chapter 5 · 5- 11 cover image p hpr p p d 0 0 1 hpr = holding period return p 0 = beginning price...
TRANSCRIPT
CHAPTER 5
Investments
Learning About
Return and Risk
from the Historical
Record Slides by
Richard D. Johnson
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved McGraw-Hill/Irwin
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5- 2
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Factors Influencing Rates
Supply
–Households
Demand
–Businesses
Government’s Net Supply and/or Demand
–Federal Reserve Actions
5- 3
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image
Figure 5.1 Determination of the Equilibrium
Real Rate of Interest
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Return for Holding Period – Zero Coupon
Bonds
1)(
100)(
TPTr f
5- 5
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Example 5.2 Annualized Rates of Return
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Formula for EARs and APRs
T
EARAPR
TrEART
T
f
1)1(
1})(1{]/1[
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Table 5.1 Annual Percentage Rates (APR) and Effective Annual
Rates (EAR)
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Table 5.2 History of T-bill Rates, Inflation and Real Rates for
Generations, 1926-2005
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Figure 5.2 Interest Rates and Inflation, 1926-
2005
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Figure 5.3 Nominal and Real Wealth Indexes,
1966-2005
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P
DPPHPR
0
101
HPR = Holding Period Return
P0 = Beginning price
P1 = Ending price
D1 = Dividend during period one
Rates of Return: Single Period
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Ending Price = 48
Beginning Price = 40
Dividend = 2
HPR = (48 - 40 + 2 )/ (40) = 25%
Rates of Return: Single Period Example
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Subjective returns
p(s) = probability of a state
r(s) = return if a state occurs
1 to s states
Mean Scenario or Subjective Returns
rprE s
s
s1
)(
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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
Scenario or Subjective Returns: Example
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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
rErp s
s
s 2
2
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Mean and Variance of Historical Returns
n
s
n
ssr
nsrsprE
11)(
1)()()(
n
s rsrn 1 )(
212
Arithmetic average or rates of
return
Average return is arithmetic
average
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Geometric Average Returns
)1()1)(1(21 rrrTV nn
TV = Terminal Value of the
Investment
1/1TVg n
g= geometric average rate of
return
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Sharpe Ratio
Sharpe Ratio for Portfolios Risk Premium
SD of Excess Return
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Figure 5.4 The Normal Distribution
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Figure 5.5A Normal and Skewed
(mean = 6% SD = 17%)
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Figure 5.5B Normal and Fat Tails Distributions
(mean = .1 SD =.2)
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Figure 5.6 Histograms of Rates of Return
for 1926-2005
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Table 5.3 History of Rates of Returns of Asset
Classes for Generations, 1926- 2005
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Table 5.4 History of Excess Returns of Asset
Classes for Generations, 1926- 2005
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Figure 5.7 Nominal and Real Equity Returns
Around the World, 1900-2000
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Figure 5.8 Standard Deviations of Real Equity and Bond
Returns Around the World, 1900-2000
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Figure 5.9 Probability of Investment Outcomes
After 25 Years with A Lognormal Distribution
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Terminal Value with Continuous Compounding
erETgTT 22/1
)](1[
5- 29
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Figure 5.10 Annually Compounded, 25-Year HPRs from
Bootstrapped History and A Normal Distribution
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Figure 5.11 Annually Compounded, 25-Year
HPRs from Bootstrapped History
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Figure 5.12 Wealth Indexes of Selected Outcomes of
Large Stock Portfolios and the Average T-bill Portfolio
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Table 5.5 Risk Measures for Non-Normal
Distributions