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Investment Management Equations
1. Rate of re turn on an asset or portfolio
Return = (End-of-period wealth - beginn ing -ofperiod weal t h )/( begi n n i n g-of~pe ri od wealth)
2. Actual margin in a stock purchase
(nXmp) -[(I-im) X /,p X ,,]
am =
>I X mp
3. Market price at which a margin purchaser
will re ceive a margin call
_ (I - ;1>1) X pp

mp-

1 - mm

4. Actual margin in a short sale

[(spXn) X ( I +im)] -(mpX>l)
X
mp n

am =

5. Market price at which a short seller will
.Ip X (1 + ;1>1)
mp =
1+ mm
6. Expe cted return o n a portfolio
,\'

rp =

; =1

7. Covariance between two securities
au = P'jUjU'j
8. Standard deviation of a portfolio
Up

=

.v

~ ~ XiXi0';,

[

] 1/2

9. Standard deviation of a two-asset portfolio
'1
') 2
~ I /~
U p = XjUI + X,1O'2 + 2XIX"PI2IT ,U 2j
10. The market model
"j = Uj + {3;'/ + e,
11. Beta from the market model
'j

[

13,. =

Uj

12. Securitv variance from the market model

u; = l3~u7 + 0';,.

13. Security cov,~riance from th e market model
U,j = f3if3 jUj
14. Variance of a portfolio (by market and unique risk)
IT~ = f3~ u; + u;p
15. Mark et risk of a portfolio

.v

e, = ;L=1 x;f3;
16. Unique risk of a portfolio
s

L XTu;,

j =1

17. Capital Market Line

r"

= 'j

Ii)] u p

( '.11 -

+ [- - - 0' .11

18. Variance of the market portfolio
.\'

.\'

L L X,.\,Xj.\fU,j

a~, =

, =1 j =1

19. Security Market Line (covariance and beta versions)

r; =

'j

+ [( r.1I ~ r/)] Ui.1I
fr .\1

r; =

'i + (1"11 -

Tj)f3,

20. Beta from the CAP:'.I
= 17, .11

13

t

U ",\1

+ (b" hJ2 + [J' 2bjl) Coo( fj f ;)
24. Arb itrage Pricing Theory (two-factor model)
1-;=A o+A,II" +A 211'2
1- i = 'i+ (<5 1 - 'i)h" + (<5 2

rl)h'2
25. Break-even tax rate for equivalence of taxexempt and taxable bond yields
I = I - ratio of tax-exempt to taxable bond yields
26. Geometric mean (compound) annual
growth rate of an index's value

-1
C"
27. Real rate of return on an asset or portfolio

RR

I + NR] - I

1 + eCL
Nil - CeL

=[

Ru »

28. Yield-to-maturity
P. = __C_'I_+~+... + C, + J l

"

(1 + y)1

(I +y)2

(I +y)'

29. Discount factor
I

,('=-(--)'

1 + 5,
30. Forward rate between years I-I and I

Uil
.,

uZ/J =

+ lr;;

_ (C,)II.'
g-

LX;r i

\'

21. Two-factor model
ri = a, + bil!'j + b'2F..! + e,
22. Variance of a -se cu ri ty (1.>)' factor and
non-factor risk . two-factor model)
u7 = 1r"ul'l + til~(T~'2 + 2h dbi 2 COV( J·j. f;)
23. Covariance between two securities (twofact or model )
U,j = bilbj,u;"1 + hiA2U;" 2

(I + s,)'

38. Bet a from a simpl e lin ear regr ession

N

)
i

(N

( T X i~ X, Y

{3 =

( TX

i~

-

Yi X

55. Intrinsic valu e of puts and ca lls
N c = MAX (O, Ps - E)
N p = ,\,1AX( O, E - p.,)
56. Pu t ca ll parity
E
PI' + p., = P" + e RT

S )

i~ Xi

t·x/ ) - ( t X,)

I -I

,- I

39. Alpha from a simpl e lin e ar reg ression

N

.....

L Yi

57. Black-Sch ole s formula for th e fai r value
of a ca ll o p tio n
E
Ve = N{ d] )p, - eR T N{ dJ

L Xi

(3 X

a=~-

i=1

T

T

40. Standard deviation of th e ra ndom error te rm
from [a
_

ri

tn;;~i(n:a~ i;)SSi: {3 X

I-I

I -I

T - 2

II" -

~

Xi

Y,)]

l'2

(

±

Xi)2]"2

'~~

j,;x,y,) - (f Y, X f x,\J
- I

•- I

t: I

_ [(I -v,.T)D] +
f3rkhl

,Bl"qll it)'

= {3r."" + ({3,;""

- (3'kh' ) (

~) ( I -

T)

47 . Ca pita lizatio n-of-inco me me tho d of valuatio n
V=

NSO,

f -( I +C
-,1<)'-

,~ I

48. Zero-growth DDM

= ar p - ar"IJ

a"

0,

(I +1<)'

]

+[

° nl

]

(l< -g)( 1 +I<)T

51. "Normal" price-earn in gs rati o with co nsta n t
growth

(I (I-

V _
+ I'
1'))
Eo -I' 1< -1' (1 - 1')
52. Lintner divid end payo ut model
0, = ap» E, + (1 - a)Dt-I
53. Annual ea rn ings as a ra ndom walk
E, = E, _I + £ ,
54. Q uarterly ea rni ngs as a n au to progressive proce ss

QE, = QEf-4

II /'

70. M"

50. Multiple-growth DDM

±

aT
- -f

_ aI'" -

.5R/' - -

I<-g

re l

a'i

13/'

69. Sh arpe ra tio

V=~

-

flrp -

p

49. Constant-growth DDM

V- [

up

66. Ex post alpha based on th e CAI' M
= arp - [ ali + (a1",11 - aTf) 13,,]
67 . Ex post characte ristic lin e
rp - rf = a p + 13,,( 1",\/ - 'i)
68. Reward-to-volat ility ra tio (Trey no r ratio )
RVOL =

V= D I
I<

(TI) .,

r/J -

65. Ex post alpha
Ct/J

+ b13.

a

- /~, N( -dl)

eRr

VY

59. Fair value of a futures con trac t
Pf = p., + I - B + C
60. Fair va lue of an ind ex futures co n trac t
Pf = 1\ + RI \ - y p.~
61. In vestment co m pa ny's ne t asse t value

