ch2 risk and rate of return

1、5-1CHAPTER 2Risk and Rates of ReturnnStand-alone risknPortfolio risknRisk & return: CAPM / SML5-2Risk and ReturnnDefining Risk and ReturnnUsing Probability Distributions to Measure RisknAttitudes Toward RisknRisk and Return in a Portfolio ContextnDiversificationnThe Capital Asset Pricing Model (CAPM

2、)5-3Defining Returnon an investment plus any , usually expressed as a percent of the of the investment.+ ()R =5-4Return ExampleThe stock price for Stock A was per share 1 year ago. The stock is currently trading at per share, and shareholders just received a . What return was earned over the past ye

3、ar?5-5Return ExampleThe stock price for Stock A was per share 1 year ago. The stock is currently trading at per share, and shareholders just received a . What return was earned over the past year?+ ( - ) = 5-6Defining Risk5-7What is investment risk?nTwo types of investment risknStand-alone risknPort

4、folio risk nInvestment risk is related to the probability of earning a low or negative actual return.nThe greater the chance of lower than expected or negative returns, the riskier the investment.5-8Investment alternativesMarting ProductUS WaterDemand for the company productProb.ReturnExpected retur

5、nReturn . Expected returnStrong0.3100%30%20%6%Normal0.415%6%15%6%Weak0.3-70%-21%10%3%1.015.0%45.0%Which stock do you prefer ? Why？5-9Probability distributionsnA listing of all possible outcomes, and the probability of each occurrence.nCan be shown graphically.Expected Rate of ReturnRate ofReturn (%)

6、100150-70Firm XFirm Y5-10Selected Realized Returns, 1926 2001 Average Standard Return DeviationSmall-company stocks17.3%33.2%Large-company stocks12.720.2Source: Based on Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2002 Yearbook (Chicago: Ibbotson Associates, 2002), 28.5-11Investment alt

7、ernativesEconomyProb.T-BillHTCollUSRMPRecession0.18.0%-22.0%28.0%10.0%-13.0%Below avg0.28.0%-2.0%14.7%-10.0%1.0%Average0.48.0%20.0%0.0%7.0%15.0%Above avg0.28.0%35.0%-10.0%45.0%29.0%Boom0.18.0%50.0%-20.0%30.0%43.0%5-12Why is the T-bill return independent of the economy? Do T-bills promise a completel

8、y risk-free return?nT-bills will return the promised 8%, regardless of the economy.nNo, T-bills do not provide a risk-free return, as they are still exposed to inflation. Although, very little unexpected inflation is likely to occur over such a short period of time.nT-bills are also risky in terms o

9、f reinvestment rate risk.nT-bills are risk-free in the default sense of the word.5-13How do the returns of HT and Coll. behave in relation to the market?nHT Moves with the economy, and has a positive correlation. This is typical.nColl. Is countercyclical with the economy, and has a negative correlat

10、ion. This is unusual.5-14Return: Calculating the expected return for each alternative 17.4% (0.1) (50%) (0.2) (35%) (0.4) (20%) (0.2) (-2%) (0.1) (-22.%) kP k k return of rate expected kHTn1iii5-15Summary of expected returns for all alternativesExp returnHT 17.4%Market 15.0%USR 13.8%T-bill 8.0%Coll.

11、 1.7%HT has the highest expected return, and appears to be the best investment alternative, but is it really? Have we failed to account for risk?5-16Risk: Calculating the standard deviation for each alternativedeviation Standard2Variancei2n1iiP)kk(5-17Standard deviation calculation15.3% 18.8% 20.0%

12、13.4% 0.0% (0.1)8.0) - (8.0 (0.2)8.0) - (8.0 (0.4)8.0) - (8.0 (0.2)8.0) - (8.0 (0.1)8.0) - (8.0 P )k (k MUSRHTCollbillsT22222billsTn1ii2i215-18Comparing standard deviationsUSRProb.T - billHT0 8 13.8 17.4 Rate of Return (%)5-19Comments on standard deviation as a measure of risknStandard deviation (i)

