1. History of Interest Rates and Risk Premiums Chapter 5

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

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

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

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

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. Symmetric distribution r s.d. Normal Distribution

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

10. StateProb. of Stater 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 Numerical Example: Subjective or Scenario Distributions

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

12. Geom.Arith.Stan. SeriesMean%Mean%Dev.% Lg Stk10.512.520.4 Sm Stk12.619.040.4 LT Gov 5.0 5.3 8.0 T-Bills 3.7 3.8 3.3 Inflation 3.1 3.2 4.5 Annual Holding Period Returns From Figure 6.1 of Text

13. Risk Real SeriesPremiums%Returns% Lg Stk 8.79.3 Sm Stk15.2 15.8 LT Gov 1.5 2.1 T-Bills --- 0.6 Inflation --- --- Annual Holding Period Risk Premiums and Real Returns