ch5-risk-and-return.ppt

5.1Chapter 5Risk and Risk and ReturnReturn5.2After studying Chapter 5,you should be able to:1.Understand the relationship(or“trade-off”)between risk and return.2.Define risk and return and show how to measure them by calculating expected return,standard deviation,and coefficient of variation.3.Discuss the different types of investor attitudes toward risk.4.Explain risk and return in a portfolio context,and distinguish between individual security and portfolio risk.5.Distinguish between avoidable(unsystematic)risk and unavoidable(systematic)risk and explain how proper diversification can eliminate one of these risks.6.Define and explain the capital-asset pricing model(CAPM),beta,and the characteristic line.7.Calculate a required rate of return using the capital-asset pricing model(CAPM).8.Demonstrate how the Security Market Line(SML)can be used to describe this relationship between expected rate of return and systematic risk.9.Explain what is meant by an“efficient financial market”and describe the three levels(or forms)of market efficiency.5.3Risk and ReturnRisk and Return Defining Risk and ReturnDefining Risk and Return Using Probability Distributions to Measure Using Probability Distributions to Measure RiskRisk Attitudes Toward RiskAttitudes Toward Risk Risk and Return in a Portfolio ContextRisk and Return in a Portfolio Context DiversificationDiversification The Capital Asset Pricing Model(CAPM)The Capital Asset Pricing Model(CAPM)Efficient Financial MarketsEfficient Financial Markets5.4Defining ReturnDefining ReturnIncome received Income received Income received on an investment plus any on an investment plus any change in change in change in market pricemarket pricemarket price,usually expressed as a percent of the,usually expressed as a percent of the beginning market price beginning market price beginning market price of the investment.of the investment.Dt+(Pt Pt-1)Pt-1R=5.5Return ExampleReturn ExampleThe stock price for Stock A was The stock price for Stock A was$10$10$10 per share 1 year per share 1 year ago.The stock is currently trading at ago.The stock is currently trading at$9.50$9.50$9.50 per share per share and shareholders just received a and shareholders just received a$1 dividend$1 dividend$1 dividend.What.What return was earned over the past year?return was earned over the past year?$1.00+($9.50$10.00)$10.00R=5%5.6Defining RiskDefining RiskWhat rate of return do you expect on your What rate of return do you expect on your What rate of return do you expect on your investment(savings)this year?investment(savings)this year?investment(savings)this year?What rate will you actually earn?What rate will you actually earn?What rate will you actually earn?Does it matter if it is a bank CD or a share of Does it matter if it is a bank CD or a share of Does it matter if it is a bank CD or a share of stock?stock?stock?The variability of returns from those that The variability of returns from those that The variability of returns from those that are expected.are expected.are expected.5.7Determining Expected Return Determining Expected Return(Discrete Dist.)(Discrete Dist.)R R=S S S S(R Ri i)()(P Pi i)R R is the expected return for the asset,is the expected return for the asset,R Ri i is the return for the i is the return for the ithth possibility,possibility,P Pi i is the probability of that return occurring,is the probability of that return occurring,n n is the total number of possibilities.is the total number of possibilities.nI=15.8How to Determine the Expected Return How to Determine the Expected Return How to Determine the Expected Return and Standard Deviationand Standard Deviationand Standard DeviationThe expected return,R,for Stock BW is.09 or 9%Stock