13、 measures total, or stand-alone, risk.nThe larger i is, the lower the probability that actual returns will be closer to expected returns.nLarger i is associated with a wider probability distribution of returns.nDifficult to compare standard deviations, because return has not been accounted for.5-20C

14、omparing risk and returnSecurityExpected returnRisk, T-bills8.0%0.0%HT17.4%20.0%Coll*1.7%13.4%USR*13.8%18.8%Market15.0%15.3%* Seem out of place.5-21Coefficient of Variation (CV)A standardized measure of dispersion about the expected value, that shows the risk per unit of return.k Meandev Std CV 5-22

15、Risk rankings, by coefficient of variation CVnCollections has the highest degree of risk per unit of return.nHT, despite having the highest standard deviation of returns, has a relatively average CV.5-23Illustrating the CV as a measure of relative riskA = B , but A is riskier because of a larger pro

16、bability of losses. In other words, the same amount of risk (as measured by ) for less returns.0ABRate of Return (%)Prob.5-24Investor attitude towards risknRisk aversion assumes investors dislike risk and require higher rates of return to encourage them to hold riskier securities.nRisk premium the d

17、ifference between the return on a risky asset and less risky asset, which serves as compensation for investors to hold riskier securities.5-25Portfolio construction:Risk and returnAssume a two-stock portfolio is created with $50,000 invested in both HT and Collections.nExpected return of a portfolio

18、 is a weighted average of each of the component assets of the portfolio.nStandard deviation is a little more tricky and requires that a new probability distribution for the portfolio returns be devised.5-26Calculating portfolio expected return9.6% (1.7%) 0.5 (17.4%) 0.5 kkw k :average weighted a is

19、kpn1iiipp5-27An alternative method for determining portfolio expected returnEconomyProb.HTCollRecession0.1-22.0%28.0%Below avg0.2-2.0%14.7%Average0.420.0%0.0%Above avg0.235.0%-10.0%Boom0.150.0%-20.0%9.6% (15.0%) 0.10 (12.5%) 0.20 (10.0%) 0.40 (6.4%) 0.20 (3.0%) 0.10 kp5-28Calculating portfolio stand

20、ard deviation and CV0.34 9.6%3.3% CV3.3% 9.6) - (15.0 0.10 9.6) - (12.5 0.20 9.6) - (10.0 0.40 9.6) - (6.4 0.20 9.6) - (3.0 0.10 p2122222p5-29Comments on portfolio risk measuresnp = 3.3% is much lower than the i of either stock (HT = 20.0%; Coll. = 13.4%).np = 3.3% is lower than the weighted average

21、 of HT and Coll.s (16.7%).n Portfolio provides average return of component stocks, but lower than average risk.nWhy? Negative correlation between stocks.5-30General comments about risknMost stocks are positively correlated with the market (k,m 0.65).n 35% for an average stock.nCombining stocks in a

22、portfolio generally lowers risk. 5-31Returns distribution for two perfectly negatively correlated stocks ( = -1.0)-101515252525150-10Stock W0Stock M-100Portfolio WM5-32Returns distribution for two perfectly positively correlated stocks ( = 1.0)Stock M01525-10Stock M01525-10Portfolio MM01525-105-33Cr

23、eating a portfolio:Beginning with one stock and adding randomly selected stocks to portfolionp decreases as stocks added, because they would not be perfectly correlated with the existing portfolio.nExpected return of the portfolio would remain relatively constant.nEventually the diversification bene

24、fits of adding more stocks dissipates (after about 10 stocks), and for large stock portfolios, p tends to converge to 20%. 5-34Illustrating diversification effects of a stock portfolio# Stocks in Portfolio10 20 30 40 2,000+Company-Specific RiskMarket Risk20 0Stand-Alone Risk, p p (%)355-35Breaking d

25、own sources of riskStand-alone risk = Market risk + Firm-specific risknMarket risk portion of a securitys stand-alone risk that cannot be eliminated through diversification. Measured by beta.nFirm-specific risk portion of a securitys stand-alone risk that can be eliminated through proper diversifica

