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Investments, 8th editionBodie, 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 AboutLearning AboutReturn and RiskReturn and Risk

from thefrom the

Historical RecordHistorical Record

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5-2

Factors Influencing Rates

Supply

± Households

Demand

± Businesses

Government¶s Net Supply and/or Demand

± Federal Reserve Actions

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5-3

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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5-4

Equilibrium Real Rate of Interest

Determined by:

± Supply

± Demand

± Government actions

± Expected rate of inflation

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5-5

Figure 5.1 Determination of the

Equilibrium Real Rate of Interest

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5-6

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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5-7

Risk and Risk Premiums

P

D P P HPR

0

101 !

HP R = Holding Period Return

P 0 = Beginning price

P 1 = Ending price

D1 = Dividend during period one

Rates of Return: Single Period

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5-8

Ending Price = 48

Beginning Price = 40

Dividend = 2

HP R = (48 - 40 + 2 )/ (40) = 25%

Rates of Return: Single Period Example

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5-9

Expected returns

p(s) = probability of a state

r (s) = return if a state occurs

s = state

Expected Return and Standard Deviation

( ) ( ) ( ) s

E r p s r s!§

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5-10

State Prob. of State r in State

1 .1 -.05

2 .2 .05

3 .4 .154 .2 .25

5 .1 .35

E (r ) = (.1)(-.05) + (.2)(.05)« + (.1)(.35)

E (r ) = .15

Scenario Returns: Example

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5-11

Standard deviation = [variance]1/2

Variance:

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

? A22 ( ) ( ) ( )

s

p s r s E r W ! §

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5-12

Time Series Analysis of Past Rates of

Return

§§ !!!!

n

s

n

s sr

n sr s pr E

11)(

1)()()(

Expected Returns and

the Arithmetic Average

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5-13

Geometric Average Return

1 2(1 )(1 ) (1 )nn

r r r x xTV ! ! K

TV = Terminal Value of the

Investment

1/1

!TV g n

g=

geometric averagerate of return

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5-14

Quoting Conventions

APR = annual percentage rate

(periods in year) X (rate for period)

EAR = effective annual rate( 1+ rate for period)Periods per yr - 1

Example: monthly r etur n of 1%

APR = 1% X 12 = 12%EAR = (1.01)12 - 1 = 12.68%

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5-16

Figure 5.5A Normal and Skewed Distributions

(mean = 6% SD = 17%)

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5-17

Figure 5.5B Normal and Fat-Tailed

Distributions (mean = .1, SD =.2)

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5-18

Figure 5.6 Frequency Distributions of

Rates of Return for 1926-2005

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5-20

Table 5.4 History of Excess Returns of Asset

Classes for Generations, 1926- 2005

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5-21

Figure 5.10 Annually Compounded, 25-Year

HPRs from Bootstrapped History and

A Normal Distribution (50,000 Observation)

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5-22

Figure 5.11 Annually Compounded,

25-Year HPRs from Bootstrapped

History(50,000 Observation)

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5-23

Figure 5.12 Wealth Indexes of Selected

Outcomes of Large Stock Portfolios and

the Average T-bill Portfolio

fin 523 ch5

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