1l ,. =

13" =

( E)N (-dJ

= d, - II
II
T
58. Black-Scholes formula for the fair valu e
of a put option

T = ( r s - T )2

f
64. Certainty equivalent ret urn

( \1"E)

45. Beta of th e firm's eq u ity
(3" I"i')

=

)T

V7

63. Risk tolerance (as implied by a cho ice
of a portfoli o)
2 ( Tr. - rf) II~

44. Beta of the firm
-

PI'

2

62. Return o n a n invest me nt co mpa ny's shares
(NAV, ~ NA \~ _]) + I, + G,
1', =
NAV, _,

43. Correlation coefficient

f3 firm

=

- SII

r

i=l

1

d2

In(~) + (R

NA V = MVA, - LIAB,

L X;

( 'J'X

+ (R+ SII" ) T
II VY

42. Standard e rro r of a lp ha fro m a si m p le linear
regression

T-

In(~)

1-1

41. Standard error of beta from a sim pie lin ear
regression

II n = [

d, =

+ a( QE,_ I - QE,_,) + b + e,

o

Mj, = flli

alP- -aTf ) lIM
+ ( --IIp

71. Ex post c ha rac ter istic c ur ve
'p - rf= a + b( 1",I1- rf) + c[(rM - rfn
72. Ex post c haracteris tic lin es
rp - 'i = a +b(r,\/ - 'i) + c[D(rM - rf)]
wher e: D = if 1',11 > rf
0 = -1 if 1",\1 < 'i
73. Return o n a fo reign in vestment

°

rf' = 1'" + 1', + 1',,1',
74. Standa rd d eviat ion of a forei,? in vestment
IIF = ( II~ + II~ + 2p" ,II"II, ) /2

-

SIXTH

EDITION

INVESTMENTS
WILLIAM

F

SHARPE

STANFORD UNIVERSITY

GORDON J. ALEXANDER
UNIVERSITY OF MINNESOTA

JEFFERY

V

BAILEY

DAYTON HUDSON CORPORATION

Prentice Ha ll, Upper Saddle River. New Jersey 07458

Senior Acquisitions Editor: Paul Donnelly
VP/ Ed itorial Director: jim Boyd
Editorial Assistant:jodi Hirsh
Marketing Manager: Patrick Lynch
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Production Manager: Susan Rifkin
Managing Editor: Dee josephson
Production Co ordinator: Carol Samet
Senior Manufacturing Supervisor: Paul Smolenski
Manufacturing Manager: Vincent Scelta
Design Manager: Pat Smythe
Cover Design: Cheryl Asherman
Cover Photo: George Diebold, The Stock Market
Full-Service Production & Composition: Prepare Inc. / Emilcomp s.r.l .

© 1999 ,1995 by Prentice H all, Inc.

Upper Saddle River, New jersey 07458

All rights reserved. No part of this book may be reproduced, in any form or by any

means, without permission in writing from the publisher.

Sharpe, William F.
Investments / William F. Sharpe , Gordonj. Alexander.jeffery
V. Bailey. - 6th ed.
p. em .
Includes bibliographical references and index.
ISBN 0-13-010130-3
1. Investments 2. Investments analysis I. Alexander, Gordon
j., II. Bailey.jeffery V. III. Title.
HG4521.S48 1998
332 .63'2--<1c21
98-40710
CIP

ISBN 0-13-010130-3
Prentice-Hall International (UK) Limited.London
Prentice-Hall of Australia Pty. Limited, Sydney
Prentice-Hall Hispanoarnericana, S.A., Mexico
Prentice-Hall of India Private Limited, New Delhi
Prentice-Hall of Japan, Inc., Tokyo
Pearson Education Asia Pte. Ltd., Singapore
Editora Prentice-Hall do Brasil, Ltda., Rio de Janeiro

Printed in the United States of America
10

9

8

7

To Kathy
WFS

To my mother and in memory
of my father

GJA

In memory of Sudhaker Rao Aiyagari,

a brilliant economist and a good friend
JVB

- B

R IE

F

CON

TEN

T

S

PREFA CE
AB O UT TH E A UTHO RS

1

INTRODU CTIO N

2

3

SFCURITY MARKETS

4

EFFICIENT M A RKETS, INVESTM ENT VALUE, AND M A RKET PRI CE

5

T HE V ALUATIO N O F RISKLESS SECURITIES

6

T H E P ORTFOLI O SELECTION PRO BLEM

7

PO RTFOLIO A NALYSIS

8

RISKFREE B O RRO WI N G AN D L EN DING

9

T HE CAPITAL A SSET P RI CIN G M O D EL

10

FACTO R M O D ELS

11

ARBITRAGE P RI CING TH EORY

12

TAXES AND IN FLATIO N

13

FIXED-INC OM E SECURITIES

14

BOND A NALYSIS

15

B O N O PORTFOLIO M A NAGEM ENT

16

COMMON STOCKS

17

THE V ALUATIO N O F C O MMO N STOCKS

18

EA RNIN GS

19

O PTIO NS

20

FUTURES

21

INVESTMENT COMPANIES

22

FINANCIAL ANALYSIS

23

INVESTMENT M A NAGEM ENT

24

PO RTFOLIO P ERFO RMA N CE EVALUATION

25

INTERNATIO NAL INV ESTIN G
G LOSSARY
SELECTED SO LUTION S
INDEX

XXV

xxix

1
22
47
85
108
139

171
204
227
256
283
305
340
386
417
457
523
559
60 1
654
699
740
792
825
876
906
93 4
939

v

CONTE

NTS

PREFACE

1

INTRODUCTION

THE INVESTMENT ENVIRONMENT
1. 1. 1 Securities
1.1 .2
Risk, Return, and Diversification
Security Markets
1.1 .3
1.1 .4
Financial Intermediaries
1.2
THE INVESTMENT PROCESS
1.2 .1
Investment Policy
1.2 .2
Security Analysis
1.2.3
Portfolio Construction
1.2 .4
Portfolio Revision
1.2.5
Portfolio Performance Evaluation
INVESTMENTS AS A CAREER
J .3
1.4