BWStock BW R Ri iP Pi i (R Ri i)()(P Pi i)-0.15 -0.15 0.10 0.10 0.015 0.015 -0.03 -0.03 0.20 0.20 0.006 0.006 0.09 0.09 0.40 0.40 0.036 0.036 0.21 0.21 0.20 0.20 0.042 0.042 0.33 0.33 0.10 0.10 0.033 0.033 SumSum 1.001.00 0.0900.0905.9Determining Standard Deviation(Risk Determining Standard Deviation(Risk Measure)Measure)s s s s=S S S S(R Ri i R R)2 2(P Pi i)Standard DeviationStandard Deviation,s s s s,is a statistical,is a statistical measure of the variability of a distribution measure of the variability of a distribution around its mean.around its mean.It is the square root of variance.It is the square root of variance.Note,this is for a Note,this is for a discrete distributiondiscrete distribution.ni=15.10How to Determine the Expected Return How to Determine the Expected Return and Standard Deviationand Standard DeviationStock BWStock BW R Ri iP Pi i (R Ri i)()(P Pi i)(R Ri i-R R)2 2(P Pi i)0.15 0.15 0.10 0.10 0.015 0.015 0.00576 0.00576 0.03 0.03 0.20 0.20 0.006 0.006 0.00288 0.00288 0.09 0.09 0.40 0.40 0.036 0.036 0.00000 0.00000 0.21 0.21 0.20 0.20 0.042 0.042 0.00288 0.00288 0.33 0.33 0.10 0.10 0.033 0.033 0.00576 0.00576 SumSum 1.001.00 0.0900.090 0.017280.017285.11Determining Standard Deviation(Risk Determining Standard Deviation(Risk Measure)Measure)ni=1s s s s=S S S S (R Ri i R R)2 2(P Pi i)s s s s=.01728.01728s s s s =0.13150.1315 or or 13.15%13.15%5.12Coefficient of VariationCoefficient of VariationThe ratio of the The ratio of the standard deviation standard deviation of of a distribution to the a distribution to the mean mean of that of that distribution.distribution.It is a measure of It is a measure of RELATIVERELATIVE risk.risk.CV=CV=s s s s/R RCV of BW =CV of BW =0.13150.1315/0.090.09=1.46=1.465.13Discrete versus.Continuous Distributions Discrete Continuous5.14Certainty EquivalentCertainty Equivalent (CECE)is the amount of cash)is the amount of cash someone would require with certainty at a someone would require with certainty at a point in time to make the individual point in time to make the individual indifferent between that certain amount and indifferent between that certain amount and an amount expected to be received with risk an amount expected to be received with risk at the same point in time.at the same point in time.Risk AttitudesRisk Attitudes5.15Certainty equivalent Expected valueCertainty equivalent Expected valueRisk PreferenceRisk PreferenceRisk PreferenceCertainty equivalent=Expected valueCertainty equivalent=Expected valueRisk IndifferenceRisk IndifferenceRisk IndifferenceCertainty equivalent Expected valueCertainty equivalent Expected valueRisk AversionRisk AversionRisk AversionMostMost individuals are individuals are Risk AverseRisk AverseRisk Averse.Risk AttitudesRisk Attitudes5.16You have the choice between(1)a guaranteed dollar reward or(2)a coin-flip gamble of$100,000(50%chance)or$0(50%chance).The expected value of the gamble is$50,000.Mary requires a guaranteed$25,000,or more,to call off the gamble.Raleigh is just as happy to take$50,000 or take the risky gamble.Shannon requires at least$52,000 to call off the gamble.Risk Attitude ExampleRisk Attitude Example5.17What are the Risk Attitude tendencies of each?Risk Attitude ExampleRisk Attitude ExampleMaryMary shows shows“risk aversion”“risk aversion”“risk aversion”because her because her“certainty equivalent”the expected value of“certainty equivalent”the expected value of“certainty equivalent”the expected value of the gamblethe gamble.5.18 R RP P=S S S S(WWj j)()(R Rj j)R RP P is the expected return for the portfolio,is the expected return for the portfolio,WWj j is the weight(investment proportion)for the is the weight(investment proportion)for the j jthth asset in the portfolio,asset in the