投资学英文版课件：Chap005 Introduction to Risk,Return,and the Historical Record

1、CHAPTER 5Introduction to Risk, Return, and the Historical Record5-1Interest Rate DeterminantsSupplyHouseholdsDemandBusinessesGovernments Net Supply and/or DemandFederal Reserve Actions5-2Real and Nominal Rates of InterestNominal interest rate: Growth rate of your moneyReal interest rate: Growth rate

2、 of your purchasing powerLet R = nominal rate, r = real rate and I = inflation rate. Then:Equilibrium Real Rate of InterestDetermined by:SupplyDemandGovernment actionsExpected rate of inflation5-4Figure 5.1 Determination of the Equilibrium Real Rate of Interest5-5Equilibrium Nominal Rate of Interest

3、As the inflation rate increases, investors will demand higher nominal rates of returnIf E(i) denotes current expectations of inflation, then we get the Fisher Equation:Nominal rate = real rate + inflation forecast5-6Taxes and the Real Rate of InterestTax liabilities are based on nominal incomeGiven

4、a tax rate (t) and nominal interest rate (R), the Real after-tax rate is:The after-tax real rate of return falls as the inflation rate rises.5-7Rates of Return for Different Holding PeriodsZero Coupon Bond, Par = $100, T=maturity, P=price, rf(T)=total risk free return5-8Example 5.2 Annualized Rates

5、of Return5-9Equation 5.7 EAREAR definition: percentage increase in funds invested over a 1-year horizon5-10Equation 5.8 APRAPR: annualizing using simple interest5-11Table 5.1 APR vs. EAR5-12Table 5.2 Statistics for T-Bill Rates, Inflation Rates and Real Rates, 1926-20095-13Bills and Inflation, 1926-

6、2009Moderate inflation can offset most of the nominal gains on low-risk investments.A dollar invested in T-bills from19262009 grew to $20.52, but with a real value of only $1.69.Negative correlation between real rate and inflation rate means the nominal rate responds less than 1:1 to changes in expe

7、cted inflation.5-14Figure 5.3 Interest Rates and Inflation, 1926-20095-15Risk and Risk PremiumsHPR = Holding Period ReturnP0 = Beginning priceP1 = Ending priceD1 = Dividend during period oneRates of Return: Single Period5-16Ending Price =110Beginning Price = 100Dividend = 4HPR = (110 - 100 + 4 )/ (1

8、00) = 14%Rates of Return: Single Period Example5-17Expected returnsp(s) = probability of a stater(s) = return if a state occurss = stateExpected Return and Standard Deviation5-18StateProb. of Stater in State Excellent.250.3100Good.450.1400Poor.25-0.0675Crash.05-0.5200E(r) = (.25)(.31) + (.45)(.14) +

9、 (.25)(-.0675) + (0.05)(-0.52)E(r) = .0976 or 9.76%Scenario Returns: Example5-19Variance (VAR):Variance and Standard DeviationStandard Deviation (STD):5-20Scenario VAR and STDExample VAR calculation:2 = .25(.31 - 0.0976)2+.45(.14 - .0976)2 + .25(-0.0675 - 0.0976)2 + .05(-.52 - .0976)2 = .038Example

10、STD calculation:5-21Time Series Analysis of Past Rates of ReturnThe Arithmetic Average of rate of return:5-22Geometric Average ReturnTV = Terminal Value of the Investmentg= geometric average rate of return5-23Geometric Variance and Standard Deviation FormulasEstimated Variance = expected value of sq

11、uared deviations5-24Geometric Variance and Standard Deviation FormulasWhen eliminating the bias, Variance and Standard Deviation become:5-25The Reward-to-Volatility (Sharpe) RatioSharpe Ratio for Portfolios:5-26The Normal DistributionInvestment management is easier when returns are normal.Standard d

12、eviation is a good measure of risk when returns are symmetric.If security returns are symmetric, portfolio returns will be, too.Future scenarios can be estimated using only the mean and the standard deviation.5-27Figure 5.4 The Normal Distribution5-28Normality and Risk MeasuresWhat if excess returns

13、 are not normally distributed?Standard deviation is no longer a complete measure of riskSharpe ratio is not a complete measure of portfolio performanceNeed to consider skew and kurtosis5-29Skew and KurtosisSkewEquation 5.19KurtosisEquation 5.205-30Figure 5.5A Normal and Skewed Distributions 5-31Figu

14、re 5.5B Normal and Fat-Tailed Distributions (mean = .1, SD =.2)5-32Value at Risk (VaR)A measure of loss most frequently associated with extreme negative returnsVaR is the quantile of a distribution below which lies q % of the possible values of that distributionThe 5% VaR , commonly estimated in pra

15、ctice, is the return at the 5th percentile when returns are sorted from high to low.5-33Expected Shortfall (ES)Also called conditional tail expectation (CTE)More conservative measure of downside risk than VaRVaR takes the highest return from the worst casesES takes an average return of the worst cas

16、es5-34Lower Partial Standard Deviation (LPSD)and the Sortino RatioIssues:Need to consider negative deviations separatelyNeed to consider deviations of returns from the risk-free rate.LPSD: similar to usual standard deviation, but uses only negative deviations from rfSortino Ratio replaces Sharpe Rat

17、io5-35Historic Returns on Risky PortfoliosReturns appear normally distributedReturns are lower over the most recent half of the period (1986-2009)SD for small stocks became smaller; SD for long-term bonds got bigger5-36Historic Returns on Risky PortfoliosBetter diversified portfolios have higher Sha

18、rpe RatiosNegative skew5-37Figure 5.7 Nominal and Real Equity Returns Around the World, 1900-20005-38Figure 5.8 Standard Deviations of Real Equity and Bond Returns Around the World, 1900-20005-39Figure 5.9 Probability of Investment Outcomes After 25 Years with a Lognormal Distribution5-40Terminal Value with Continuous Compounding When the continuously compounded rate of return on an asset is normally distributed, the effective