GLOBALIZATION
1.5
SUMMARY
INSTITUTIONAL ISSUES: INSTITUTIONAL INVESTORS
INSTITUTIONAL ISSUES: INVESTMENT POLICY
1.1

2

XXV

xxix
1
2
2
8

9
10
11
1J
12
13
14
14
14
16
17
4
13

22

ORDER SIZE
TIME liMIT
TYPES OF ORDERS
Market Orders
2.3.1
2.3 .2
Limit Orders
Stop Orders
2 .3.3
2.3 .4
Stop Limit Orders
2.4
MARGIN ACCOUNTS
2.4 .1
Margin Purchases
2 .4.2
Short Sales
2.4.3
Securities Lending
2 .4.4 Aggregation
2.5
SUMMARY
INSTITUTIONAL ISSUES: MARKET NEUTRAL STRATEGIES
INSTITUTIONAL ISSUES: HEDGE FUNDS

23
23
24
24
24
24
25
25
26
30
37
38
41
32
40

2 .1
2 .2
2.3

vii

3

SECURITY MARKETS

47

3. J

47
47
47
48
48
56
57
59
60
63

CALL AND CONTINUOUS MARKETS
Call Markets
Continuous Markets
MAJOR MARKETS IN THE UNITED STATES
3.2
3.2 .1 New York Stock Exchange
3.2 .2 Other Exchanges
3.2.3 Over-the-Counter Market
3.2 .4 Third and Fourth Markets
3.2.5 Preferencing
3.2.6 Foreign Markets
INFORMATION-MOTIVATED
3.3
3.4
CENTRAL MARKET
3.5
CLEARING PROCEDURES

3.6
INSURANCE
3.7
COMMISSIONS
3.7.1 Fixed Commissions
3.7.2 Competitive Commissions
TRANSACTIONS COSTS
3.8
3.8.2 Price Impact
3.9
REGULATION OF SECURITY MARKETS
3.10
SUMMARY
INSTITUTIONAL ISSUES: CI~OSSING SYSTEMS :
EVOLUTION OF THE FOURTH MARKET
INSTITUTIONAL ISSUES: SOFT DOLLARS

3.1 .1
3.1.2

4

62
70

EFFICIENT MARKETS, INVESTMENT VALUE,
AND MARKET PRICE

85

4.1

85
86
86
87

4.2

viii

65
67
68
69
69
69
69
71
71
72
74
76

DEMAND AND SUPPLY SCHEDULES
4.1 .2 Supply-to-Sell Schedule
4.1.3 Interaction of Schedules
4.1 .4 Elasticity of the Demand-to-Buy

Schedule
and Supply-to-Sell Schedules
4.1.6 Summary
MARKET EFFICIENCY
4.2.1 The Efficient Market Model
4.2.2 Famas Formulation
of the Efficient Market Model
4.2.3 Security Price Changes
as a Random Walk

89
89
91
92
93
94
95
Contents

4.2.4

5

Efficient Markets
Efficient Markets With Transactions Costs
TESTING FOR MARKET EFFICIENCY

4.3
4.3.1 Event Studies
4.3.2 Looking for Patterns
4.3.3 Examining Performance
SUMMARY OF MARKET EFFICIENCY TEST RESULTS
4.4
4.4.1 Weak-Form Tests
4.4.2 Semistrong-Form Tests
4.4.3 Strong-Form Tests
4.4.4 Summary of Efficient Markets
SUMMARY
4.5
INSTITUTIONAL ISSUES: THE ARIZONA STOCK EXCHANGE:
A BETTER MOUSETRAP
INSTITUTIONAL ISSUES: THE AOIVE VERSUS PASSIVE DEBATE

97
97
98
102
102
103
103
103
103
103
104

THE VALUATION OF RISKLESS SECURITIES

108

5.1
5.2

J 08
112
112
114
115
116
118
118
119
1J9
120
120
124
127
127
127
128
130
135
110

NOMINAL VERSUSREAL INTEREST RATES
YIELD-To-MATURITY
5.2.1 Calculating Yield-to-Maturity
SPOT RATES

5.3
DISCOUNT FACTORS
5.4
FORWARD RATES
5.5
FORWARD RATES AND DISCOUNT FAOORS
5.6
COMPOUNDING
5.7
THE BANK DISCOUNT METHOD
5.8
YIELD CURVES
5.9
5.10 TERM STRUOURE THEORIES
5.10.1 The Unbiased Expectations Theory
5.10.2 The Liquidity Preference Theory
5.10 .3 The Market Segmentation Theory
5.10 .4 The Preferred Habitat Theory
5.10 .5 Empirical Evidence on the Theories
HOLDING-PERIOD RETURN
5.11
SUMMARY
5.12
ApPENDIX: CONTINUOUS COMPOUNDING
INSTITUTIONAL ISSUES : ALMOST RISKFREE SECURITIES

6

THE PORTFOLIO SELECTION PROBLEM

6.1

Contents

INITIAL AND TERMINAL WEALTH
6.1 .1 Determining the Rate of Return
on a Portfolio
6.1.2 An Example

96

90
98

139

140
140
141
ix

NONSATIATION AND RISK AVERSION
Nonsatiation
Risk Aversion
UTILITY
6.3
6.3.1 Marginal Utility
6.3.2 Certainty Equivalents and Risk Premiums
INDIFFERENCE CURVES

6.4
CALCULATING EXPECTED RETURNS AND STANDARD
6.5
DEVIATIONS FOR PORTFOLIOS
6.5.1 Expected Returns
6.5.2 Standard Deviations
SUMMARY
6.6
ApPENDIX A: CHARACTERISTICS OF PROBABILITY DISTRIBUTIONS
AI
Probability Distributions
A2
Central Tendency
A3
Dispersion
Comovement
A4
APPENDIX B: RISK-NEUTRAL AND RISK-SEEKING INVESTORS
INSTITUTIONAL ISSUES: BEHAVIORIAL FINANCE
INSTITUTIONAL ISSUES: ALTERNATIVE RISK MEASURES

141
141
142
142
142
144
144

PORTFOLIO ANALYSIS

171

7.1

171
172

6.2

6.2.1
6.2.2

7

THE EFFICIENT SET THEOREM
7.1.1 The Feasible Set
7.1.2 The Efficient Set Theorem Applied
to the Feasible Set
7.1.3 Selection of the Optimal Portfolio
CONCAVITY OF THE EFFICIENT SET
7.2
7.2.1 Bounds on the Location of Portfolios
7.2.2 Actual Locations of the Portfolios
THE MARKET MODEL
7.3
7.3.1 Random Error Terms
7.3.2 Graphical Representation
of the Market Model
7.3.3 Beta

