Chapter 8-Spreadsheet Model - A B C D E F G 1 Chapter 8...

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Chapter 8. Risk and Rates of Return 12/11/08 Table 8-1. Probability Distributions and Expected Returns Martin Products U.S. Water Rate of Rate of Economy, Probability Return Probability Return Which of This If This of This If This Affects Demand Demand Product Demand Demand Product Demand Occurring Occurs (2)x(3) Occurring Occurs (5)x(6) (1) (2) (3) (4) (5) (6) (7) Strong 0.30 80% 24% 0.30 15% 4.5% Normal 0.40 10% 4% 0.40 10% 4.0% Weak 0.30 -60% -18% 0.30 5% 1.5% 1.00 Expected return= 10% 1.00 Expected return= 10% We use Excel to do the calculations shown in black boldface type. TABLE 8-2. Calculating Martin Product’s Standard Deviation Rate of Deviation: Economy, Probability Return Actual - Which of This If This 10% Squared Affects Demand Demand Expected Deviation Deviation Demand Occurring Occurs Return Squared x Prob. (1) (2) (3) (4) (5) (6) Strong 0.30 80% 70% 0.4900 0.1470 Normal 0.40 10% 0% 0.0000 0.0000 Weak 0.30 -60% -70% 0.4900 0.1470 1.00 ∑ = Variance: 0.294 Standard deviation = square root of variance: σ = 0.5422 Standard deviation expressed as a percentage: σ = 54.2% TABLE 8-3. Finding σ Based On Historical Data Deviation from Squared Year Return Average Deviation (1) (2) (3) (4) 2005 30.0% 19.8% 3.9% 2006 -10.0% -20.3% 4.1% 2007 -19.0% -29.3% 8.6% 2008 40.0% 29.8% 8.9% Average 10.3% Variance = ∑: 25.4% Variance / (N-1) = Variance/3: 8.5% Standard deviation = Square root of variance: σ = 29.1% Excel Function: STDEV(B41:B44) σ = 29.1% Expected Dollars Percent of Product: Stock Return Invested (2)x(4) (1) (2) (3) (4) (5) Microsoft 12.00% \$25,000 25.0% 3.000% IBM 11.50% \$25,000 25.0% 2.875% GE 10.00% \$25,000 25.0% 2.500% Exxon 9.50% \$25,000 25.0% 2.375% 10.75% \$100,000 100.0% 10.750% Figure 8-4. Returns With Perfect Negative Correlation, ρ = -1.0 Stocks W and M, held separately -20% 15% 40% Rate of Return (%) Portfolio WM -20% 15% 40% Rate of Return (%) Year Stock W Stock M Portfolio WM 2004 40% -10% 15% 2005 -10% 40% 15% 2006 40% -10% 15% 2007 -10% 40% 15% 2008 15% 15% 15% Avg return = 15.00% 15.00% 15.00% =AVERAGE(D88:D92) σ = 25.00% 25.00% 0.00% =STDEV(D88:D92) Correlation coefficient = -1.00 =CORREL(B88:B92,C88:C92) Figure 8-5. Partial Correlation, ρ = + 0.35 Stocks W and Y, held separately -20% 15% 40% Rate of Return (%) Portfolio WY -20% 15% 40% Rate of Return (%) Year Stock W Stock Y

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