portfolio,R Rj j is the expected return of the j is the expected return of the jthth asset,asset,mm is the total number of assets in the portfolio.is the total number of assets in the portfolio.Determining Determining Portfolio Expected Portfolio Expected ReturnReturnmJ=15.19Determining Portfolio Determining Portfolio Standard DeviationStandard DeviationmJ=1mK=1s s s sP P=S SS SS SS S WWj j WWk k s s s s j jk k WWj j is the weight(investment proportion)is the weight(investment proportion)for the for the j jthth asset in the portfolio,asset in the portfolio,WWk k is the weight(investment proportion)is the weight(investment proportion)for the for the k kthth asset in the portfolio,asset in the portfolio,s s s sj jk k is the covariance between returns for is the covariance between returns for the the j jthth and and k kthth assets in the portfolio.assets in the portfolio.5.20s s s s j jk k=s s s s j j s s s s k k r r j jk k s s s sj j is the standard deviation of the is the standard deviation of the j jthth asset in the portfolio,asset in the portfolio,s s s sk k is the standard deviation of the is the standard deviation of the k kthth asset in the portfolio,asset in the portfolio,r rj jk k is the correlation coefficient between the is the correlation coefficient between the j jthth and and k kthth assets in the portfolio.assets in the portfolio.What is Covariance?What is Covariance?5.21A standardized statistical measure A standardized statistical measure of the linear relationship between of the linear relationship between two variables.two variables.Its range is from Its range is from 1.0 1.0(perfect perfect negative correlationnegative correlation),through),through 0 0 (no correlationno correlation),to),to+1.0+1.0(perfect perfect positive correlationpositive correlation).).Correlation CoefficientCorrelation Coefficient5.22A three asset portfolio:A three asset portfolio:Col 1 Col 1 Col 2 Col 2 Col 3 Col 3Row 1Row 1WW1 1WW1 1s s s s1 1,1 1 WW1 1WW2 2s s s s1 1,2 2 WW1 1WW3 3s s s s1 1,3 3Row 2Row 2WW2 2WW1 1s s s s2 2,1 1 WW2 2WW2 2s s s s2 2,2 2 WW2 2WW3 3s s s s2 2,3 3Row 3Row 3WW3 3WW1 1s s s s3 3,1 1 WW3 3WW2 2s s s s3 3,2 2 WW3 3WW3 3s s s s3 3,3 3s s s sj j,k k=is the covariance between returns for =is the covariance between returns for the the j jthth and and k kthth assets in the portfolio.assets in the portfolio.Variance Covariance MatrixVariance Covariance MatrixVariance Covariance Matrix5.23You are creating a portfolio of You are creating a portfolio of Stock D Stock D Stock D and and Stock Stock Stock BW BW BW(from earlier).You are investing(from earlier).You are investing$2,000$2,000$2,000 in in Stock BW Stock BW Stock BW and and$3,000$3,000$3,000 in in Stock DStock DStock D.Remember that.Remember that the expected return and standard deviation ofthe expected return and standard deviation of Stock BWStock BWStock BW is is 9%9%9%and and 13.15%13.15%13.15%respectively.The respectively.The expected return and standard deviation ofexpected return and standard deviation of Stock D Stock D Stock D is is 8%8%8%and and 10.65%10.65%10.65%respectively.The respectively.The correlation correlation correlation coefficient coefficient coefficient between BW and D is between BW and D is 0.750.750.75.What is the expected return and standard What is the expected return and standard What is the expected return and standard deviation of the portfolio?deviation of the portfolio?deviation of the portfolio?Portfolio Risk and Expected Return ExamplePortfolio Risk and Expected Return ExamplePortfolio Risk and Expected Return Example5.24WWBWBW=$2,000/$5,000=$2,000/$5,000=0.40.4WWD D =$3,000/$5,000=$3,000/$5,000=0.6 0.6R RP P =(WWBWBW)()(R RBWBW)+()+(WWD D)()(R RD D)R RP P=(=(0.40.4)()(9%9%)+()+(0.60.6)()(8%8%)R