7.3.4 Actual Returns
DIVERSIFICATION
7.4
7.4.1 Portfolio Total Risk
7.4.2 Portfolio Market Risk
7.4.3 Portfolio Unique Risk
7.4.4 An Example
7.4.5 Random versus Efficient Diversification
SUMMARY
7.5
ApPENDIX A: THE MARKOWITZ MODEL
AI
Determining the Composition
and Location of the Efficient Set
x

148
149
151
155
162
162
163
164
165
166
146
156

172

173
J75
175
179
181
181
182
183
184
184
185
186
186
187
190
190
193
193
Contents

A.2

Determining the Composition
of the Optimal Portfolio
ApPENDIX B: DETERMINING THE INPUTS NEEDED
FOR LOCATING THE EFFICIENT SET
INSTITUTIONAL ISSUES: THE TROUBLE WITH OPTIMIZERS
INSTITUTIONAL ISSUES: THE ACTIVE MANAGER PORTFOLIO
SELECTION PROBLEM

8

9

197
198
176
188

RISKFREE BORROWING AND LENDING

204

8.1
8.2

204
205

DEf'INING THE RISKFREE AsSET
ALLOWING FOR RISKFREE LENDING
8.2.1 Investing in Both a Riskfree Asset
and a Risky Asset
8.2.2 Investing in Both the Riskfree Asset
and a Risky Portfolio
8.2 .3 The Effect of Riskfree Lending
on the Efficient Set
8.2.4 The Effect of Riskfree Lending
on Portfolio Selection

ALLOWING
FOR RISKFREE BORROWING
8.3
8.3.1 Borrowing and Investing
in a Risky Security
8.3.2 Borrowing and Investing
in a Risky Portfolio
ALLOWING FOR BOTH RISKFREE BORROWING
8.4
AND LENDING
8.4.1 The Effect of Riskfree Borrowing
and Lending on the Efficient Set
8.4.2 The Effect of Riskfree Borrowing
and Lending on Portfolio Selection
SUMMARY
8.5
ApPENDIX A: ALLOWING FOR DIFFERENT BORROWING
AND LENDING RATES
APPENDIX B: DETERMINING THE COMPOSITION
OF THE INVESTOR'S OPTIMAL PORTFOLIO 0 *
INSTITUTIONAL ISSUES: THE COST OF SHORT-TERM BORROWING

223
2J8

THE CAPITAL AsSET PRICING MODEL

227

9.1

9.2

227
229
229
230
231
233
233
236

9.3

Contents

AsSUMPTIONS
THE CAPITAL MARKET LINE
9.2.1 The Separation Theorem
9.2.2 The Market Portfolio
9.2.3 The Efficient Set
THE SECURITY MARKET LINE
9.3 .1 Implications for Individual Risky Assets
9.3.2 An Example

206
208
210
21 I
211
211

215
215
215
217
218
221

xi

THE MARKET MODEL
9.4.1 Market Indices
9.4.2 Market and Non-Market Risk
9.4.3 An Example
9.4.4 Motivation for the Partitioning of Risk
SUMMARY
9.5
ApPENDIX A: SOME EXTENDED VERSIONS OF THE CAPM
AI
Imposing Restrictions
on Riskfree Borrowing
AI . J The Capital Market Line
AI.2 The Security Market Line
A2
Introducing Heterogeneous
Expectations
A3
liquidity
ApPENDIX B: A DERIVATION OF THE SECURITY MARKET LINE
INSTITUTIONAL ISSUES: THE ELUSIVE MARKET PORTFOLIO

238
239
240
240
241
241
245

FACTOR MODELS

256

FACTOR MODELS AND RETURN-GENERATING PROCESSES
10.1.1 Factor Models
10.1.2 Application
10.2 ONE-FACTOR MODELS
10.2. J An Example
10.2.2 Generalizing the Example
J 0.2.3 The Market Model
10.2.4 Two Important Features
of One-Factor Models
10.3 MULTIPLE-FACTOR MODELS
10.3.1 Two-Factor Models
10.3.2 Sector-Factor Models
10.3.3 Extending the Model
10.3.4 An Alternative
ESTIMATING FACTOR MODELS
J 0.4
10.4.1 Time-Series Approaches

10.4.2 Cross-Sectional Approaches
10.4.3 Factor-Analytic Approaches
10.4.4 Limitations
FACTOR MODELS AND EOUILIBRIUM
J 0.5
10.6 SUMMARY
INSTITUTIONAL ISSUES: THE BARRA U.S. EOUITY
MULTIPLE-FACTOR MODEL

256
256
257
257
258
259
260

9.4

10

10.1

11

ARBITRAGE PRICING THEORY
J

xii

1.1

FACTOR MODELS
I 1. 1. 1 Principle of Arbitrage
I 1. 1.2 Arbitrage Portfolios

245
245
246
247
248
250
232

260
262
262
266
267
267
270
270
271
275
275
275
276
268
283

283
284
284
Contents

I I . 1.3 The Investors Position
PRICING EFFECTS
11.2 . I A Graphical Illustration
11, .2 .2 Interpreting the APT Pricing Equation
Two-FACTOR MODELS
11 .3
I 1.3. I Arbitrage Portfol ios
11 .3 .2 Pricing Effects
MULTIPLE-FACTOR MODELS
11.4
A SYNTHESIS OF THE APT AND THE CAPM
J J.5
11 .5 .1 One-Factor Models
11.5 .2 Multiple-Factor Models
IDENTIFYING THE FACTORS
11.6
SUMMARY
11.7
INSTITUTIONAL ISSUES: ApPLYING ARBITRAGE PRICING THEORY
11.2

12

TAXES AND INFLATION

305

TAXES IN THE UNITED STATES
12. J.l Corporate Income Taxes
12.1.2 Personal Income Taxes
12.1.3 Before-Tax Investing
INFLATION IN THE UNITED STATES
12.2
12.2 .1 Measuring Inflation
12.2.2 Price Indices
NOMINAL AND REAL RETURNS
12.3
12.3.1 Nominal Returns
12.3.2 Fisher Model of Real Returns
12.3 .3 The Effect of Investor Expectations
INTEREST RATES AND INFLATION
12.4
THE EFFECT OF INFLATION ON BORROWERS AND LENDERS
12.5
INDEXATION
12.6
12.6.1 Government Bonds
12.6.2 Indexing Other Contracts
STOCK RETURNS AND INFLATION
12.7
12.7. I Long-Term Historical Relationships
12.7.2 Short-Term Historical Relationships
J2.7.3 Relationships Involving Expected
Inflation

