Investment Science

by Luenberger, David G.

• ISBN13: 9780195108095
• ISBN10: 0195108094
• Format: Hardcover
• Copyright: 1997-07-03
• Publisher: Oxford University Press

Summary

Fueled in part by some extraordinary theoretical developments in finance, an explosive growth of information and computing technology, and the global expansion of investment activity, investment theory currently commands a high level of intellectual attention. Recent developments in the field are being infused into university classrooms, financial service organizations, business ventures, and into the awareness of many individual investors. Modern investment theory using the language of mathematics is now an essential aspect of academic and practitioner training. Representing a breakthrough in the organization of finance topics,Investment Sciencewill be an indispensable tool in teaching modern investment theory. It presents sound fundamentals and shows how real problems can be solved with modern, yet simple, methods. David Luenberger gives thorough yet highly accessible mathematical coverage of standard and recent topics of introductory investments: fixed-income securities, modern portfolio theory and capital asset pricing theory, derivatives (futures, options, and swaps), and innovations in optimal portfolio growth and valuation of multiperiod risky investments. Throughout the book, he uses mathematics to present essential ideas of investments and their applications in business practice. The creative use of binomial lattices to formulate and solve a wide variety of important finance problems is a special feature of the book. In moving from fixed-income securities to derivatives, Luenberger increases naturally the level of mathematical sophistication, but never goes beyond algebra, elementary statistics/probability, and calculus. He includes appendices on probability and calculus at the end of the book for student reference. Creative examples and end-of-chapter exercises are also included to provide additional applications of principles given in the text. Ideal for investment or investment management courses in finance, engineering economics, operations research, and management science departments,Investment Sciencehas been successfully class-tested at Boston University, Stanford University, and the University of Strathclyde, Scotland, and used in several firms where knowledge of investment principles is essential. Executives, managers, financial analysts, and project engineers responsible for evaluation and structuring of investments will also find the book beneficial. The methods described are useful in almost every field, including high-technology, utilities, financial service organizations, and manufacturing companies.

Author Biography

David G. Luenberger, Professor in Engineering-Economics Systems & Operations Research, Stanford University. He has written several successful books with Addison-Wesley and John Wiley publishers.

