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Chapter 11. Risk and return - Opportunity cost and CAPM

# Chapter 11. Risk and return - Opportunity cost and CAPM -...

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Risk and return - Opportunity cost and CAPM Chapter 11 Finance 357

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Expected Return and Variance Analysts believe that two companies, Supertech Inc. R A and Slowpoke Inc. R B will perform according to the chart below next year. The returns of Supertech follow the economy closely, while Slowpoke does not. State of the Economy Probability of State of the Economy Supertech Returns R A Slowpoke Return R B Depression .10 -30% 0% Recession .20 -10% 5% Normal .50 20% 20% Boom .20 50% -5%
Expected Return We calculate the expected return exactly as we would in a statistics class. Multiply the returns by the probabilities and sum them. Supertech Inc. .10(-.30) + .2(-10) + .50(.20) + .20(.50) = 15% Slowpoke Inc. .10(.00) + .2(.05) + .50(.20) + .20(-.05) = 10%

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Steps for Calculating Variance and Standard Deviation 1. Calculate Expected Returns 2. Calculate deviation from expected return 3. Square deviations from expected return 4. Multiply squared deviation by its probability and sum the products to get the variance 5. Take the square root of the variance to get the standard deviation
Calculating Variance and Standard Deviation (1) State of the Economy (2) Probability of State of the Economy (3) Rate of Return (4) Deviation from Expected Return (5) Squared Value of Deviation (6) Product (2) x (5) Supertech (Expected return = .15) R A R A – E(R A ) (R A – E(R A )) 2 Depression .10 -.30 -.45 .2025 .02025 Recession .20 -.10 -.25 .0625 .01250 Normal .50 .20 .05 .0025 .00125 Boom .20 .50 .35 .1225 .02450 Var(R A ) = σ 2 A = .05850 Standard Deviation =Var(R σ Square Root of .0585 = 24.2% (1) State of the Economy (2) Probability of State of the Economy (3) Rate of Return (4) Deviation from Expected Return (5) Squared Value of Deviation (6) Product (2) x (5) Slowpoke (Expected return = .10) R A R A – E(R A ) (R A – E(R A )) 2 Depression .10 .0 -.10 .0100 .00100 Recession .20 .05 -.05 .0025 .00050 Normal .50 .20 .10 .0100 .00500 Boom .20 -.05 -.15 .0225 .00450 Var(R B ) = σ 2 B = .01100 Standard Deviation= Var(R A ) = σ 2 A = Square Root of .0110 = 10.5%

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Meaningful Statistics The variance and standard deviations of stocks tell us about the variability of the individual stocks. To measure the relationship between two stocks, we use covariance and correlation. Remember that a correlation value of 1 means that two securities move perfectly together and a -1 correlation means that the securities move perfectly opposite of each other
Graphical Correlations

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Covariance and Correlation Calculate Correlation of the returns Supertech and Slowpoke are negatively correlated (1) State of the Economy (2) Probability of State of the Economy (3) Supertech (4) Slowpoke (5) Product of Deviations (6) Product of (2) x (5) Deviation from Expected Return Depression .10 -.45 -.10 .0450 .00450 Recession .20 -.25 -.05 .0125 .00250 Normal .50 .05 .10 .0050 .00250 Boom .20 .35 -.15 -.0525 -.01050 Cov(R A, R B ) = σ A,B -.001
Portfolio Statistics Portfolio – a combination of securities The expected return on a portfolio is the weighted average of the expected returns on the individual securities

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Portfolio Expected Return The expected return of a portfolio composed of 60% Supertech and 40% Slowpoke =(.6 x .15) + (.4 x .10) = 13% Item Symbol Value Expected Return on Supertech E(R Super ) 15% Expected return on Slowpoke E(R slow ) 10%
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