Investments, 8 th edition Bodie, Kane and Marcus Slides by Susan Hine McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved. CHAPTER 5 Learning About Return and Risk from the Historical Record

5-2 Factors Influencing Rates Supply –Households Demand –Businesses Government’s Net Supply and/or Demand –Federal Reserve Actions

5-3 Real and Nominal Rates of Interest Nominal interest rate –Growth rate of your money Real interest rate –Growth rate of your purchasing power If R is the nominal rate and r the real rate and i is the inflation rate:

5-4 Equilibrium Real Rate of Interest Determined by: –Supply –Demand –Government actions –Expected rate of inflation

5-5 Figure 5.1 Determination of the Equilibrium Real Rate of Interest

5-6 Equilibrium Nominal Rate of Interest As the inflation rate increases, investors will demand higher nominal rates of return If E(i) denotes current expectations of inflation, then we get the Fisher Equation:

5-7 Taxes and the Real Rate of Interest Tax liabilities are based on nominal income –Given a tax rate (t), nominal interest rate (R), after-tax interest rate is R(1-t) –Real after-tax rate is:

5-8 Comparing Rates of Return for Different Holding Periods Zero Coupon Bond

5-9 Example 5.2 Annualized Rates of Return

5-10 Formula for EARs and APRs

5-11 Table 5.1 Annual Percentage Rates (APR) and Effective Annual Rates (EAR)

5-12 Bills and Inflation, Entire post-1926 history of annual rates: – Average real rate of return on T-bills for the entire period was 0.72 percent Real rates are larger in late periods

5-13 Table 5.2 History of T-bill Rates, Inflation and Real Rates for Generations,

5-14 Figure 5.2 Interest Rates and Inflation,

5-15 Figure 5.3 Nominal and Real Wealth Indexes for Investment in Treasury Bills,

5-16 Risk and Risk Premiums HPR = Holding Period Return P 0 = Beginning price P 1 = Ending price D 1 = Dividend during period one Rates of Return: Single Period

5-17 Ending Price =48 Beginning Price = 40 Dividend = 2 HPR = ( )/ (40) = 25% Rates of Return: Single Period Example

5-18 Expected returns p(s) = probability of a state r(s) = return if a state occurs s = state Expected Return and Standard Deviation

5-19 StateProb. of Stater in State E(r) = (.1)(-.05) + (.2)(.05)… + (.1)(.35) E(r) =.15 Scenario Returns: Example

5-20 Standard deviation = [variance] 1/2 Variance: Var =[(.1)( ) 2 +(.2)( ) 2 …+.1( ) 2 ] Var= S.D.= [.01199] 1/2 =.1095 Using Our Example: Variance or Dispersion of Returns

5-21 Time Series Analysis of Past Rates of Return Expected Returns and the Arithmetic Average

5-22 Geometric Average Return TV = Terminal Value of the Investment g= geometric average rate of return

5-23 Geometric Variance and Standard Deviation Formulas Variance = expected value of squared deviations When eliminating the bias, Variance and Standard Deviation become:

5-24 The Reward-to-Volatility (Sharpe) Ratio Sharpe Ratio for Portfolios = Risk Premium SD of Excess Return

5-25 Figure 5.4 The Normal Distribution

5-26 Figure 5.5A Normal and Skewed Distributions (mean = 6% SD = 17%)

5-27 Figure 5.5B Normal and Fat-Tailed Distributions (mean =.1, SD =.2)

5-28 Figure 5.6 Frequency Distributions of Rates of Return for

5-29 Table 5.3 History of Rates of Returns of Asset Classes for Generations,

5-30 Table 5.4 History of Excess Returns of Asset Classes for Generations,

5-31 Figure 5.7 Nominal and Real Equity Returns Around the World,

5-32 Figure 5.8 Standard Deviations of Real Equity and Bond Returns Around the World,

5-33 Figure 5.9 Probability of Investment Outcomes After 25 Years with A Lognormal Distribution

5-34 Terminal 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 distributed  The Terminal Value will then be:

5-35 Figure 5.10 Annually Compounded, 25-Year HPRs from Bootstrapped History and A Normal Distribution (50,000 Observation)

5-36 Figure 5.11 Annually Compounded, 25-Year HPRs from Bootstrapped History(50,000 Observation)

5-37 Figure 5.12 Wealth Indexes of Selected Outcomes of Large Stock Portfolios and the Average T-bill Portfolio

5-38 Table 5.5 Risk Measures for Non-Normal Distributions