SUMMARY
12.8
INSTITUTIONAL ISSUES: TAXING PENSION FUNDS
INSTITUTIONAL ISSUES: ADJUSTING CAPITAL GAINS TAXES
FOR INFLATION

305
306
309
319
322
322
323
325
325
325
326
327
327
328
328
330
330
330
331

12.1

13

286
286
287
288
289
289
291
291
292
292
295
296
297
294

FIXED-INCOME SECURITIES

13.1

Contents

SAVINGS DEPOSITS
13.1 .1 Commercial Banks
13.1.2 Other Types of Personal
Savings Accounts

331
333
310
320

340
340
340
341
xiii

13.2

INSTITUTIONAL ISSUES: DISTRESSED SECURITIES

343
343
343
344
345
345
345
348
350
351
352
353
354
354
355
357
358
360

361
364
364
365
366
367
367
367
368
369
370
370
370
374
376
376
377
378
362
372

BOND ANALYSIS

386

MONEY MARKET INSTRUMENTS

3.2. 1
13.2.2
13.2.3

13.2.4
J 3.2.5
J

13.3

U .S. GOVERNMENT SECURITIES

13.3.1
J 3.3 .2
13.3.3
13.3.4
13.3.5
13.4

Bonds of Federal Agencies
Participation Certificates
Collateralized Mortgage Obligations

STATE AND LOCAL GOVERNMENTAL SECURITIES

13.5. I
13.5.2
J 3.5.3
13.5.4
13.5.5
13.6

U.S. Treasury Bills

U.S. Treasury Notes
U.S. Treasury Bonds
U.S. Savings Bonds
Zero-Coupon Treasury Security Receipts

FEDERAL AGENCY SECURITIES

13.4. I
13.4.2
13.4.3
13.4.4
13.5

Commercial Paper
Certificates of Deposit
Bankers' Acceptances
Eurodollars
Repurchase Agreements

Issuing Agencies
Types of Municipal Bonds
Tax Treatment
The Market for Municipal Bonds
Municipal Bond Insurance

COI~PORATE BONDS

13.6.1
13.6.2
13.6.3

13.6.4
13.6.5
13.6.6
13.6.7
13.6.8
I 3.7
13.8
13.9
13.10

Tax Treatment
The Indenture
Types of Bonds
Call Provisions
Sinking Funds
Private Placements
Bankruptcy

FOREIGN BONDS
EUROBONDS
PREFERRED STOCK
SUMMARY

INSTITUTIONAL ISSUES: COLLATERALIZED BOND OBLIGATIONS

14

I 4. I

ApPLYING THE CAPITALIZATION OF INCOME METHOD
TO BONDS

14.1. I Promised Yield-to-Maturity
14.1 .2 Intrinsic Value

xiv

386
387
387

Contents

BOND ATTRIBUTES
14.2 .1 Coupon Rate and Length
of Time Until Maturity
14.2.2 Call and Put Provisions
14.2 .3 Tax Status
14.2.4 Marketability
14.2.5 Likelihood of Default
THE RISK STRUCTURE OF INTEREST RATES
14.3
14.4
FINANCIAL RATIOS AS PREDICTORS OF DEFAULT
14.5
14.5. J Univariate Methods
14.5.2 Multivariate Methods

14.5 .3 Investment Implications
SUMMARY
14.6
OF THE BOND RATING PROCESS
INSTITUTIONAL ISSUES: MATRIX BOND PRICING
14.2

15

BOND PORTFOLIO MANAGEMENT

15. J

15.2
15.3
15.4

) 5.5

15.6

15.7
15.8

Contents

BOND MARKET EFFICIENCY
J 5.1. J Price Behavior of Treasury Bills
15.1 .2 Expert Predictions of Interest Rates

15.1.3 Price Reaction to Bond Rating Changes
J 5.1.4 Money Supply Announcements
15.1.5 Performance of Bond Portfolio
Managers
15.1.6 Summary
BOND PRICING THEOREMS
CONVEXITY
DURATION
15.4 .1 The Formula
15.4.2 Relationship to Bond Price Changes
15.4 .3 Relationship Between Convexity
and Duration
J 5.4 .4 Changes in the Term Structure
IMMUNIZATION
15.5.1 How Immunization Is Accomplished
15.5.2 Problems with Immunization
ACTIVE MANAGEMENT
J 5.6 . 1 Horizon Analysis
15.6 .2 Bond Swaps
Contingent Immunization
J 5.6.3
J 5.6.4 Riding the Yield Curve
PASSIVE MANAGEMENT
BONDS VERSUS STOCKS

388
389
390
391
392

392
402
404
406
406
407
408
408
396
402

417
417
418
418
4J9
419
420
420
421
423
424
425
426
427
428
429
429
431
433

433
437
438
439
442
443

xv

16

SUMrvlARY
15.9
ApPENDIX: EMPIRICAL REejULARITIES IN THE BOND MARKET
A. 1
The January Effect
The Day-of-the-Week Effect
A2
INSTITUTIONAL ISSUES: SURPLUS MANAGEMENT
INSTITUTIONAL ISSUES: MODIFIED DURATION
AND KEY RATE DURATIONS

444
448
448
449
434

COMMON STOCKS

457
457
458
458
458
460
461
461
466
467
467
468
469
471
471
471
474
474
474
480
480
48J
482
482
483
483
484
485
486

487
488
489
492
496
496
497
497

THE CORPORATE FORM
16.1 .1 Stock Certificates
16.1.2 Voting
J6.1 .3 Proxy Fight
J6.1 .4 Takeovers
16.1.5 Ownership Versus Control
J6.1.6 Stockholders' Equity
CAsH DIVIDENDS
16.2
STOCK DIVIDENDS AND STOCK SPLITS
16.3
16.3.1 Ex-Distribution Dates
16.3.2 Reasons for Stock Dividends and Splits
PREEMPTIVE RIGHTS
16.4
STOCK QUOTATIONS
16.5
16.5.1 Nasdaq
16.5.2 U.S. Stock Exchanges
16.5.3 Foreign Stock Exchanges
Ex ANTE AND Ex POST VALUES

