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

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Return, Risk, and the Security Market Line Chapter Thirteen

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Chapter Outline Expected Returns and Variances Portfolios Announcements, Surprises, and Expected Returns Risk: Systematic and Unsystematic Diversification and Portfolio Risk Systematic Risk and Beta The Security Market Line The SML and the Cost of Capital: A Preview
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 1 1 2 2 ( ) n n E R p R p R p R = + +⋅⋅⋅+

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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 .2 0.02
Variance and Standard Deviation Variance and standard deviation still measure the volatility of returns Using unequal probabilities for the entire range of possibilities Weighted average of squared deviations 2 2 2 2 1 1 2 2 σ ( ( )) ( ( )) ( ( )) n n p R E R p R E R p R E R = - + - + ⋅⋅⋅ + -

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Example: Var and SD 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 σ 2 = .002029 => σ = 4.5% Stock T σ 2 = .3 (.25 - .177 ) 2 + .5 (.2 -.177 ) 2 +.2 ( .01 -.177 ) 2 σ 2 = => σ = 8.63%
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

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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 NT => 2,000/15,000= .133 \$3000 of TXN => 3k/15k=.2 \$4000 of EDS => 4k/15k= .267 \$6000 of EAT => 6k/15k=.4 Sum up to 1
Portfolio Expected Returns The expected return of a portfolio is the weighted average of the expected returns for each asset in the portfolio 1 1 2 2 ( ) ( ) ( ) ( ) P m m E R w E R w E R w E R = + +⋅⋅⋅+

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If the individual stocks have the following expected returns, what is the expected return for the portfolio? NT:
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13 - Return Risk and the Security Market Line Chapter...

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