ch 13 (Risk Return and CAPM)

# ch 13 (Risk Return and CAPM) - 13 Return Risk and the...

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13 Return, Risk, and the Security Market Line Slide 13 - 1 Key Concepts and Skills ± Know how to calculate expected returns and variance for individual asset and for portfolios ± Understand systematic and unsystematic risks and the effect of diversification ± Understand the risk-return trade off ± Be able to use the Capital Asset Pricing Model

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Slide 13 - 2 Expected Returns ± Calculating the Expected Return The expected return, denoted as E(R), is the return investors expected on a risky asset in the future. It is based on the probabilities of possible return outcomes: In this context, “expected” means average if the process is repeated many times. The “expected” return does not even have to be a possible return. = = n i i i R p R E 1 ) ( Slide 13 - 3 Expected Returns ± Example You have predicted the following returns for stocks C and T in three possible states of nature. What are the expected returns? State Probability C T Boom 0.3 15% 25% Normal 0.5 10% 20% Recession ? 2% 1% E(R C ) = .3(15) + .5(10) + .2(2) = 9.9% E(R T ) = .3(25) + .5(20) + .2(1) = 17.7%
Slide 13 - 4 Variance, Standard Deviation ± Calculating the Return Volatility Variance ( σ 2 ) and standard deviation ( σ ) measure the volatility of returns. The variance is the weighted average of squared deviations: [] = = n i i i R E R p 1 2 2 ) ( σ Note: (i) Usually unequal probabilities ( p i ). (ii) The standard deviation is the square root of the variance. (iii) The formula is for a population, which is different from the formulas for a sample (see chapter 12 for historical returns). Slide 13 - 5 ± Example Consider the previous example for stocks C and T. What are the variance and standard deviation for each stock? Stock C: σ 2 = .3(15-9.9) 2 + .5(10-9.9) 2 + .2(2-9.9) 2 = 20.29, σ = 4.5 Stock T: σ 2 = .3(25-17.7) 2 + .5(20-17.7) 2 + .2(1-17.7) 2 = 74.41 σ = 8.63 Variance, Standard Deviation

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Slide 13 - 6 ± Example: ABC, Inc. State Probability ABC, Inc. Boom .25 15% Normal .50 8% Slowdown .15 4% Recession .10 -3% What is the expected return? What is the variance? What is the standard deviation? Expected return: E(R) = 0.25(15)+0.5(8)+0.15(4)+0.1(-3) = 8.05% Return variance = 0.25(15-8.05) 2 + 0.5(8-8.05) 2 + 0.15(4-8.05) 2 + 0.1(-3-8.05) 2 = 26.7475 Standard Deviation = 5.1717985% Variance, Standard Deviation Slide 13 - 7 Portfolios ± Concept z A portfolio is a collection of assets, such as stocks and bonds, held by an investor. z The risk and return of the portfolio depend on the risk and return of each asset in the portfolio. z The risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets
Slide 13 - 8 Portfolio Expected Returns ± Computing Portfolio Expected Return The expected return of a portfolio is the weighted average of the expected returns of the respective assets in the portfolio You can also find the expected return by finding the portfolio return in each possible state (as below) and computing the

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ch 13 (Risk Return and CAPM) - 13 Return Risk and the...

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