Financial Market Analytics

Contents......Page 4
Preface......Page 8
1.A Analytics and the Scientific Method in Finance\n......Page 12
1.B Financial Models......Page 14
1.C Empirical Studies\n......Page 15
1.D Research in Finance\n......Page 16
1.E Applications and Organization of this Book\n......Page 24
2.A Time Value Mathematics......Page 26
2.B Geometric Series and Expansions......Page 28
Application 2.1 Annuities and Perpetuities......Page 29
Application 2.2 Growth Models......Page 30
Application 2.3 Money and Income Multipliers......Page 31
2.C Return Measurement......Page 32
2.D Mean, Variance and Standard Deviation......Page 34
Application 2.4 Risk Measurement......Page 35
2.E Comovement Statistics......Page 37
Application 2.5 Security Comovement......Page 38
2.F Introduction to Simple OLS Regressions......Page 40
Application 2.6 Relative Risk Measurement......Page 41
Exercises......Page 43
3.A Introduction to Portfolio Analysis......Page 48
3.B Single Index Models......Page 51
3.C Multi-Index Models......Page 54
Exercises......Page 56
4.A Matrices, Vectors and Scalars......Page 60
4.B Addition, Subtraction and Transposes of Matrices......Page 61
Application 4.1 (continued) Portfolio Mathematics......Page 63
4.D Inversion of Matrices......Page 65
4.E Solving Systems of Equations......Page 66
Application 4.2 Coupon Bonds and Deriving Yield Curves......Page 68
Application 4.3 Arbitrage with Riskless Bonds......Page 70
Application 4.4 Fixed Income Portfolio Dedication......Page 71
4.F Vectors, Vector Spaces and Spanning......Page 72
Application 4.5 The State Preference Model......Page 76
Application 4.6 Binomial Option Pricing......Page 80
Application 4.7 Put-Call Parity......Page 82
4.G. Orthogonal Vectors......Page 84
Application 4.8 Arbitrage Pricing Theory......Page 85
Exercises......Page 89
5.A Functions and Limits......Page 94
5.B Slopes, Derivatives, Maxima and Minima......Page 95
Application 5.2 Utility of Wealth......Page 98
5.C Derivatives of Polynomials......Page 100
Application 5.4 The Baumol Cash Management Model......Page 102
Application 5.5 Duration......Page 105
Application 5.7 Portfolio Risk and Diversification......Page 108
Application 5.8 Deriving the Simple OLS Regression Equation......Page 110
Application 5.9 Deriving Multiple Regression Coefficients......Page 112
5.E The Chain Rule, Product Rule and Quotient Rule......Page 113
Application 5.10 Plotting the Capital Market Line......Page 115
5.F Taylor Series Expansions......Page 123
Application 5.11 Convexity and Immunization......Page 124
Application 5.12 Risk Aversion Coefficients......Page 126
5.G The Method of LaGrange Multipliers......Page 127
Application 5.13 Optimal Portfolio Selection......Page 129
Application 5.14 Plotting the Capital Market Line, Second Method......Page 130
Application 5.15 Deriving the Capital Asset Pricing Model......Page 133
Application 5.16 Constrained Utility Maximization......Page 135
Exercises......Page 138
Appendix 5.A Derivatives of Polynomials......Page 142
Appendix 5.B Rules for Finding Derivatives......Page 143
Appendix 5.C Portfolio Risk Minimization on a Spreadsheet......Page 144
6. A Antidifferentiation and the Indefinite Integral......Page 148
6.B Definite Integrals and Areas......Page 149
Application 6.1 Cumulative Densities......Page 153
Application 6.2 Expected Value and Variance......Page 155
Application 6.3 Stochastic Dominance......Page 156
Application 6.4 Valuing Continuous Dividend Payments......Page 160
Application 6.5 Expected Option Values......Page 161
6.C Differential Equations......Page 162
Application 6.6 Continuous Time Security Returns......Page 163
Exercises......Page 166
Appendix 6.A Rules for Finding Integrals......Page 168
7.A Random Variables and Probability Spaces......Page 170
7.B Distributions and Moments......Page 171
7.C Binomial Distributions......Page 172
Application 7.1 Estimating Probability of Option Exercise......Page 175
7.D The Normal Distribution......Page 177
Application 7.2 Common Stock Returns......Page 178
Application 7.3 Option Pricing — Conditional Exercise......Page 180
Application 7.4 The Binomial Option Pricing Model......Page 181
Exercises......Page 184
8.A Introduction to Hypothesis Testing......Page 186
Application 8.1 Minimum Acceptable Returns......Page 187
Application 8.2 Bank Ownership Structure......Page 190
8.C Interpreting the Simple OLS Regression......Page 192
Application 8.3 The Capital Asset Pricing Model......Page 195
Application 8.4 Analysis of Weak Form Efficiency......Page 200
Application 8.5 Portfolio Performance Evaluation......Page 202
8.D Multiple OLS Regressions......Page 204
Application 8.6 Estimating the Yield Curve......Page 209
8.E Event Studies......Page 210
Application 8.7 Analysis of Merger Returns......Page 212
8.F Models with Binary Variables......Page 219
Exercises......Page 222
9.A Random Walks and Martingales......Page 224
9.B Binomial Processes......Page 225
9.C Brownian Motion, Weiner and Ito Processes......Page 226
9.D Itô\'s Lemma......Page 229
Application 9.1 Geometric Weiner Processes......Page 232
Application 9.2 Option Prices — Estimating Exercise Probability......Page 233
Application 9.3 Option Prices — Estimating Expected Conditional Option Prices......Page 234
Application 9.4 Deriving the Black-Scholes Option Pricing Model......Page 235
Exercises......Page 241
10.B The Binomial Method......Page 244
Application 10.1 The Binomial Option Pricing Model......Page 246
Application 10.2 American Put Option Valuation......Page 248
10.C The Method of Bisection......Page 251
Application 10.3 Estimating Bond Yields......Page 252
Application 10.4 Estimating Implied Variances......Page 253
10.D The Newton-Ralphson Method......Page 256
Application 10.4 (continued) Estimating Implied Variances......Page 257
Exercises......Page 259
Appendix A Solutions to End-of-Chapter Exercises......Page 260
Appendix B Statistics Tables......Page 304
Appendix C Notation Definitions......Page 306
C......Page 310
E......Page 311
M......Page 312
S......Page 313
Z......Page 314
References......Page 316
C......Page 324
M......Page 325
S......Page 326
Z......Page 327