Bài giảng Investment - chapter 5: Learning About Return and Risk from the Historical Record

CHAPTER 5Learning About Return and Risk from the Historical RecordFactors Influencing RatesSupplyHouseholdsDemandBusinessesGovernment’s Net Supply and/or DemandFederal Reserve ActionsReal and Nominal Rates of InterestNominal interest rateGrowth rate of your moneyReal interest rateGrowth rate of your purchasing powerIf R is the nominal rate and r the real rate and i is the inflation rate:Equilibrium Real Rate of InterestDetermined by:SupplyDemandGovernment actionsExpected rate of inflationFigure 5.1 Determination of the Equilibrium Real Rate of InterestEquilibrium Nominal Rate of InterestAs 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:Taxes and the Real Rate of InterestTax liabilities are based on nominal incomeGiven a tax rate (t), nominal interest rate (R), after-tax interest rate is R(1-t)Real after-tax rate is:Comparing Rates of Return for Different Holding PeriodsZero Coupon BondExample 5.2 Annualized Rates of Return Formula for EARs and APRsTable 5.1 Annual Percentage Rates (APR) and Effective Annual Rates (EAR)Bills and Inflation, 1926-2005Entire post-1926 history of annual rates:www.mhhe.com/bkmAverage real rate of return on T-bills for the entire period was 0.72 percentReal rates are larger in late periodsTable 5.2 History of T-bill Rates, Inflation and Real Rates for Generations, 1926-2005Figure 5.2 Interest Rates and Inflation, 1926-2005 Figure 5.3 Nominal and Real Wealth Indexes for Investment in Treasury Bills, 1966-2005 Risk and Risk PremiumsHPR = Holding Period ReturnP0 = Beginning priceP1 = Ending priceD1 = Dividend during period oneRates of Return: Single PeriodEnding Price = 48Beginning Price = 40Dividend = 2HPR = (48 - 40 + 2 )/ (40) = 25%Rates of Return: Single Period ExampleExpected returnsp(s) = probability of a stater(s) = return if a state occurss = stateExpected Return and Standard Deviation State Prob. of State r in State 1 .1 -.05 2 .2 .05 3 .4 .15 4 .2 .25 5 .1 .35E(r) = (.1)(-.05) + (.2)(.05) + (.1)(.35)E(r) = .15Scenario Returns: ExampleStandard deviation = [variance]1/2Variance:Var =[(.1)(-.05-.15)2+(.2)(.05- .15)2+ .1(.35-.15)2]Var= .01199S.D.= [ .01199] 1/2 = .1095Using Our Example:Variance or Dispersion of ReturnsTime Series Analysis of Past Rates of ReturnExpected Returns and the Arithmetic AverageGeometric Average ReturnTV = Terminal Value of the Investmentg= geometric average rate of returnGeometric Variance and Standard Deviation FormulasVariance = expected value of squared deviationsWhen eliminating the bias, Variance and Standard Deviation become:The Reward-to-Volatility (Sharpe) RatioSharpe Ratio for Portfolios =Risk PremiumSD of Excess ReturnFigure 5.4 The Normal DistributionFigure 5.5A Normal and Skewed Distributions (mean = 6% SD = 17%)Figure 5.5B Normal and Fat-Tailed Distributions (mean = .1, SD =.2)Figure 5.6 Frequency Distributions of Rates of Return for 1926-2005Table 5.3 History of Rates of Returns of Asset Classes for Generations, 1926- 2005Table 5.4 History of Excess Returns of Asset Classes for Generations, 1926- 2005Figure 5.7 Nominal and Real Equity Returns Around the World, 1900-2000Figure 5.8 Standard Deviations of Real Equity and Bond Returns Around the World, 1900-2000Figure 5.9 Probability of Investment Outcomes After 25 Years with A Lognormal DistributionTerminal Value with Continuous Compounding When the continuously compounded rate of return on an asset is normally distributed, the effective rate of return will be lognormally distributedThe Terminal Value will then be:Figure 5.10 Annually Compounded, 25-Year HPRs from Bootstrapped History and A Normal Distribution (50,000 Observation) Figure 5.11 Annually Compounded, 25-Year HPRs from Bootstrapped History(50,000 Observation) Figure 5.12 Wealth Indexes of Selected Outcomes of Large Stock Portfolios and the Average T-bill PortfolioTable 5.5 Risk Measures for Non-Normal Distributions