Chapter 5. Tool Kit for Risk and Return: Portfolio Theory and Asset Pricing Models PROBABILITY DISTRIBUTIONS The probability distribution is a listing of all possible outcomes and the corresponding probability. Rate of Return Distribution E F G H 0.10 10% 6% 14% 4% 0.20 10% 8% 12% 6% 0.40 10% 10% 10% 8% 0.20 10% 12% 8% 15% 0.10 10% 14% 6% 22% 1.00 EXPECTED RATE OF RETURN AND STANDARD DEVIATION Calculation of expected return and standard deviation for E Expected rate of return for E Standard deviation for E Rate of Return Product Sq Dev * Prob. 10% 10% 1.00% 0% 0.00% 0.00% 20% 10% 2.00% 0% 0.00% 0.00% 40% 10% 4.00% 0% 0.00% 0.00% 20% 10% 2.00% 0% 0.00% 0.00% 10% 10% 1.00% 0% 0.00% 0.00% 100% Sum: 0.00% 10% 0.00% Indirect method r hat = 10% 0.00% Calculation of expected return and standard deviation for F Expected rate of return for F Standard deviation for F Rate of Return Product Sq Dev * Prob. 10% 6% 0.60% -4% 0.16% 0.02% 20% 8% 1.60% -2% 0.04% 0.01% 40% 10% 4.00% 0% 0.00% 0.00% 20% 12% 2.40% 2% 0.04% 0.01% 10% 14% 1.40% 4% 0.16% 0.02% 100% Sum: 0.05% 10% 2.19% Indirect method r hat = 10% 2.19% Calculation of expected return and standard deviation for G Expected rate of return for G Standard deviation for G Rate of Return Product Sq Dev * Prob. 10% 14% 1.40% 4% 0.16% 0.02% 20% 12% 2.40% 2% 0.04% 0.01% 40% 10% 4.00% 0% 0.00% 0.00% 20% 8% 1.60% -2% 0.04% 0.01% 10% 6% 0.60% -4% 0.16% 0.02% 100% Sum: 0.05% 10% 2.19% Indirect method r hat = 10.00% 2.19% Calculation of expected return and standard deviation for H Expected rate of return for H Standard deviation for H Rate of Return Product Sq Dev * Prob. 10% 4% 0.40% -6% 0.36% 0.04% 20% 6% 1.20% -4% 0.16% 0.03% 40% 8% 3.20% -2% 0.04% 0.02% 20% 15% 3.00% 5% 0.25% 0.05% 10% 22% 2.20% 12% 1.44% 0.14% 100% Sum: 0.28% 10.00% 5.27% Indirect method r hat = 10.00% 5.27% COVARIANCE Calculation of covariance between F and G 10% -4% 4% -0.1600% -0.02% 20% -2% 2% -0.0400% -0.01% 40% 0% 0% 0.0000% 0.00% 20% 2% -2% -0.0400% -0.01% 10% 4% -4% -0.1600% -0.02% 100% -0.048% Calculation of covariance between F and H 10% -4% -6% 0.2400% 0.02% 20% -2% -4% 0.0800% 0.02% 40% 0% -2% 0.0000% 0.00% 20% 2% 5% 0.1000% 0.02% 10% 4% 12% 0.4800% 0.05% 100% 0.108% Calculation of covariance between F and E 10% -4% 0% 0.0000% 0.00% 20% -2% 0% 0.0000% 0.00% 40% 0% 0% 0.0000% 0.00% 20% 2% 0% 0.0000% 0.00% 10% 4% 0% 0.0000% 0.00% 100% 0.000% CORRELATION