Preface 

xiii  


1  (12) 


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) 


18  (1) 

2.3 Present and Future Values of Streams 


19  (3) 

2.4 Internal Rate of Return 


22  (2) 


24  (4) 

2.6 Applications and Extensions(*) 


28  (6) 


34  (1) 


35  (3) 


38  (2) 

3 FIXEDINCOME SECURITIES 


40  (32) 

3.1 The Market for Future Cash 


41  (3) 


44  (5) 


49  (3) 


52  (5) 


57  (5) 


62  (3) 


65  (1) 


66  (2) 


68  (3) 


71  (1) 

4 THE TERM STRUCTURE OF INTEREST RATES 


72  (30) 


72  (1) 


73  (4) 


77  (3) 

4.4 Term Structure Explanations 


80  (3) 

4.5 Expectations Dynamics 


83  (5) 

4.6 Running Present Value 


88  (2) 


90  (1) 


91  (3) 


94  (2) 


96  (1) 


97  (4) 


101  (1) 

5 APPLIED INTEREST RATE ANALYSIS 


102  (35) 


103  (5) 


108  (3) 

5.3 Dynamic Cash Flow Processes 


111  (3) 


114  (7) 

5.5 The Harmony Theorem(*) 


121  (3) 

5.6 Valuation of a Firm(*) 


124  (4) 


128  (2) 


130  (4) 


134  (3) 
Part II SINGLEPERIOD RANDOM CASH FLOWS 

137  (126) 

6 MEANVARIANCE PORTFOLIO THEORY 


137  (36) 


137  (4) 


141  (5) 


146  (4) 

6.4 Portfolio Mean and Variance 


150  (5) 


155  (2) 


157  (5) 

6.7 The TwoFund Theorem(*) 


162  (3) 

6.8 Inclusion of a RiskFree Asset 


165  (1) 


166  (3) 


169  (1) 


170  (2) 


172  (1) 

7 THE CAPITAL ASSET PRICING MODEL 


173  (24) 


173  (2) 

7.2 The Capital Market Line 


175  (2) 


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) 


190  (2) 


192  (1) 


193  (2) 


195  (2) 


197  (31) 


197  (1) 


198  (7) 

8.3 The CAPM as a Factor Model 


205  (2) 

8.4 Arbitrage Pricing Theory(*) 


207  (5) 


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) 


222  (2) 


224  (3) 


227  (1) 


228  (35) 


228  (1) 


228  (3) 


231  (3) 

9.4 Specification of Utility Functions(*) 


234  (3) 

9.5 Utility Functions and the MeanVariance Criterion(*) 


237  (3) 


240  (2) 


242  (3) 

9.8 LogOptimal Pricing(*) 


245  (2) 


247  (4) 

9.10 RiskNeutral Pricing(*) 


251  (1) 

9.11 Pricing Alternatives(*) 


252  (2) 


254  (1) 


255  (3) 


258  (5) 
Part III DERIVATIVE SECURITIES 

263  (154) 

10 FORWARDS, FUTURES, AND SWAPS 


263  (33) 


263  (1) 


264  (2) 


266  (7) 

10.4 The Value of a Forward Contract 


273  (1) 


273  (2) 

10.6 Basics of Futures Contracts 


275  (3) 


278  (3) 

10.8 Relation to Expected Spot Price(*) 


281  (1) 


282  (1) 

10.10 The MinimumVariance Hedge 


283  (2) 


285  (2) 

10.12 Hedging Nonlinear Risk(*) 


287  (4) 


291  (1) 


291  (4) 


295  (1) 

11 MODELS OF ASSET DYNAMICS 


296  (23) 

11.1 Binomial Lattice Model 


297  (2) 


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) 


312  (1) 

11.9 Binomial Lattice Revisited 


313  (2) 


315  (1) 


316  (2) 


318  (1) 


319  (32) 


320  (2) 

12.2 The Nature of Option Values 


322  (3) 

12.3 Option Combinations and PutCall Parity 


325  (2) 


327  (1) 

12.5 SinglePeriod Binomial Options Theory 


327  (3) 


330  (3) 

12.7 More General Binomial Problems 


333  (4) 

12.8 Evaluating Real Investment Opportunities 


337  (7) 

12.9 General RiskNeutral Pricing(*) 


344  (1) 


345  (1) 


346  (4) 


350  (1) 

13 ADDITIONAL OPTIONS TOPICS 


351  (31) 


351  (1) 

13.2 The BlackScholes Equation 


351  (4) 


355  (2) 

13.4 RiskNeutral Valuation(*) 


357  (1) 


358  (2) 

13.6 Replication, Synthetic Options, and Portfolio Insurance(*) 


360  (2) 

13.7 Computational Methods 


362  (6) 


368  (3) 

13.9 Storage Costs and Dividends(*) 


371  (2) 

13.10 Martingale Pricing(*) 


373  (2) 


375  (1) 

Appendix: Alternative BlackScholes Derivation(*) 


376  (2) 


378  (3) 


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 AdjustableRate Loans(*) 


391  (4) 

14.6 The Forward Equation 


395  (2) 

14.7 Matching the Term Structure 


397  (3) 


400  (2) 

14.9 Collateralized Mortgage Obligations(*) 


402  (4) 

14.10 Models of Interest Rate Dynamics(*) 


406  (2) 

14.11 ContinuousTime Solutions(*) 


408  (2) 


410  (1) 


411  (2) 


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 LogOptimal Strategy(*) 


425  (1) 

15.4 Alternative Approaches(*) 


425  (2) 

15.5 ContinuousTime Growth 


427  (3) 


430  (5) 

15.7 The LogOptimal Pricing Formula(*) 


435  (3) 

15.8 LogOptimal Pricing and the BlackScholes Equation(*) 


438  (2) 


440  (1) 


441  (2) 


443  (1) 

16 GENERAL INVESTMENT EVALUATION 


444  (31) 

16.1 Multiperiod Securities 


444  (3) 

16.2 RiskNeutral Pricing 


447  (1) 


448  (4) 


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 ContinuousTime Evaluation(*) 


469  (2) 


471  (1) 


472  (2) 


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  