26、tion.5-36Failure to diversifynIf an investor chooses to hold a one-stock portfolio (exposed to more risk than a diversified investor), would the investor be compensated for the risk they bear?nNO!nStand-alone risk is not important to a well-diversified investor.nRational, risk-averse investors are c

27、oncerned with p, which is based upon market risk.nThere can be only one price (the market return) for a given security.nNo compensation should be earned for holding unnecessary, diversifiable risk.5-37Capital Asset Pricing Model (CAPM)nModel based upon concept that a stocks required rate of return i

28、s equal to the risk-free rate of return plus a risk premium that reflects the riskiness of the stock after diversification.nPrimary conclusion: The relevant riskiness of a stock is its contribution to the riskiness of a well-diversified portfolio.5-38BetanMeasures a stocks market risk, and shows a s

29、tocks volatility relative to the market.nIndicates how risky a stock is if the stock is held in a well-diversified portfolio.5-39Calculating betasnRun a regression of past returns of a security against past returns on the market.nThe slope of the regression line (sometimes called the securitys chara

30、cteristic line) is defined as the beta coefficient for the security. 5-40Illustrating the calculation of beta.ki _kM_-5051015202015105-5-10Regression line:ki = -2.59 + 1.44 kMYearkM ki 115% 18% 2 -5-10 312 165-41Comments on betanIf beta = 1.0, the security is just as risky as the average stock.nIf b

31、eta 1.0, the security is riskier than average.nIf beta 1.0, the security is less risky than average.nMost stocks have betas in the range of 0.5 to 1.5.5-42Can the beta of a security be negative?nYes, if the correlation between Stock i and the market is negative (i.e., i,m 0).nIf the correlation is n

32、egative, the regression line would slope downward, and the beta would be negative.nHowever, a negative beta is highly unlikely.5-43Beta coefficients for HT, Coll, and T-Billski_kM_-20 0 20 404020-20HT: = 1.30T-bills: = 0Coll: = -0.875-44Comparing expected return and beta coefficientsSecurityExp. Ret

33、. Beta T-Bills Coll. Riskier securities have higher returns, so the rank order is OK.5-45The Security Market Line (SML):Calculating required rates of returnSML: ki = kRF + (kM kRF) i nAssume kRF = 8% and kM = 15%.nThe market (or equity) risk premium is RPM = kM kRF = 15% 8% = 7%.5-46What is the mark

34、et risk premium?nAdditional return over the risk-free rate needed to compensate investors for assuming an average amount of risk.nIts size depends on the perceived risk of the stock market and investors degree of risk aversion.nVaries from year to year, but most estimates suggest that it ranges betw

35、een 4% and 8% per year.5-47Calculating required rates of returnnkHT = 8.0% + (15.0% - 8.0%)(1.30)= 8.0% + (7.0%)(1.30)= 8.0% + 9.1%= 17.10%nkM = 8.0% + (7.0%)(1.00)= 15.00%nkUSR= 8.0% + (7.0%)(0.89)= 14.23%nkT-bill= 8.0% + (7.0%)(0.00)= 8.00%nkColl = 8.0% + (7.0%)(-0.87)= 1.91%5-48Expected vs. Requi

36、red returnsk) k( Overvalued 1.9 1.7 Coll.k) k( uedFairly val 8.0 8.0 bills-Tk) k( Overvalued 14.2 13.8 USRk) k( uedFairly val 15.0 15.0 Market k) k( dUndervalue 17.1% 17.4% HT k k 5-49Illustrating the Security Market Line.Coll.HTT-bills.USRSMLkM = 15 kRF = 8-1 0 1 2.SML: ki = 8% + (15% 8%) i ki (%)R

37、isk, i5-50An example:Equally-weighted two-stock portfolionCreate a portfolio with 50% invested in HT and 50% invested in Collections.nThe beta of a portfolio is the weighted average of each of the stocks betas.P = wHT HT + wColl Coll P = 0.5 (1.30) + 0.5 (-0.87)P5-51Calculating portfolio required returnsnThe required return of a portfolio is the weighted average o