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Chap013s

# Chap013s - Return Risk and the Security Market Line Chapter...

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Return, Risk, and the Security Market Line Chapter Thirteen 1

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Expected Returns Expected returns are based on the probabilities of possible 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 ) ( 2
Example: Expected Returns Suppose 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 0.15 0.25 Normal 0.5 0.10 0.20 Recession 0.2 0.02 0.01 • R C = .3(.15) + .5(.10) + .2(.02) = .099 = 9.99% • R T = .3(.25) + .5(.20) + .2(.01) = .177 = 17.7% 3

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Variance and Standard Deviation Variance and standard deviation still measure the volatility of returns Weighted average of squared deviations = - = n i i i R E R p 1 2 2 )) ( ( σ 4
Example: Variance and Standard Deviation Consider the previous example. What are the variance and standard deviation for each stock? Stock C σ 2 = .3(.15-.099) 2 + .5(.1-.099) 2 + . 2(.02-.099) 2 = .002029 σ = .045 Stock T σ 2 = .3(.25-.177) 2 + .5(.2-.177) 2 + . 2(.01-.177) 2 = .007441 σ = .0863 5

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Another Example Consider the following information: State Probability ABC, Inc. Boom .25 .15 Normal .50 .08 Slowdown .15 .04 Recession .10 -.03 What is the expected return? What is the variance? What is the standard deviation? 6
Portfolios A portfolio is a collection of assets An asset’s risk and return is important in how it affects the risk and return of the portfolio The risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets 7

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Example: Portfolio Weights Suppose you have \$15,000 to invest and you have purchased securities in the following amounts. What are your portfolio weights in each security? \$2000 of DCLK \$3000 of KO \$4000 of INTC \$6000 of KEI DCLK: 2K/15K = .133 KO: 3K/15K = .2 INTC: 4K/15K = .267 KEI: 6K/15K = .4 8
Portfolio Expected Returns The expected return of a portfolio is the weighted average of the expected returns for each asset in the portfolio You can also find the expected return by finding the portfolio return in each possible state and computing the expected value as we did with individual securities = = m j j j P R E w R E 1 ) ( ) ( 9

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Example: Expected Portfolio Returns Consider the portfolio weights computed previously. If the individual stocks have the following expected returns, what is the expected return for the portfolio?
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