COEFFICIENT Calculation of the correlation between F and G Covariance FG ÷ = -0.048% ÷ 2.19% 2.19% = -0.048% ÷ 0.048% -1.0 Calculation of the correlation between F and H Covariance FH ÷ = 0.108% ÷ 2.19% 5.27% = 0.108% ÷ 0.116% 0.935 PORTFOLIO RISK AND RETURN: THE TWO-ASSET CASE ATTAINABLE PORTFOLIOS: THE TWO ASSET-CASE Asset A Asset B Expected return, r hat 5% 8% 4% 10% Correlation = 1 1.00 0.00 5.00% 4.0% 0.90 0.10 5.30% 4.6% 0.80 0.20 5.60% 5.2% 0.70 0.30 5.90% 5.8% 0.60 0.40 6.20% 6.4% 0.50 0.50 6.50% 7.0% 0.40 0.60 6.80% 7.6% 0.30 0.70 7.10% 8.2% 0.20 0.80 7.40% 8.8% 0.10 0.90 7.70% 9.4% 0.00 1.00 8.00% 10.0% Correlation = 0 1.00 0.00 5.00% 4.0% 0.90 0.10 5.30% 3.7% 0.80 0.20 5.60% 3.8% 0.70 0.30 5.90% 4.1% 0.60 0.40 6.20% 4.7% 0.50 0.50 6.50% 5.4% 0.40 0.60 6.80% 6.2% 0.30 0.70 7.10% 7.1% 0.20 0.80 7.40% 8.0% 0.10 0.90 7.70% 9.0% 0.00 1.00 8.00% 10.0% Correlation = -1 1.00 0.00 5.00% 4.0% 0.90 0.10 5.30% 2.6% 0.80 0.20 5.60% 1.2% 0.70 0.30 5.90% 0.2% 0.60 0.40 6.20% 1.6% 0.50 0.50 6.50% 3.0% 0.40 0.60 6.80% 4.4% 0.30 0.70 7.10% 5.8% 0.20 0.80 7.40% 7.2% 0.10 0.90 7.70% 8.6% 0.00 1.00 8.00% 10.0% ATTAINABLE AND EFFICIENT PORTFOLIOS: MANY ASSETS OPTIMAL PORTFOLIOS EFFICIENT SET WITH A RISK-FREE ASSET OPTIMAL PORTFOLIO WITH A RISK-FREE ASSET CALCULATING BETAS Date March 2003 0.8% 6.0% 1.1% 0.09% 0.7% 5.9% February 2003 -1.7% 4.7% -1.2% 0.10% -1.8% 4.6% January 2003 -2.7% -5.0% -2.8% 0.10% -2.8% -5.1% December 2002 -6.0% -9.5% -7.2% 0.10% -6.1% -9.6% November 2002 5.7% 7.4% 5.2% 0.10% 5.6% 7.3% October 2002 8.6% 2.4% 9.4% 0.13% 8.5% 2.3% September 2002 -11.0% -17.7% -10.8% 0.14% -11.1% -17.8% August 2002 0.5% -6.4% 1.0% 0.14% 0.4% -6.5% July 2002 -7.9% 10.8% -7.2% 0.14% -8.0% 10.7% June 2002 -7.2% -6.1% -7.7% 0.14% -7.4% -6.3% May 2002 -0.9% -1.3% -0.3% 0.14% -1.1% -1.4% April 2002 -6.1% -15.6% -6.4% 0.14% -6.3% -15.8% March 2002 3.7% -2.9% 3.4% 0.15% 3.5% -3.0% February 2002 -2.1% 4.1% -1.7% 0.14% -2.2% 4.0% January 2002 -1.6% -7.3% -3.1% 0.14% -1.7% -7.4% December 2001 0.8% 4.6% 0.7% 0.14% 0.6% 4.4% November 2001 7.5% 5.7% 7.5% 0.16% 7.4% 5.6% October 2001 1.8% -2.1% 2.4% 0.18% 1.6% -2.3% September 2001 -8.2% -8.6% -8.1% 0.22% -8.4% -8.8% August 2001 -6.4% -6.0% -6.5% 0.28% -6.7% -6.3% July 2001 -1.1% -10.9% -1.5% 0.29% -1.4% -11.2% June 2001 -2.5% 0.0% -2.5% 0.29% -2.8% -0.3% May 2001 0.5% 1.0% 0.9% 0.30% 0.2%
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