History of Interest Rates and Risk Premiums

1
Chapter 5

• History ofInterest Rates andRisk Premiums

2
Factors Influencing Rates

• Supply
• Households
• Demand
• Businesses
• Governments Net Supply and/or Demand
• Federal Reserve Actions

3
Level of Rates
4
Real vs. Nominal Rates

• 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

5
Rates of Return Single Period

HPR Holding Period Return P0 Beginning
price P1 Ending price D1 Dividend during
period one
6
Rates of Return Single Period Example

• Ending Price 48
• Beginning Price 40
• Dividend 2
• HPR (48 - 40 2 )/ (40) 25

7
Characteristics of Probability Distributions

• 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

8
Normal Distribution
s.d.
s.d.
r
Symmetric distribution
9
Measuring Mean Scenario or Subjective Returns
Subjective returns
p(s) probability of a state r(s) return if a
state occurs 1 to s states
10
Numerical Example Subjective or Scenario
Distributions
State Prob. 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
11
Measuring Variance or Dispersion of Returns

• Subjective or Scenario

Standard deviation variance1/2
Using Our Example
Var (.1)(-.05-.15)2(.2)(.05- .15)2...
.1(.35-.15)2 Var .01199 S.D. .01199 1/2
.1095
12
Annual Holding Period ReturnsFrom Figure 6.1 of
Text

• Geom. Arith. Stan.
• Series Mean Mean Dev.
• Lg Stk 10.5 12.5 20.4
• Sm Stk 12.6 19.0 40.4
• LT Gov 5.0 5.3 8.0
• T-Bills 3.7 3.8 3.3
• Inflation 3.1 3.2 4.5

13
Annual Holding Period Risk Premiums and Real
Returns

• Risk Real
• Series Premiums Returns
• Lg Stk 8.7 9.3
• Sm Stk 15.2 15.8
• LT Gov 1.5 2.1
• T-Bills --- 0.6
• Inflation --- ---