1. Learning About Return and Risk from the Historical Record
Investments
Cover image
CHAPTER 5
Learning About Return and Risk from the Historical Record
Slides by
Richard D. Johnson
McGraw-Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved

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. Return for Holding Period – Zero Coupon Bonds

5. Example 5.2 Annualized Rates of Return

6. Formula for EARs and APRs

7. Table 5.1 Annual Percentage Rates (APR) and Effective Annual Rates (EAR)

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

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

10. Figure 5.3 Nominal and Real Wealth Indexes, 1966-2005

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

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

13. Mean Scenario or Subjective Returns
p(s) = probability of a state
r(s) = return if a state occurs
1 to s states

14. Scenario or Subjective Returns: Example
State Prob. of State r in State
E(r) = (.1)(-.05) + (.2)(.05)...+ (.1)(.35)
E(r) = .15

15. Variance or Dispersion of Returns
Subjective or Scenario
Standard deviation = [variance]1/2
Using Our Example:
Var =[(.1)( )2+(.2)( ) ( )2]
Var=
S.D.= [ ] 1/2 = .1095

16. Mean and Variance of Historical Returns
Arithmetic average or rates of return
Average return is arithmetic average

17. Geometric Average Returns
TV = Terminal Value of the Investment
g= geometric average rate of return

18. Sharpe Ratio Risk Premium Sharpe Ratio for Portfolios
SD of Excess Return

19. Figure 5.4 The Normal Distribution

20. Figure 5.5A Normal and Skewed (mean = 6% SD = 17%)

21. Figure 5.5B Normal and Fat Tails Distributions (mean = .1 SD =.2)

22. Figure 5.6 Histograms 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

27. Figure 5.9 Probability of Investment Outcomes After 25 Years with A Lognormal Distribution

28. Terminal Value with Continuous Compounding

29. Figure 5.10 Annually Compounded, 25-Year HPRs from Bootstrapped History and A Normal Distribution

30. Figure 5.11 Annually Compounded, 25-Year HPRs from Bootstrapped History

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

32. Table 5.5 Risk Measures for Non-Normal Distributions