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13-0 Return, Risk, and the Security Market Line Chapter 13 Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin
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Chapter Outline Expected Returns and Variances of Individual Securities Expected Returns and Variances of Portfolios Systematic and Unsystematic Risk Diversification Systematic Risk and Beta The Security Market Line & the Capital Asset Pricing Model (CAPM) 1
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Expected Returns of Individual Securities The expected return is based on future returns and the probabilities of possible outcomes where 1, 2, 3…i = states p = probability that a state occurs R = future return 2
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Variance of Individual Securities where 1, 2, 3…i = states p = probability that a state occurs R = future return E(R)= expected return 3
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Example: E(R) and VAR of Individual Security Security A: StateR p 1.30.40 2.15.50 3.05.10 1.00 E( R A ) = VAR A = Security B: State R p 1.25.30 2.17.40 3.10.30 1.00 E( R B ) = VAR B = 4
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Expected Portfolio Returns The expected return of a portfolio is the weighted average of the expected returns for each asset in the portfolio where A, B, …j = securities 5
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Example: Expected Portfolio Return You have a total of $15,000 to invest and have purchased $12,000 worth of security A and $3,000 worth of security B. Assume that E(R A )=.20 and E(R B ) =.173 What are the portfolio weights and what is the expected portfolio return E(R P )? 6
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Variance of Portfolio Returns 1. Compute the future return of the portfolio for each state 2. Compute the expected portfolio return 3. Compute the portfolio variance where 1, 2, 3…i = states p = probability that a state occurs R = future return E(R)= expected return 7
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Example: Variance of Portfolio Returns Assuming that 30% of the portfolio is invested in Stock A and 70% in stock B, what is the portfolio variance? State R A (w A =.3) R B (w B =.7)p R p 1.20.2540% 2.18.1560% E(R p )= VAR p = 8
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Systematic & Unsystematic Risk Realized returns are generally not equal to expected returns There is the expected component and the unexpected component R = E(R)+U U = systematic (non-diversifiable) portion + unsystematic (diversifiable) portion 9
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Diversification 10
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Diversification 11
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Systematic Risk and Beta We use the beta coefficient to measure systematic (non- diversifiable) risk What does beta tell us? –A beta of 1 implies the asset has the same systematic risk as the overall market –A beta < 1 implies the asset has less systematic risk than the overall market –A beta > 1 implies the asset has more systematic risk than the overall market 12
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Sample Company Betas 13 http://screener.finance.yahoo.com/stocks.html
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Security Market Line & The Capital Asset Pricing Model (CAPM) In equilibrium, all assets and portfolios must have the same reward-to-risk ratio and they all must equal the reward-to-risk ratio for the market 14
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Security Market Line & the CAPM The security market line (SML) is the representation of market equilibrium The slope of the SML is the reward- to-risk ratio 15
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The CAPM The capital asset pricing model defines the relationship between risk and return E(R i ) = R f + i (E(R M ) – R f ) 16
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CAPM Example: Assume the risk-free rate is 3%, the return on the market is 9% and a particular stock has a beta of 1.5. What is the expected return of the stock? 17
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