Table of Contents

Preface	xiii
1 INTRODUCTION	1	(12)
1.1 Cash Flows	2	(1)
1.2 Investments and Markets	3	(3)
1.3 Typical Investment Problems	6	(2)
1.4 Organization of the Book	8	(5)
Part I DETERMINISTIC CASH FLOW STREAMS	13	(124)
2 THE BASIC THEORY OF INTEREST	13	(27)
2.1 Principal and Interest	13	(5)
2.2 Present Value	18	(1)
2.3 Present and Future Values of Streams	19	(3)
2.4 Internal Rate of Return	22	(2)
2.5 Evaluation Criteria	24	(4)
2.6 Applications and Extensions(*)	28	(6)
2.7 Summary	34	(1)
Exercises	35	(3)
References	38	(2)
3 FIXED-INCOME SECURITIES	40	(32)
3.1 The Market for Future Cash	41	(3)
3.2 Value Formulas	44	(5)
3.3 Bond Details	49	(3)
3.4 Yield	52	(5)
3.5 Duration	57	(5)
3.6 Immunization	62	(3)
3.7 Convexity(*)	65	(1)
3.8 Summary	66	(2)
Exercises	68	(3)
References	71	(1)
4 THE TERM STRUCTURE OF INTEREST RATES	72	(30)
4.1 The Yield Curve	72	(1)
4.2 The Term Structure	73	(4)
4.3 Forward Rates	77	(3)
4.4 Term Structure Explanations	80	(3)
4.5 Expectations Dynamics	83	(5)
4.6 Running Present Value	88	(2)
4.7 Floating Rate Bonds	90	(1)
4.8 Duration	91	(3)
4.9 Immunization	94	(2)
4.10 Summary	96	(1)
Exercises	97	(4)
References	101	(1)
5 APPLIED INTEREST RATE ANALYSIS	102	(35)
5.1 Capital Budgeting	103	(5)
5.2 Optimal Portfolios	108	(3)
5.3 Dynamic Cash Flow Processes	111	(3)
5.4 Optimal Management	114	(7)
5.5 The Harmony Theorem(*)	121	(3)
5.6 Valuation of a Firm(*)	124	(4)
5.7 Summary	128	(2)
Exercises	130	(4)
References	134	(3)
Part II SINGLE-PERIOD RANDOM CASH FLOWS	137	(126)
6 MEAN-VARIANCE PORTFOLIO THEORY	137	(36)
6.1 Asset Return	137	(4)
6.2 Random Variables	141	(5)
6.3 Random Returns	146	(4)
6.4 Portfolio Mean and Variance	150	(5)
6.5 The Feasible Set	155	(2)
6.6 The Markowitz Model	157	(5)
6.7 The Two-Fund Theorem(*)	162	(3)
6.8 Inclusion of a Risk-Free Asset	165	(1)
6.9 The One-Fund Theorem	166	(3)
6.10 Summary	169	(1)
Exercises	170	(2)
References	172	(1)
7 THE CAPITAL ASSET PRICING MODEL	173	(24)
7.1 Market Equilibrium	173	(2)
7.2 The Capital Market Line	175	(2)
7.3 The Pricing Model	177	(4)
7.4 The Security Market Line	181	(2)
7.5 Investment Implications	183	(1)
7.6 Performance Evaluation	184	(3)
7.7 CAPM as a Pricing Formula	187	(3)
7.8 Project Choice(*)	190	(2)
7.9 Summary	192	(1)
Exercises	193	(2)
References	195	(2)
8 MODELS AND DATA	197	(31)
8.1 Introduction	197	(1)
8.2 Factor Models	198	(7)
8.3 The CAPM as a Factor Model	205	(2)
8.4 Arbitrage Pricing Theory(*)	207	(5)
8.5 Data and Statistics	212	(5)
8.6 Estimation of Other Parameters	217	(1)
8.7 Tilting Away from Equilibrium	218	(3)
8.8 A Multiperiod Fallacy	221	(1)
8.9 Summary	222	(2)
Exercises	224	(3)
References	227	(1)
9 GENERAL PRINCIPLES	228	(35)
9.1 Introduction	228	(1)
9.2 Utility Functions	228	(3)
9.3 Risk Aversion	231	(3)
9.4 Specification of Utility Functions(*)	234	(3)
9.5 Utility Functions and the Mean-Variance Criterion(*)	237	(3)
9.6 Linear Pricing	240	(2)
9.7 Portfolio Choice	242	(3)
9.8 Log-Optimal Pricing(*)	245	(2)
9.9 Finite State Models	247	(4)
9.10 Risk-Neutral Pricing(*)	251	(1)
9.11 Pricing Alternatives(*)	252	(2)
9.12 Summary	254	(1)
Exercises	255	(3)
References	258	(5)
Part III DERIVATIVE SECURITIES	263	(154)
10 FORWARDS, FUTURES, AND SWAPS	263	(33)
10.1 Introduction	263	(1)
10.2 Forward Contracts	264	(2)
10.3 Forward Prices	266	(7)
10.4 The Value of a Forward Contract	273	(1)
10.5 Swaps(*)	273	(2)
10.6 Basics of Futures Contracts	275	(3)
10.7 Futures Prices	278	(3)