16.6
COMMON STOCKS BETAS
16.7
GROWTH VERSUS VALUE
16.8
J6.8.1 Book-Value-to-Market-Value Ratio
J6.8.2 Earnings-to-Price Ratio
16.8.3 Size
16.8.4 Interrelationships
PRlrvlARY MARKETS
16.9
16.9.1 Private Placements
16.9.2 Public Sale
16.9.3 Underpricing of lpos
16.9.4 Seasoned Offerings
16.9.5 Shelf Registration
16.9.6 Rule I 44A Securities
16.9.7 Secondary Distributions
J6.10 SUMrvlARY
ApPENDIX A: EMPIRICAL REGULARITIES IN THE STOCK MARKET
AI
Seasonality in Stock Returns
AI. 1 January Effect
A1.2 Day-of-the-Week Effect
16.1

xvi

440

Contents

A.2

Interrelationship of Size
and January Effects
A.3
International Evidence
A.3.1 Size Effect
A.3 .2 January Effect
A.3 .3 Day-of-the-Week Effect
A.3.4 Size and January Effects
A.4
Summary of Empirical Requtarities
ApPENDIX B: ADJUSTMENTS TO HISTORICAL COMMON
STOCK BETAS
B.1
Leverage and Beta
B.2
Industry Beta Values
8.2.1 Forecasting Beta
B.2.2 Multiple-Industry Firms
on Financial Characteristics
8.2.4 Example
8.3
Beta Services
INSTITUTIONAL ISSUES: CORPORATE GOVERNANCE
INSTITUTIONAL ISSUES: How FIRMS IN THE PEOPLE'S REPUBLIC

OF CHINA RAISE FUNDS
17

THE VALUATION OF COMMON STOCKS

17.1

17.2

17.3

17.4

17.5
17.6

Contents

CAPITALIZATION OF INCOME METHOD OF VALUATION
17.1. J Net Present Value
17.1.2 Internal Rate of Return
17.1.3 Application to Common Stocks
THE ZERO-GROWTH MODEL
17.2. J Net Present Value
17.2.2 Internal Rate of Return
17.2.3 Application
THE CONSTANT-GROWTH MODEL
17.3.1 Net Present Value
17.3.2 Internal Rate of Return
17.3.3 Relationship to the Zero-Growth Model

THE MULTIPLE-GROWTH MODEL
17.4.1 Net Present Value
J 7.4.2 Internal Rate of Return
J 7.4.3 Relationship to the Constant-Growth
Model
17.4.4 Two-Stage and Three-Stage Models
VALUATION BASED ON A FINITE HOLDING PERIOD
MODELS BASED ON PRICE-EARNINGS RATIOS
17.6.1 The Zero-Growth Model
J 7.6.2 The Constant-Growth Model
17.6.3 The MUltiple-Growth Model

499
501
501
501
502
502
503
503
506
508
508
509
510
5r J
511
462
490

523
523
524
524
525
526
526
527
527
527
528
529
529
529
530
531
532
532
533
534
536
537
538
xvii

SOURCES OF EARNINGS GROWTH
A THREE-STAGE DDM
17.8 .1 Making Forecasts
17.8.2 Estimating the Intrinsic Value

17.8.3 Implied Returns
17.8 .4 The Security Market Line
17.8 .5 Required Returns and Alphas
17.8 .6 The Implied Return on the Stock Market
DIVIDEND DISCOUNT MODELS AND EXPECTED RETURNS
17.9
17.9.1 Rate of Convergence of Investors'
Predictions
17.9 .2 Predicted Versus Actual Returns
17.10 SUMtvlARY
INSTITUTIONAL ISSUES: ApPLYING DIVIDEND DISCOUNT MODELS
INSTITUTIONAL ISSUES : MULTIPLE VALUATION MODELS

539
542
542
545
545
545
546
547
547

EARNINGS

559
559
560
563
564

564
565
566
567
567
568
569
570
570
570
572
572

17.7
17.8

18

18.1

18.2

18.3

18.4

18.5

18.6

18.7

xviii

STOCK VALUATION BASED ON EARNINGS
18.1 .1 Earnings, Dividends, and Investment
18.1 .2 Earnings Determine Market Value
DETERMINANTS OF DiVIDENDS
18.2 .1 Changes in Earnings and Dividends
18.2 .2 The LIntner Model
18.2.3 Test Results
THE INFORtvlATION CONTENT OF DIVIDENDS
18.3 .1 Signaling
18.3.2 Dividend Initiations and Omissions
18.3.3 Dividends and Losses
ACCOUNTING EARNINGS VERSUS ECONOMIC EARNINGS
18.4.1 Accounting Earnings
18.4.2 Economic Earnings
PRICE-EARNINGS RATIOS
18.5.1 The Historical Record
18.5.2 Permanent and Transitory Components
of Earnings
RELATIVE GROWTH RATES OF FIRMS' EARNINGS
18.6.1 Earnings Growth Rates
18.6.2 Annual Earnings
18.6.3 Quarterly Earnings
EARNINGS ANNOUNCEMENTS AND PRICE CHANGES
18.7 .1 Deviations from Time-Series Models
of Earnings
18.7.2 Unexpected Earnings

and Abnormal Returns
18.7.3 Security Analysts' Forecasts
of Future Earnings

547
549
549
542
550

573
575
576
577
577
578
579
582
582
Contents

18.7.4 Management Forecasts
of Future Earnings
18.7.5 Sources of Errors in Forecasting
18.9

SUMrv1I\RY

INSTITUTIONAL ISSUES : CONSENSUS EARNINGS EXPECTATIONS

19

OPTIONS

19.1

TYPES OF OPTION CONTRACTS

9. 1. J Call Options
19.1 .2 Put Options
J

19.2

19.2.1
19.2.2
19.2.3
19.2.4
19.3
19.4

Most Active Options
Commissions

MARGIN

VALUATION OF OPTIONS

19.4. J Valuation at Expiration
19.4.2 Profits and Losses on Calls and Puts
J 9.4.3 Profits and Losses from Some Option
Strategies
J

9.5

THE BINOMIAL OPTION PRICING MODEL

9.5. J Call Options
9.5.2 Put Options
J 9.5.3 Put-Call Parity
J
J

J

9.6

THE BLACK-SCHOLES MODEL FOR CALL OPTIONS

9.6. J The Formula
9.6.2 Comparison with the Binomial
Option Pricing Model
19.6.3 Static Analysis
J 9.6.4 Estimating a Stocks Risk
from Historical Prices

J 9.6.5 The Market Consensus of a Stocks Risk
J 9.6.6 More on Hedge Ratios
19.6.7 Limitations on Its Use
J

