ch 13 (Risk Return and CAPM)

ch 13 (Risk Return and CAPM) - Key Concepts and Skills Know...

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Chapter 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 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%
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Slide 13 - 4 Variance, Standard Deviation ± Calculating the Return Volatility z Variance ( σ 2 ) and standard deviation ( σ ) They measure the volatility of returns. The variance is the weighted average of squared deviations: ¾ Usually with unequal probabilities ( p i ). ¾ The standard deviation is the square root of the variance. ¾ The formula is for a population, which is different from the formulas for a sample (see chapter 12 for historical returns). [] = = n i i i R E R p 1 2 2 ) ( σ 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 =0.3(15 - 9.9) 2 +0.5(10 - 9.9) 2 +0.2(2 - 9.9) 2 = 20.29 σ = 4.5 Stock T: σ 2 =0.3(25 - 17.7) 2 +0.5(20 - 17.7) 2 +0.2(1-17.7) 2 =74.41 σ = 8.63 Variance, Standard Deviation Slide 13 - 6 Example : Consider the return for ABC, Inc. State Probability ABC, Inc. Boom 0.25 15% Normal 0.50 8% Slowdown 0.15 4% Recession 0.10 -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 and return for a portfolio are measured by the portfolio expected return and standard deviation, just as with individual assets.
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Slide 13 - 8 Portfolio Expected Returns ± Computing Portfolio Expected Return z Find the portfolio return in each possible state (as below) and compute the expected value as we did with individual securities: R P = w 1 R 1 + w 2 R 2 + … + w m R m
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ch 13 (Risk Return and CAPM) - Key Concepts and Skills Know...

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