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1、INVESTMENTS | BODIE, KANE, MARCUSCopyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/IrwinCHAPTER 5Introduction to Risk, Return, and the Historical RecordINVESTMENTS | BODIE, KANE, MARCUSInterest Rate DeterminantsSupplyHouseholdsDemandBusinessesGovernments Net Supply an
2、d/or DemandFederal Reserve Actions5-2INVESTMENTS | BODIE, KANE, MARCUSReal and Nominal Rates of InterestNominal interest rate: Growth rate of your moneyReal interest rate: Growth rate of your purchasing powerLet R = nominal rate, r = real rate and I = inflation rate. Then:INVESTMENTS | BODIE, KANE,
3、MARCUSEquilibrium Real Rate of InterestDetermined by:SupplyDemandGovernment actionsExpected rate of inflation5-4INVESTMENTS | BODIE, KANE, MARCUSFigure 5.1 Determination of the Equilibrium Real Rate of Interest5-5INVESTMENTS | BODIE, KANE, MARCUSEquilibrium Nominal Rate of InterestAs the inflation r
4、ate 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 forecast5-6INVESTMENTS | BODIE, KANE, MARCUSTaxes and the Real Rate of InterestTax liabilities are based on nomin
5、al incomeGiven 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.5-7INVESTMENTS | BODIE, KANE, MARCUSRates of Return for Different Holding PeriodsZero Coupon Bond, Par = $100, T=maturity, P=price, rf(T)=total
6、risk free return5-8INVESTMENTS | BODIE, KANE, MARCUSExample 5.2 Annualized Rates of Return5-9INVESTMENTS | BODIE, KANE, MARCUSEquation 5.7 EAREAR definition: percentage increase in funds invested over a 1-year horizon5-10INVESTMENTS | BODIE, KANE, MARCUSEquation 5.8 APRAPR: annualizing using simple
7、interest5-11INVESTMENTS | BODIE, KANE, MARCUSTable 5.1 APR vs. EAR5-12INVESTMENTS | BODIE, KANE, MARCUSTable 5.2 Statistics for T-Bill Rates, Inflation Rates and Real Rates, 1926-20095-13INVESTMENTS | BODIE, KANE, MARCUSBills and Inflation, 1926-2009Moderate inflation can offset most of the nominal
8、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 expected inflation.5-14INVESTMENTS | BODIE, KANE, MARCUSFi
9、gure 5.3 Interest Rates and Inflation, 1926-20095-15INVESTMENTS | BODIE, KANE, MARCUSRisk and Risk PremiumsHPR = Holding Period ReturnP0 = Beginning priceP1 = Ending priceD1 = Dividend during period oneRates of Return: Single Period5-16INVESTMENTS | BODIE, KANE, MARCUSEnding Price =110Beginning Pric
10、e = 100Dividend = 4HPR = (110 - 100 + 4 )/ (100) = 14%Rates of Return: Single Period Example5-17INVESTMENTS | BODIE, KANE, MARCUSExpected returnsp(s) = probability of a stater(s) = return if a state occurss = stateExpected Return and Standard Deviation5-18INVESTMENTS | BODIE, KANE, MARCUSStateProb.
11、of Stater in State Excellent.250.3100Good.450.1400Poor.25-0.0675Crash.05-0.5200E(r) = (.25)(.31) + (.45)(.14) + (.25)(-.0675) + (0.05)(-0.52)E(r) = .0976 or 9.76%Scenario Returns: Example5-19INVESTMENTS | BODIE, KANE, MARCUSVariance (VAR):Variance and Standard DeviationStandard Deviation (STD):5-20I
12、NVESTMENTS | BODIE, KANE, MARCUSScenario 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 STD calculation:5-21INVESTMENTS | BODIE, KANE, MARCUSTime Series Analysis of Past Rates of ReturnThe Arithmetic Average of
13、rate of return:5-22INVESTMENTS | BODIE, KANE, MARCUSGeometric Average ReturnTV = Terminal Value of the Investmentg= geometric average rate of return5-23INVESTMENTS | BODIE, KANE, MARCUSGeometric Variance and Standard Deviation FormulasEstimated Variance = expected value of squared deviations5-24INVE
14、STMENTS | BODIE, KANE, MARCUSGeometric Variance and Standard Deviation FormulasWhen eliminating the bias, Variance and Standard Deviation become:5-25INVESTMENTS | BODIE, KANE, MARCUSThe Reward-to-Volatility (Sharpe) RatioSharpe Ratio for Portfolios:5-26INVESTMENTS | BODIE, KANE, MARCUSThe Normal Dis
15、tributionInvestment management is easier when returns are normal.Standard deviation 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.5-27INVESTMENTS
16、| BODIE, KANE, MARCUSFigure 5.4 The Normal Distribution5-28INVESTMENTS | BODIE, KANE, MARCUSNormality and Risk MeasuresWhat if excess returns are not normally distributed?Standard deviation is no longer a complete measure of riskSharpe ratio is not a complete measure of portfolio performanceNeed to
17、consider skew and kurtosis5-29INVESTMENTS | BODIE, KANE, MARCUSSkew and KurtosisSkewEquation 5.19KurtosisEquation 5.205-30INVESTMENTS | BODIE, KANE, MARCUSFigure 5.5A Normal and Skewed Distributions 5-31INVESTMENTS | BODIE, KANE, MARCUSFigure 5.5B Normal and Fat-Tailed Distributions (mean = .1, SD =
18、.2)5-32INVESTMENTS | BODIE, KANE, MARCUSValue 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 practice, is the return at the
19、 5th percentile when returns are sorted from high to low.5-33INVESTMENTS | BODIE, KANE, MARCUSExpected 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 wor
20、st cases5-34INVESTMENTS | BODIE, KANE, MARCUSLower 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 f
21、rom rfSortino Ratio replaces Sharpe Ratio5-35INVESTMENTS | BODIE, KANE, MARCUSHistoric 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 bigger5-36INVESTMEN
22、TS | BODIE, KANE, MARCUSHistoric Returns on Risky PortfoliosBetter diversified portfolios have higher Sharpe RatiosNegative skew5-37INVESTMENTS | BODIE, KANE, MARCUSFigure 5.7 Nominal and Real Equity Returns Around the World, 1900-20005-38INVESTMENTS | BODIE, KANE, MARCUSFigure 5.8 Standard Deviatio
23、ns of Real Equity and Bond Returns Around the World, 1900-20005-39INVESTMENTS | BODIE, KANE, MARCUSFigure 5.9 Probability of Investment Outcomes After 25 Years with a Lognormal Distribution5-40INVESTMENTS | BODIE, KANE, MARCUSTerminal Value with Continuous Compounding When the continuously compounde
24、d rate of return on an asset is normally distributed, the effective rate of return will be lognormally distributed.The Terminal Value will then be:5-41INVESTMENTS | BODIE, KANE, MARCUSFigure 5.10 Annually Compounded, 25-Year HPRs5-42INVESTMENTS | BODIE, KANE, MARCUSFigure 5.11 Annually Compounded, 25-Year HPRs5-43INVESTMENTS | BODIE, KANE, MARCUSFigure 5.12 Wealth Indexes of Selected Outcomes of Large Stock Portfolios and the Average T-bill Portfolio5-44