10.8 Relation to Expected Spot Price(*)	281	(1)
10.9 The Perfect Hedge	282	(1)
10.10 The Minimum-Variance Hedge	283	(2)
10.11 Optimal Hedging(*)	285	(2)
10.12 Hedging Nonlinear Risk(*)	287	(4)
10.13 Summary	291	(1)
Exercises	291	(4)
References	295	(1)
11 MODELS OF ASSET DYNAMICS	296	(23)
11.1 Binomial Lattice Model	297	(2)
11.2 The Additive Model	299	(1)
11.3 The Multiplicative Model	300	(3)
11.4 Typical Parameter Values(*)	303	(1)
11.5 Lognormal Random Variables	304	(1)
11.6 Random Walks and Wiener Processes	305	(3)
11.7 A Stock Price Process	308	(4)
11.8 Ito's Lemma(*)	312	(1)
11.9 Binomial Lattice Revisited	313	(2)
11.10 Summary	315	(1)
Exercises	316	(2)
References	318	(1)
12 BASIC OPTIONS THEORY	319	(32)
12.1 Option Concepts	320	(2)
12.2 The Nature of Option Values	322	(3)
12.3 Option Combinations and Put-Call Parity	325	(2)
12.4 Early Exercise	327	(1)
12.5 Single-Period Binomial Options Theory	327	(3)
12.6 Multiperiod Options	330	(3)
12.7 More General Binomial Problems	333	(4)
12.8 Evaluating Real Investment Opportunities	337	(7)
12.9 General Risk-Neutral Pricing(*)	344	(1)
12.10 Summary	345	(1)
Exercises	346	(4)
References	350	(1)
13 ADDITIONAL OPTIONS TOPICS	351	(31)
13.1 Introduction	351	(1)
13.2 The Black-Scholes Equation	351	(4)
13.3 Call Option Formula	355	(2)
13.4 Risk-Neutral Valuation(*)	357	(1)
13.5 Delta	358	(2)
13.6 Replication, Synthetic Options, and Portfolio Insurance(*)	360	(2)
13.7 Computational Methods	362	(6)
13.8 Exotic Options	368	(3)
13.9 Storage Costs and Dividends(*)	371	(2)
13.10 Martingale Pricing(*)	373	(2)
13.11 Summary	375	(1)
Appendix: Alternative Black-Scholes Derivation(*)	376	(2)
Exercises	378	(3)
References	381	(1)
14 INTEREST RATE DERIVATIVES	382	(35)
14.1 Examples of Interest Rate Derivatives	382	(2)
14.2 The Need for a Theory	384	(1)
14.3 The Binomial Approach	385	(4)
14.4 Pricing Applications	389	(2)
14.5 Leveling and Adjustable-Rate Loans(*)	391	(4)
14.6 The Forward Equation	395	(2)
14.7 Matching the Term Structure	397	(3)
14.8 Immunization	400	(2)
14.9 Collateralized Mortgage Obligations(*)	402	(4)
14.10 Models of Interest Rate Dynamics(*)	406	(2)
14.11 Continuous-Time Solutions(*)	408	(2)
14.12 Summary	410	(1)
Exercises	411	(2)
References	413	(4)
Part IV GENERAL CASH FLOW STREAMS	417	(58)
15 OPTIMAL PORTFOLIO GROWTH	417	(27)
15.1 The Investment Wheel	417	(2)
15.2 The Log Utility Approach to Growth	419	(6)
15.3 Properties of the Log-Optimal Strategy(*)	425	(1)
15.4 Alternative Approaches(*)	425	(2)
15.5 Continuous-Time Growth	427	(3)
15.6 The Feasible Region	430	(5)
15.7 The Log-Optimal Pricing Formula(*)	435	(3)
15.8 Log-Optimal Pricing and the Black-Scholes Equation(*)	438	(2)
15.9 Summary	440	(1)
Exercises	441	(2)
References	443	(1)
16 GENERAL INVESTMENT EVALUATION	444	(31)
16.1 Multiperiod Securities	444	(3)
16.2 Risk-Neutral Pricing	447	(1)
16.3 Optimal Pricing	448	(4)
16.4 The Double Lattice	452	(2)
16.5 Pricing in a Double Lattice	454	(4)
16.6 Investments with Private Uncertainty	458	(5)
16.7 Buying Price Analysis	463	(6)
16.8 Continuous-Time Evaluation(*)	469	(2)
16.9 Summary	471	(1)
Exercises	472	(2)
References	474	(1)
Appendix A BASIC PROBABILITY THEORY	475	(4)
A.1 General Concepts	475	(1)
A.2 Normal Random Variables	476	(1)
A.3 Lognormal Random Variables	477	(2)
Appendix B CALCULUS AND OPTIMIZATION	479	(5)
B.1 Functions	479	(1)
B.2 Differential Calculus	480	(1)
B.3 Optimization	481	(3)
Answers to Exercises	484	(5)
Index	489