1. Learning About Return and Risk from the Historical Record
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,
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

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

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
State Prob. of State r in State
E(r) = (.1)(-.05) + (.2)(.05)… + (.1)(.35)
E(r) = .15

16. Variance or Dispersion of Returns
Standard deviation = [variance]1/2
Using Our Example:
Var =[(.1)( )2+(.2)( )2…+ .1( )2]
Var=
S.D.= [ ] 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
Sharpe Ratio for Portfolios =
Risk Premium
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