585
587
587
588
601
601
60 J
604
605
605
606
607
609
609
610
6 J0
6J1

6I4
6 I6
6 J6
621
622
623

623

J

J

9.7

THE VALUATION OF PUT OPTIONS

19.7. J Put-Call Parity
J 9.7.2 Static Analysis
J 9.7.3 Early Exercise and Dividends
J

9.8

INDEX OPTIONS

19.8.1 Cash Settlement
J 9.8.2 The Contract
J 9.8.3 Flex Options
19.9

PORTFOLIO INSURANCE
J

Contents

9.9. 1 .Purchase a Protective Put

625
626
626
627
628
629
630
632
633
633
634
635
635
635
637
637
637
xix

20

19.9.2 Create a Synthetic Put
SUMMARY
19.10
ApPENDIX: SECURITIES WITH OPTIONLIKE FEATur~Es
Warrants
A.l
Rights

A.2
Bond Call Provisions
A.3
A.4
Convertible Securities
INSTITUTIONAL ISSUES: OPEN OUTCRY
INSTITUTIONAl. ISSUES: OPTION OVERWRITING

639
641
645
645
646
647
647
608
614

FUTURES

654

HEDGERS AND SPECULATORS
20.1.1 Example of Hedging
20. J.2 Example of Speculating
THE FUTURES CONTRACT
20.2
FUTURES MARKETS
20.3
20.3.1 The Clearinghouse

20.3 .2 Initial Margin
20.3.3 Marking to Market
20.3.4 Maintenance Margin
20.3.6 Futures Positions
20.3.7 Open Interest
20.3.8 Price Limits
BASIS
20.4
20.4.1 SpeCUlating on the Basis
RETURNS ON FUTURES
20.5
FUTURES PRICES AND EXPECTED SPOT PRICES
20 .6
20.6.1 Certainty
20.6.2 Uncertainty
FUTURES PRICES AND CURRENT SPOT PRICES
20.7
20.7. J Introducing the Problem
20.7.2 No Costs or Benefits of Ownership
20.7.3 Benefits from Ownership
20.7.4 Costs of Ownership
FINANCIAL FUTURES
20.8
20.8.1 Foreign Currency Futures
20.8.2 Interest-Rate Futures
20 .8.3 Market Index Futures
FUTURES VERSUS OPTIONS
20 .9

20.10 SYNTHETIC FUTURES
20.11 SUMMARY
APPENDIX: FUTURES OPTIONS
A.I
Call Options on Futures Contracts

654
654
655
655
656
658
659
659
660
661
662
662
663
664
664
664
665
666
666
666
667
668
668
668

669
669
669
675
676
681
683
687
690
690

20.1

xx

Contents

21

A.2
Put Options on Futures Contracts
A.3
Comparison with Futures
A.4
Comparison with Options
INSTITUTIONAL ISSUES: COMMODITY FUTURES :
THE SELLING OF AN AsSET CLASS
INSTITUTIONAL ISSUES: TRANSPORTABLE ALPHA

692
693
693

INVESTMENT COMPANIES

NET AsSET VALUE
MAJOR TYPES OF INVESTMENT COMPANIES
2J .2. J Unit Investment Trusts
21.2.2 Managed Companies
INVESTMENT POLICIES
21.3
MUTUAL FUND TAXATION
2 J.4
MUTUAL FUND PERFORMANCE
21.5
21 .5.1 Calculating Returns
21.5.2 Average Return
21 .5.3 Equity Funds
21 .5.4 Bond Mutual Funds
EVALUATING MUTUAL FUNDS
21.6
21.6.1 Performance
2J .6.2 Ratings
21.6.3 Historical Profile
21.6.4 Category Rating and Other Measures
21.6.5 Investment Style
21.6.6 Caveats
21.7

21.7 .1 Pricing of Shares
21.7.2 Investing in Fund Shares
21.7.3 Open-Ending Closed-End Funds
SUMMARY
21.8
INSTITUTIONAL ISSUES: VARIABLE ANNUITIES
INSTITUTIONAL ISSUES: REAL ESTATE INVESTMENT TRUSTS

699
700
701
701
702
709
711
712
712
713
717
720
720
720
721
723
723
724
725
726
726
726

727
730
714
728

FINANCIAL ANALYSIS

740

21. J
21.2

22

22.1
22.2

22.3

Contents

PROFESSIONAL ORGANIZATIONS
REASONS FOR FINANCIAL ANALYSIS
22 .2.1 Determining Security Characteristics
22.2.2 Attempting to Identify Mispriced
Securities
the Market
22.2.4 Financial Analysis and Market Efficiency
22 .2.5 Needed Skills

TECHNICAL ANALYSIS
22.3.1 Momentum and Contrarian Strategies

670
684

740
741
741
741
744
745
745
746
746
xxi

22.3.2 Moving Average and Trading Range
Breakout Strategies
22 .3.3 The Bottom Line
FUNDAMENTAL ANALYSIS
22.4
22.4. I Top-Down versus Bottom-Up
Forecasting
22.4.2 Probabilistic Forecasting
22.4.3 Econometric Models
FINANCIAL SrATEMENT ANALYSIS
22.5
22.5. I Company Background

22.5 .2 Review of Accounting Statements
22.5.3 Ratio Analysis
ANALYSTS'
RECOMMENDATIONS AND STOCK PRICES
22 .6
ANALYST FOLLOWING AND STOCK RETURNS
22.7
22.8
SOUIKES OF INVESTMENT INFORMATION
22.9
22.9.1 Publications
22.9.2 Electronically Delivered Data
22 .10 SUMMARY
ApPENDIX: TECHNICAL ANALYSIS
A.I
Charts
A.2
Moving Averages
Relative Strength Measures
A.3
A.4
Contrary Opinion
INSTITUTIONAL ISSUES: THECHARTERED FINANCIAL
ANALYST PROGRAM
INSTITUTIONAL ISSUES: INSIDE INFORMATION

23

INVESTMENT MANAGEMENT

23.1
23 .2
23.3

23.4

23.5

23 .6
23.7
xxii

INVESTMENT MANAGEMENT FUNGIONS
SETTING INVESTMENT POLICY
23.3.1 Estimating Risk Tolerance
23 .3.2 Constant Risk Tolerance
23.3.3 Certainty Equivalent Return
SECURITY ANALYSIS AND PORTFOLIO CONSTRUGION
23 .4.1 Passive and Active Management
23.4 .2 Security Selection, Asset Allocation,
and Market Timing
23.4.3 International Investing
PORTFOLIO REVISION
23.5.1 Cost-Benefit Analysis
23.5.2 Swaps
MANAGER-CLIENT RELATIONS
SUMMARY

