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# 7 - Chapter 13 Return Risk and the Security Market Line...

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Faculty of Business and Economics University of Hong Kong Dr. T. Lin Chapter 13: Return, Risk and the Security Market Line

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2 Chapter 12 Sample portfolios Measurement Facts and Evidence Efficient Market Hypothesis Return Risk Chapter13 Population Individual stocks and portfolio stocks Measurement Diversification SML/CAPM
Basic Probability 3 Expected Return Variance and standard deviation Covariance and correlation

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An Example 4 Stock A and B have the following probability distribution of possible outcomes: Probability Return on A Return on B 0.30 10% 35% 0.50 14% 20% 0.20 20% 10%
Expected Return 5 Expected Return for A: Similarly the expected return for B is 22.5%. 3 1 0.30(10%) 0.50(14%) 0.20(20%) 14.00% A n n n px

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Expected versus Unexpected Returns 6 Realized returns are generally not equal to expected returns There is the expected component and the unexpected component At any point in time, the unexpected return can be either positive or negative Over time, the average of the unexpected component is zero
Variance and Standard Deviation 7 The variance of stock A: The standard deviation is     2 2 1 2 22 0.30(.1 .14) 0.50 .14 .14 0.20(.20 .14) .12% N A n n A n px         2 .12% 3.46% AA    

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Covariance 8 The covariance of A and B is:    1 0.30(.1 .14)(.35 .225) 0.50(.14 .14)(.2 .225) 0.20(.2 .14)(.1 .225) .3% AB N n n A n B n p x y 
Correlation Coefficient 9 The correlation coefficient between A and B is:    .3% 3.46% 9.01% 0.96 AB AB AB  

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Summary Results for A and B 10 A B Mean Standard Deviation 14.00% 3.46% 22.50% 9.01% Correlation Coefficient -0.96
Portfolio Mean and Variance 11 A Portfolio is a combination of two or more stocks. Suppose that you have \$100 and invest \$20 in stock A and the remaining \$80 in stock B, what are the portfolio expected return and variance?

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Portfolio Mean 12 Portfolio weights: Stock A: W A = 20% Stock B: W B = 80% Portfolio expected return:       20% 14% 80% 22.5% 20.8% P A A B B ww 
Portfolio Variance and Standard Deviation 13 Portfolio Variance Portfolio standard deviation         2 2 2 2 2 22 2 20% .12% 80% .81% 2 20% 80% .3% 0.43% P A A B B A B AB w w w w  2 .43 6.55% pp    

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Portfolio Expected Return & Risk 14 Expected Return Risk
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7 - Chapter 13 Return Risk and the Security Market Line...

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