chap005
TRANSCRIPT
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Investments, 8th edition
Bodie, Kane and Marcus
Slides by Susan HineSlides by Susan Hine
McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved.
CHAPTER 5CHAPTER 5 Learning About Learning About Return and Risk Return and Risk from the from the Historical RecordHistorical Record
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Factors Influencing Rates
• Supply
– Households
• Demand
– Businesses
• Government’s Net Supply and/or Demand
– Federal Reserve Actions
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Real and Nominal Rates of Interest
• Nominal interest rate
– Growth rate of your money
• Real interest rate
– Growth rate of your purchasing power
• If R is the nominal rate and r the real rate and i is the inflation rate:
r R i
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Equilibrium Real Rate of Interest
• Determined by:
– Supply
– Demand
– Government actions
– Expected rate of inflation
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Figure 5.1 Determination of the Equilibrium Real Rate of Interest
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Equilibrium Nominal Rate of Interest
• As the inflation rate increases, investors will demand higher nominal rates of return
• If E(i) denotes current expectations of inflation, then we get the Fisher Equation:
( )R r E i
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Taxes and the Real Rate of Interest
• Tax liabilities are based on nominal income
– Given a tax rate (t), nominal interest rate (R), after-tax interest rate is R(1-t)
– Real after-tax rate is:
(1 ) ( )(1 ) (1 )R t i r i t i r t it
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Comparing Rates of Return for Different Holding Periods
100( ) 1
( )fr T P T
Zero Coupon Bond
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Example 5.2 Annualized Rates of Return
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Formula for EARs and APRs
1
{ } 11 ( )
1(1 )T
TfEAR r T
EARAPRT
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Table 5.1 Annual Percentage Rates (APR) and Effective Annual Rates (EAR)
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Bills and Inflation, 1926-2005
• Entire post-1926 history of annual rates:
– www.mhhe.com/bkm
• Average real rate of return on T-bills for the entire period was 0.72 percent
• Real rates are larger in late periods
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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 for Investment in Treasury Bills,
1966-2005
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Risk and Risk Premiums
P
DPPHPR0
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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Expected returns
p(s) = probability of a stater(s) = return if a state occurss = state
Expected Return and Standard Deviation
( ) ( ) ( )s
E r p s r s
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State Prob. of State r in State 1 .1 -.052 .2 .053 .4 .154 .2 .255 .1 .35
E(r) = (.1)(-.05) + (.2)(.05)… + (.1)(.35)E(r) = .15
Scenario Returns: Example
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Standard deviation = [variance]1/2
Variance:
Var =[(.1)(-.05-.15)2+(.2)(.05- .15)2…+ .1(.35-.15)2]Var= .01199S.D.= [ .01199] 1/2 = .1095
Using Our Example:
Variance or Dispersion of Returns
22 ( ) ( ) ( )s
p s r s E r
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Time Series Analysis of Past Rates of Return
n
s
n
ssr
nsrsprE
11)(
1)()()(
Expected Returns and the Arithmetic Average
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Geometric Average Return
1 2(1 )(1 ) (1 )nnr r rx xTV
TV = Terminal Value of the Investment
1/1 TVg n
g= geometric average rate of return
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Geometric Variance and Standard Deviation Formulas
• Variance = expected value of squared deviations
• When eliminating the bias, Variance and Standard Deviation become:
22
1
1( )
n
s
r s rn
2
1
1( )
1
n
j
r s rn
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The Reward-to-Volatility (Sharpe) Ratio
Sharpe Ratio for Portfolios =Risk PremiumSD of Excess Return
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Figure 5.4 The Normal Distribution
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Figure 5.5A Normal and Skewed Distributions (mean = 6% SD = 17%)
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Figure 5.5B Normal and Fat-Tailed Distributions (mean = .1, SD =.2)
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Figure 5.6 Frequency Distributions 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
2 21 1
20 20[1 ( )]T
g gT TTe eE r
When the continuously compounded rate of return on an asset is normally distributed, the effective rate of return will be lognormally distributed
The Terminal Value will then be:
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Figure 5.10 Annually Compounded, 25-Year HPRs from Bootstrapped History and
A Normal Distribution (50,000 Observation)
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Figure 5.11 Annually Compounded, 25-Year HPRs from Bootstrapped
History(50,000 Observation)
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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