RP P=(=(3.6%3.6%)+()+(4.8%4.8%)=)=8.4%8.4%Determining Portfolio Expected ReturnDetermining Portfolio Expected ReturnDetermining Portfolio Expected Return5.25Two-asset portfolioTwo-asset portfolio:Col 1 Col 1 Col 2 Col 2Row 1Row 1WWBW BW WWBW BW s s s sBW,BW BW,BW WWBW BW WWD D s s s sBW,DBW,DRow 2Row 2 WWD D WWBW BW s s s sD,BW D,BW WWD D WWD D s s s sD,DD,DThis represents the variance covariance This represents the variance covariance matrix for the two-asset portfolio.matrix for the two-asset portfolio.Determining Portfolio Standard DeviationDetermining Portfolio Standard DeviationDetermining Portfolio Standard Deviation5.26Two-asset portfolioTwo-asset portfolio:Col 1 Col 1 Col 2 Col 2Row 1Row 1 (0.40.4)()(0.40.4)()(0.01730.0173)(0.40.4)()(0.60.6)()(0.01050.0105)Row 2Row 2 (0.60.6)()(0.40.4)()(0.01050.0105)()(0.60.6)()(0.60.6)()(0.01130.0113)This represents substitution into the This represents substitution into the variance covariance matrix.variance covariance matrix.Determining Portfolio Standard DeviationDetermining Portfolio Standard DeviationDetermining Portfolio Standard Deviation5.27Two-asset portfolioTwo-asset portfolio:Col 1 Col 1 Col 2 Col 2Row 1Row 1 (0.00280.0028)(0.00250.0025)Row 2Row 2 (0.00250.0025)(0.00410.0041)This represents the actual element values This represents the actual element values in the variance covariance matrix.in the variance covariance matrix.Determining Portfolio Standard DeviationDetermining Portfolio Standard DeviationDetermining Portfolio Standard Deviation5.28s s s sP P=0.00280.0028+(2)(+(2)(0.00250.0025)+)+0.00410.0041s s s sP P=SQRT(=SQRT(0.01190.0119)s s s sP P=0.10910.1091 or or 10.91%10.91%A weighted average of the individual A weighted average of the individual standard deviations is standard deviations is INCORRECTINCORRECT.Determining Portfolio Standard DeviationDetermining Portfolio Standard DeviationDetermining Portfolio Standard Deviation5.29The WRONG way to calculate is a weighted The WRONG way to calculate is a weighted average like:average like:s s s sP P=0.40.4 (13.15%)(13.15%)+0.6(10.65%)0.6(10.65%)s s s sP P=5.265.26+6.396.39=11.65%11.65%10.91%10.91%=11.65%11.65%This is This is INCORRECTINCORRECT.Determining Portfolio Standard DeviationDetermining Portfolio Standard DeviationDetermining Portfolio Standard Deviation5.30Stock CStock C Stock DStock D PortfolioPortfolioReturnReturn 9.00%9.00%8.00%8.00%8.64%8.64%Stand.Stand.Dev.Dev.13.15%13.15%10.65%10.65%10.91%10.91%CVCV 1.46 1.46 1.33 1.33 1.26 1.26The portfolio has the The portfolio has the LOWESTLOWEST coefficient coefficient of variation due to diversification.of variation due to diversification.Summary of the Portfolio Return and Risk Summary of the Portfolio Return and Risk Summary of the Portfolio Return and Risk CalculationCalculationCalculation5.31Combining securities that are not perfectly,Combining securities that are not perfectly,positively correlated reduces risk.positively correlated reduces risk.INVESTMENT RETURNTIMETIMETIMESECURITY ESECURITY ESECURITY FSECURITY FCombinationCombinationE and FE and FDiversification and the Correlation Diversification and the Correlation Diversification and the Correlation CoefficientCoefficientCoefficient5.32Systematic Risk Systematic Risk Systematic Risk is the variability of return is the variability of return on stocks or portfolios associated with on stocks or portfolios associated with changes in return on the market as a whole.changes in return on the market as a whole.Unsystematic Risk Unsystematic Risk Unsystematic Risk is the variability of return is the variability of return on stocks or portfolios not explained by on stocks or portfolios not explained by general market movements.It is avoidable general market movem