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1、Lecture 3 Risk and ReturnKey Concepts and SkillslKnow how to calculate the return on an investmentlUnderstand the historical returns on various types of investmentslUnderstand the historical risks on various types of investmentsRisk, Return and Financial MarketslWe can examine returns in the financi
2、al markets to help us determine the appropriate returns on non-financial assetslLessons from capital market historyThere is a reward for bearing riskThe greater the potential reward, the greater the riskThis is called the risk-return trade-offDollar ReturnslTotal dollar return = income from investme
3、nt + capital gain (loss) due to change in pricelExample:You bought a bond for $950 one year ago. You have received two coupons of $30 each. You can sell the bond for $975 today. What is your total dollar return?lIncome = 30 + 30 = 60lCapital gain = 975 950 = 25lTotal dollar return = 60 + 25 = $85Per
4、centage ReturnslIt is generally more intuitive to think in terms of percentages than in dollar returnslDividend yield = income / beginning pricelCapital gains yield = (ending price beginning price) / beginning pricelTotal percentage return = dividend yield + capital gains yieldExample Calculating Re
5、turnslYou bought a stock for $35 and you received dividends of $1.25. The stock is now selling for $40.What is your dollar return?lDollar return = 1.25 + (40 35) = $6.25What is your percentage return?lDividend yield = 1.25 / 35 = 3.57%lCapital gains yield = (40 35) / 35 = 14.29%lTotal percentage ret
6、urn = 3.57 + 14.29 = 17.86%Compound returnConventions for quoting rates of return :Usually we use APR, annual percentage rate APR=per-period rate*periods per yearSometimes we use EAR(effective annual rate) In continuous time, EAR=eAPR-1 St=S0ert, so rate of return equal Ln(St/S0) Rate of Return-exam
7、plelSuppose you buy T-bill maturing in one month for $9,900. lHPR=(10000-9900)/9900=1.01%lAPR=1.01%*12=12.12%lEAR=(1+1.01%)12-1=12.82%Figure 12.4Year-to-Year Total ReturnsLarge-Company Stock ReturnsLong-Term GovernmentBond ReturnsU.S. Treasury Bill ReturnsAverage ReturnsInvestmentAverage ReturnLarge
8、 stocks12.4%Small Stocks17.5%Long-term Corporate Bonds6.2%Long-term Government Bonds5.8%U.S. Treasury Bills3.8%Inflation3.1%Risk PremiumslThe “extra” return earned for taking on risklTreasury bills are considered to be risk-freelThe risk premium is the return over and above the risk-free rateAverage
9、 Annual Returns and Risk PremiumsInvestmentAverage ReturnRisk PremiumLarge stocks12.4%8.6%Small Stocks17.5%13.7%Long-term Corporate Bonds6.2%2.4%Long-term Government Bonds5.8%2.0%U.S. Treasury Bills3.8%0.0%RisklRisk means the uncertainty of future outcomelRisk is unobservablelFinance literates have
10、developed many measurements for risk, the simplest risk measurement is the standard deviation of asset returnThe population expected value and variancelThe expected rate of return is the weighted average rate of return, weighted by its possibility lThe variance is the deviation of the return from it
11、s expected valuelThe square root of variance is the riskStateProb. of Stater in State .1-.052.2.053.4.154.2.255.1.35E(r) = (.1)(-.05) + (.2)(.05).+ (.1)(.35)E(r) = .15Scenario or Subjective Returns: ExampleStandard deviation = variance1/2Subjective or ScenarioVar =(.1)(-.05-.15)2+(.2)(.05- .15)2.+ .
12、1(.35-.15)2Var= .01199S.D.= .01199 1/2 = .1095Using Our Example:Variance or Dispersion of ReturnsThe sample mean and variancelThe actual population mean and variance are unknown, we have to estimate these values by samplinglThe sample mean and variance Figure 5.7 Nominal and Real Equity Returns Arou
13、nd the World, 1900-2000Figure 5.8 Standard Deviations of Real Equity and Bond Returns Around the World, 1900-2000Normal distribution1) Mean: most likely value2) Variance or standard deviation3) Skewness* If a distribution is approximately normal, the distribution is described by characteristics 1 an
14、d 2.Characteristics of Probability DistributionsPossibility of losslSuppose asset return follows normal distribution, it is easy to compute the possibility of achieving a specified return level. Investors are particularly interested in the possibility that asset return is below zerolExample:suppose
15、asset returns follow normal distribution with mean 10% and standard deviation of 20%, what is the possibility that asset return will below zero, what is the possibility that asset return will be above 20%? What is the possibility that asset return is between 5% and 15%? Z-value Possibility of losslT
16、he possibility that asset return is negative:lThe possibility that asset return is above 20%Figure 5.12 Wealth Indexes of Selected Outcomes of Large Stock Portfolios and the Average T-bill PortfolioValue at risklMeasures at q% that asset return will below certain level, practitioners commonly call the 5% quantile the VaR of the distribution.Table 5.5 Risk Measures for Non-Normal Distributions