749
750
751
751
751
752
752
753
754
762
768
770
771
775
775
777
777
780
781
783
784
784
742
772

792
792
794
794
794

796
798
799
799
801
806
806
807
807
814
814
Contents

ApPENDIX: DETERMINING THE RISK TOLERANCE OF AN INVESTOR
INSnruTloNAL ISSUES: EVALUATING INVESTMENT SYSTEMS
INSTITUTIONAL ISSUES: MANAGER SmUaURING

24

PORTFOLIO PERFORMANCE EVALUATION

825

MEASURES OF RETURN
24. 1.1 Dollar-Weighted Returns
24.1.2 Time-Weighted Returns
24. 1.3 Comparing Dollar-Weighted
and Time-Weighted Returns
24.1.4 Annualizing Returns

MAKING RELEVANT COMPARISONS
24.2
MARKET INDICES
24 .3
24.3 .1 Price Weighting
24.3 .2 Value Weighting
24.3.3 Equal Weighting
24.3.4 Geometric Mean
24.4
24.4.1 Ex Post Characteristic Lines
24.4.2 The Reward-to-Volatility Ratio
24.4.3 The Sharpe Ratio
24.4.4 M2
24.4 .5 Comparing the Risk-Adjusted Measures
of Performa nce
MARKET TIMING
24.5
24.5.2 Dummy Variable Regression
24 .6
24 .6.1 Use of a Market Surrogate
24 .6.2 Distinguishing Skill from Luck
24.6 .3 Measuring the Riskfree Rate
24.6.4 Validity of the CAPM
BOND PORTFOLIO PERFORMANCE EVALUATION
24.7
24.7 .1 Bond Indices

24 .7.2 Time-Series and Cross-Sectional
Comparisons
SUMMARY
24.8
INSTITUTIONAL ISSUES: CUSTOM BENCHMARK PORTFOLIOS
INSTITUTIONAL ISSUES: AsSESSING MANAGER SKILL

826
827
827

859
860
867
848
856

INTERNATIONAL INVESTING

876

24. I

25

818
804
812

25. I

Contents

THE TOTAL INVESTABLE CAPITAL MARKET PORTFOLIO
25. I. I International EqUity Indices
25. J.2 Emerging Markets

827
828
829
829
830
833
834
834
835
837
843
844
846
848
850
851
852
853
854
854
854
855

855
855
858

876
877
880
xxiii

25.2

25 .3
25.4
25 .5

RISK AND RETURN FROM FOREIGN INVESTING

880

25 .2. I
25 .2.2
25.2 .3
25 .2.4

881
884
885
886
888

892
893
896
896
897

Managing Exchange Risk
Foreign and Domestic Returns
Expected Returns
Foreign and Domestic Risks

INTEr~NATIONAL LISTINGS

CORRELATIONS BETWEEN MARKETS
SUMMARY

ApPENDIX : TANGIBLE AsSETS

A. 1
A.2

Collectible Assets
Gold

INSTITUTIONAL ISSUES: CURRENCY RISK : To HEDGE
OR

NOT TO

HEDGE

882

INSTITUTIONAL ISSUES: THE STOCK EXCHANGE
OF HONG KONG: ANOTHER AsIAN EXCHANGE SWITCHES
TO AUTOMATED MATCHING

890

INSTITUTIONAL ISSUES: ALTERNATIVE INVESTMENTS

898

GLOSSARY

906

SELEaED SOLUTIONS TO END-OF-CHAPTER

xxiv

OUESTIONS AND PROBLEMS

934

INDEX

939

Contents

PRE

F

ACE

Investment management once seemed a simple process. Well-heeled investors would
hold portfolios composed, for the most part, of stocks and bonds of blue chip U. S.
industrial companies, as well as U.S. Treasury bonds, notes, and bills. The choices
available to less well-off investors were much more limited, confined primarily to
passbook savings accounts and U.S. Savings Bonds. Ifthe investment environment can
be thought of as an ice cream parlor, then the customers of past decades were offered
only chocolate and vanilla.
Mirroring the diversity of modern society, the investment ice cream parlor now
makes available a myriad of flavors to the investing public. Investors face a dizzying
array of choices. The stocks and bonds of large U.S.-based companies and the debt
securities of the U.S. Treasury remain the predominant favorites. However, to mention only a few additional choices, investors can now own the stocks of small U.S.based companies, the stocks and bonds of companies headquartered from London
to Auckland, high-yield bonds, collateralized mortgage obligations, floating rate
notes, swaps, puts, calls, and futures contracts. The list is seemingly endless, and it continues to grow. Furthermore, the ability to purchase these securities has become both
less expensive and more convenient with the advent of advanced communications and
computer networks, along with the proliferating market for mutual funds that has developed to serve large and small investors alike.
The difficulty of writing a textbook on investing has increased as the investment
environment has become more complex. Virtually all types of securities, be the)' traditional or of recent origin, merit at least some discussion. The challenge to us as textbook writers, therefore, is daunting. We must enumerate and describe the various
securities and markets in a clear and concise manner that accurately blends theory
and practice. However, with the rapid evolution that the investment industry is undergoing, we must also present a discussion of new investment management techniques. Preventing the textbook from reaching encyclopedic proportions thus
becomes a difficult project in itself.
The subject matter for this edition of Investments has evolved considerably since
1978 when the first edition was published. For example, in the last several years international investing has expanded rapidly, securities such as swaps and mortgage derivatives have become increasingly popular, and investors have placed much more

emphasis on investment styles. Our task has been to keep Investments fresh and stimulating and to continue to offer students and instructors the most thorough survey
of the investment environment available. We believe that we have accomplished these
objectives and hope that you agree.
We designed Investments, Sixth Edition for advanced undergraduate and graduate students. In doing so, we assumed that such students would have been exposed
to basic economics, accounting, statistics, and algebra. Furthermore, it is our belief
that serious students of investments should receive a balanced presentation of theory and practical information without being burdened by excessive details. A textbook
that focuses solely on institutional features leaves students unable to appreciate the
subtle and important issues faced by investment professionals.
Some people will wonder how Investments, Sixth Edition compares with the textbook entitled Fundamentals ofInvestments that we have also written. Although both are
intended to be comprehensive, they are dissimilar in three significant ways. First,

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