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History of Interest Rates and
Risk Premiums
Chapter 5
McGraw-Hill/Irwin
Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved.
Factors Influencing Rates
Supply
Households
Demand
Businesses
Government’s Net Supply and/or
Demand
Federal Reserve Actions
5-2
»Level of Interest Rates
Interest Rates
Supply
r1
r0
Demand
Q0 Q1
Funds
5-3
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
5-4
Rates of Return: Single Period
P
1  P0  D1
HPR 
P0
HPR = Holding Period Return
P0 = Beginning price
P1 = Ending price
D1 = Dividend during period one
5-5
Rates of Return: Single Period Example
Ending Price =
Beginning Price =
Dividend =
48
40
2
HPR = (48 - 40 + 2 )/ (40) = 25%
5-6
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.
5-7
Normal Distribution
s.d.
s.d.
mean
Symmetric distribution
5-8
Mean Scenario or Subjective Returns
Subjective returns
s
E (r )   p s r s
1
p(s) = probability of a state
r(s) = return if a state occurs
1 to s states
5-9
Scenario or Subjective Returns: Example
State
Prob. of State
r 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
5-10
Variance or Dispersion of Returns
Subjective or Scenario
  
   p s  r s  E r 
2
s

2
Standard deviation = [variance]1/2
Using Our Example:
Var =[(.1)(-.05-.15)2+(.2)(.05- .15)2...+ .1(.35-.15)2]
Var= .01199
S.D.= [ .01199] 1/2 = .1095
5-11
Table 5.2 History of T-bill Rates, Inflation and Real Rates for
Generations, 1926-2005
5-12
Figure 5.2 Interest Rates and Inflation, 1926-2005
5-13
Geometric Average Returns
TV
n
 (1  r1)(1  r 2)  (1  r n)
TV = Terminal Value of the
Investment
g  TV
1/ n
1
g= geometric average rate of
return
5-14
Annual Holding Period Returns (Arithmetic)
Geom.
Series Mean%
Sm Stk 11.6
Lg Stk 10.0
LT Gov
5.4
T-Bills
3.8
Inflation 3.1
Arith.
Mean%
17.7
12.0
5.7
3.8
3.1
Stan.
Dev.%
39.3
20.6
8.2
3.2
4.4
5-15
Risk Premiums Real Returns
Risk
Series Premiums%
Sm Stk
13.9
Lg Stk
9.3
LT Gov
1.9
T-Bills
--Inflation
---
Real
Returns%
14.6
8.9
2.6
0.7
--5-16
Figure 5.6 Histograms of Rates of Return
for 1926-2005
5-17
Table 5.3 History of Rates of Returns of Asset
Classes for Generations, 1926- 2005
5-18
Table 5.4 History of Excess Returns of Asset
Classes for Generations, 1926- 2005
5-19
Figure 5.7 Nominal and Real Equity Returns
Around the World, 1900-2000
5-20
Figure 5.8 Standard Deviations of Real Equity and Bond
Returns Around the World, 1900-2000
5-21