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Historical Insights on Return and Risk: Analyzing Rates and Their Influencing Factors

This chapter delves into the intricate relationship between return and risk, drawing on historical data to elucidate key factors influencing rates of return. It discusses the impact of inflation on investor expectations and examines the Fisher Equation, highlighting the role of taxes on real interest rates. In addition, it covers comparative rates of return for various holding periods, risk premiums, and standard deviations. With visual aids such as graphs and tables, it presents a comprehensive overview of interest rates, inflation, and their evolution from 1926 to 2005.

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Historical Insights on Return and Risk: Analyzing Rates and Their Influencing Factors

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Presentation Transcript

  1. CHAPTER 5 Learning About Return and Risk from the Historical Record

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

  3. Figure 5.1 Determination of the Equilibrium Real Rate of Interest

  4. 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. 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:

  6. Comparing Rates of Return for Different Holding Periods Zero Coupon Bond

  7. Formula for EARs and APRs

  8. Bills and Inflation, 1926-2005 Entire post-1926 history of annual rates: www.mhhe.com/bkm Average real rate of return on T-bills for the entire period was 0.72 percent Real rates are larger in late periods

  9. Table 5.2 History of T-bill Rates, Inflation and Real Rates for Generations, 1926-2005

  10. Figure 5.2 Interest Rates and Inflation, 1926-2005

  11. Figure 5.3 Nominal and Real Wealth Indexes for Investment in Treasury Bills, 1966-2005

  12. Risk and Risk Premiums Rates of Return: Single Period HPR = Holding Period Return P0 = Beginning price P1 = Ending price D1 = Dividend during period one

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

  14. Expected Return and Standard Deviation Expected returns p(s) = probability of a state r(s) = return if a state occurs s = state

  15. Scenario Returns: Example StateProb. of State r in State 1 .1 -.05 2 .2 .05 3 .4 .15 4 .2 .25 5 .1 .35 E(r) = (.1)(-.05) + (.2)(.05)… + (.1)(.35) E(r) = .15

  16. Variance: Variance or Dispersion of Returns Standard deviation = [variance]1/2 Using Our Example: Var =[(.1)(-.05-.15)2+(.2)(.05- .15)2…+ .1(.35-.15)2] Var= .01199 S.D.= [ .01199] 1/2 = .1095

  17. Time Series Analysis of Past Rates of Return Expected Returns and the Arithmetic Average

  18. Geometric Average Return TV = Terminal Value of the Investment g= geometric average rate of return

  19. Variance and Standard Deviation Formulas Variance = expected value of squared deviations When eliminating the bias, Variance and Standard Deviation become:

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

  21. Figure 5.4 The Normal Distribution

  22. Figure 5.6 Frequency Distributions of Rates of Return for 1926-2005

  23. Table 5.3 History of Rates of Returns of Asset Classes for Generations, 1926- 2005

  24. Table 5.4 History of Excess Returns of Asset Classes for Generations, 1926- 2005

  25. Figure 5.7 Nominal and Real Equity Returns Around the World, 1900-2000

  26. Figure 5.8 Standard Deviations of Real Equity and Bond Returns Around the World, 1900-2000

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