Chapter3

# Chapter3 - volatility of a stock’s returns with the...

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Economy Probability Stock X Stock Y Boom 60% 11% 14% Average 30% 5% 4% Bust 10% -4% -6% Expected Return X = (.6*11) + (.3*5) + (.1 * - 4) = 7.7 % Expected Return Y = (.6*14) + (.3*4) + (.1* - 6) = 9.0 % σ 2 x = [(11 - 7.7) 2 * .6] + [(5 - 7.7) 2 *.3] + [(-4 - 7.7) 2 * .1] = 6.534 + 2.187 + 13.689 = 22.41 σ x = 4.73% σ 2 y = [(14 - 9) 2 * .6] + [(4 - 9) 2 * .3] + [(-6 - 9) 2 * .1] = 15 + 7.5 + 22.5 = 45.0 σ y = 6.71%

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CV of X = 4.73/7.7 = 0.61 CV of Y = 6.71/9.0 = 0.75
Forming a portfolio made up of 40% X and 60% Y What is the expected return for the portfolio? Portfolio expected return = (.4*7.7) + (.6*9.0) = 3.08 + 5.4 = 8.48 % What is the risk for the portfolio? Portfolio Variance = w 2 x σ 2 x + w 2 y σ y 2 + 2w x w y r xy σ x σ y At this point we know all the variables for variance except r xy r xy is the correlation coefficient for stocks x and y r xy ranges for –1 to + 1 r xy measures the degree of co-movement between two variables

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r xy = Cov (xy)/ σ x σ y Cov (xy) is the covariance between stocks x and y Covariance is a measure which combines the

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Unformatted text preview: volatility of a stock’s returns with the tendency of those returns to move up or down at the same time other stocks move up or down. Cov (xy) = Σ (x i – Expected x) * (y i – Expected y) (Probability) Cov (xy) = [(11 - 7.7)*(14 - 9.0)*.6] + [(5 - 7.7) *(4 - 9.0)*.3] + = [(-4 - 7.7)*(-6 - 9.0)*.1] = 9.9 + 4.05 + 17.55 = 31.50 r xy = 31.50/(4.73*6.71) = 31.50/31.74 = 0.99 Portfolio Variance = w 2 x σ 2 x + w 2 y σ y 2 + 2w x w y r xy σ x σ y = (.4 2 *22.41) + (.6 2 *45.0) + 2*.4*.6*.99*4.73*6.71 = 3.586 + 16.20 + 15.082 = 34.868 Portfolio Std. Dev = 5.90% What if we form a portfolio of 20% X and 80%Y? What is the expected return of the portfolio? What is the portfolio standard deviation? Expected return = (.2 * 7.7) + (.8 * 9.0) = 1.54 + 7.2 = 8.74 % Portfolio Variance = = (.2 2 *22.41) + (.8 2 *45.0) + 2*.2*.8*.99*4.73*6.71 = 0.896 + 28.80 + 10.055 = 39.751 Portfolio Standard Deviation = 6.30%...
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Chapter3 - volatility of a stock’s returns with the...

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