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# chap011 with additions - Chapter 11 Risk and Return...

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1 Chapter 11 - Risk and Return Expected Returns and Variances Portfolios and Diversification Announcements, Surprises, and Expected Returns Risk: Systematic and Unsystematic Systematic Risk and Beta Capital Asset Pricing Model (CAPM) an the Security Market Line (SML) equation

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2 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 ) (
3 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 ??? 0.02 0.01 R C = .3(.15) + .5(.10) + .2(.02) = .099 = 9.99% R T = .3(.25) + .5(.20) + .2(.01) = .177 = 17.7%

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4 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 = - = n i i i R E R p 1 2 2 )) ( ( σ
5 The Normal Distribution - Bell Curve From Ch. 10, Figure 10.11. p.308 σ 68.26894921371% 95.44997361036% 99.73002039367% 99.99366575163% 99.99994266969% 99.99999980268% 99.99999999974% Expected Return is midpoint.

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6 Example: Variance and Standard Deviation Consider the previous example. What are the variance and standard deviation for each stock? Stock C Variance = σ 2 = .3(.15-.099) 2 + .5(.1-.099) 2 + .2(.02-.099) 2 = . 002029 Standard Deviation = σ = .045 So, expect C’s return to be 9.99% +/- multiples of σ = 4.5% Stock T Variance = σ 2 = .3(.25-.177) 2 + .5(.2-.177) 2 + .2(.01-.177) 2 = . 007441 Standard Deviation = σ = .0863 So, expect T’s return to be 17.7% +/- multiples of σ = 8.63%
7 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? 0.0805 What is the variance? .00267 What is the standard deviation? .0517

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8 Portfolios Standalone investments are more risky, but investing within a portfolio allows mitigation of some (but not all) risk. 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
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

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chap011 with additions - Chapter 11 Risk and Return...

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