1. McGraw-Hill/Irwin Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 5 History of Interest Rates and Risk Premiums

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

3. 5-3 Q0Q0 Q1Q1 r0r0 r1r1 Funds Interest Rates Supply Demand Interest Rates Supply Q0Q0 Q1Q1 r0r0 r1r1 Funds Demand »Level of Interest Rates

4. 5-4 Fisher effect: Approximation nominal rate = real rate + inflation premium R = r + i or r = R - i Example r = 3%, i = 6% R = 9% = 3% + 6% or 3% = 9% - 6% Fisher effect: Exact r = (R - i) / (1 + i) 2.83% = (9%-6%) / (1.06) Empirical Relationship: Inflation and interest rates move closely together Real vs. Nominal Rates

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

6. 5-6 Ending Price =48 Beginning Price = 40 Dividend = 2 HPR = (48 - 40 + 2 )/ (40) = 25% Rates of Return: Single Period Example

7. 5-7 1) Mean: most likely value 2) Variance or standard deviation 3) Skewness * If a distribution is approximately normal, the distribution is described by characteristics 1 and 2. Characteristics of Probability Distributions

8. 5-8 Symmetric distribution mean s.d. Normal Distribution

9. 5-9 Subjective returns p(s) = probability of a state r(s) = return if a state occurs 1 to s states Mean Scenario or Subjective Returns

10. 5-10 StateProb. of Stater in State.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 Scenario or Subjective Returns: Example

11. 5-11 Standard deviation = [variance] 1/2 Subjective or Scenario Var =[(.1)(-.05-.15) 2 +(.2)(.05-.15) 2...+.1(.35-.15) 2 ] Var=.01199 S.D.= [.01199] 1/2 =.1095 Using Our Example : Variance or Dispersion of Returns

12. 5-12 Table 5.2 History of T-bill Rates, Inflation and Real Rates for Generations, 1926-2005

13. 5-13 Figure 5.2 Interest Rates and Inflation, 1926-2005

14. 5-14 Geometric Average Returns TV = Terminal Value of the Investment g= geometric average rate of return

15. 5-15 Geom.Arith.Stan. SeriesMean%Mean%Dev.% Sm Stk11.617.739.3 Lg Stk10.012.020.6 LT Gov 5.4 5.7 8.2 T-Bills 3.8 3.8 3.2 Inflation 3.1 3.1 4.4 Annual Holding Period Returns (Arithmetic)

16. 5-16 Risk Real SeriesPremiums%Returns% Sm Stk 13.914.6 Lg Stk 9.3 8.9 LT Gov 1.9 2.6 T-Bills --- 0.7 Inflation --- --- Risk Premiums Real Returns

17. 5-17 Figure 5.6 Histograms of Rates of Return for 1926-2005

18. 5-18 Table 5.3 History of Rates of Returns of Asset Classes for Generations, 1926- 2005

19. 5-19 Table 5.4 History of Excess Returns of Asset Classes for Generations, 1926- 2005

20. 5-20 Figure 5.7 Nominal and Real Equity Returns Around the World, 1900-2000

21. 5-21 Figure 5.8 Standard Deviations of Real Equity and Bond Returns Around the World, 1900-2000