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1、Lecture 3 Risk and Return,Key Concepts and Skills,Know how to calculate the return on an investmentUnderstand the historical returns on various types of investmentsUnderstand the historical risks on various types of investments,Risk,Return and Financial Markets,We can examine returns in the financia
2、l markets to help us determine the appropriate returns on non-financial assetsLessons from capital market historyThere is a reward for bearing riskThe greater the potential reward,the greater the riskThis is called the risk-return trade-off,Dollar Returns,Total dollar return=income from investment+c
3、apital gain(loss)due to change in priceExample: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?Income=30+30=60Capital gain=975 950=25Total dollar return=60+25=$85,Percentage Returns,It is generally m
4、ore intuitive to think in terms of percentages than in dollar returnsDividend yield=income/beginning priceCapital gains yield=(ending price beginning price)/beginning priceTotal percentage return=dividend yield+capital gains yield,Example Calculating Returns,You bought a stock for$35 and you receive
5、d dividends of$1.25.The stock is now selling for$40.What is your dollar return?Dollar return=1.25+(40 35)=$6.25What is your percentage return?Dividend yield=1.25/35=3.57%Capital gains yield=(40 35)/35=14.29%Total percentage return=3.57+14.29=17.86%,Compound return,Conventions for quoting rates of re
6、turn: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-example,Suppose you buy T-bill maturing in one month for$9,900.HPR=(10000-9900)/9900=1
7、.01%APR=1.01%*12=12.12%EAR=(1+1.01%)12-1=12.82%,Figure 12.4,Year-to-Year Total Returns,Large-Company Stock Returns,Long-Term GovernmentBond Returns,U.S.Treasury Bill Returns,Average Returns,Risk Premiums,The“extra”return earned for taking on riskTreasury bills are considered to be risk-freeThe risk
8、premium is the return over and above the risk-free rate,Average Annual Returns and Risk Premiums,Risk,Risk means the uncertainty of future outcomeRisk is unobservableFinance literates have developed many measurements for risk,the simplest risk measurement is the standard deviation of asset return,Th
9、e population expected value and variance,The expected rate of return is the weighted average rate of return,weighted by its possibility The variance is the deviation of the return from its expected valueThe square root of variance is the risk,StateProb.of Stater in State.1-.052.2.053.4.154.2.255.1.3
10、5,E(r)=(.1)(-.05)+(.2)(.05).+(.1)(.35)E(r)=.15,Scenario or Subjective Returns:Example,Standard deviation=variance1/2,Subjective or Scenario,Var=(.1)(-.05-.15)2+(.2)(.05-.15)2.+.1(.35-.15)2Var=.01199S.D.=.01199 1/2=.1095,Using Our Example:,Variance or Dispersion of Returns,The sample mean and varianc
11、e,The actual population mean and variance are unknown,we have to estimate these values by samplingThe sample mean and variance,Figure 5.7 Nominal and Real Equity Returns Around the World,1900-2000,Figure 5.8 Standard Deviations of Real Equity and Bond Returns Around the World,1900-2000,Normal distri
12、bution,1)Mean:most likely value2)Variance or standard deviation3)Skewness*If a distribution is approximately normal,the distribution is described by characteristics 1 and 2.,Characteristics of Probability Distributions,Possibility of loss,Suppose asset return follows normal distribution,it is easy t
13、o compute the possibility of achieving a specified return level.Investors are particularly interested in the possibility that asset return is below zeroExample:suppose asset returns follow normal distribution with mean 10%and standard deviation of 20%,what is the possibility that asset return will b
14、elow 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 loss,The possibility that asset return is negative:The possibility that asset return is above 20%,Figure 5.12 Wealth Indexes of Selected Outcomes of Large Stock Portfolios and the Average T-bill Portfolio,Value at risk,Measures 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,
