Quantitative Methods for Finance and Investments

John L. Teall is Professor of Finance at Pace University. He has published numerous articles in scholarly journals and has served on university faculties around the world. Dr Teall is a former member of the American Stock Exchange and has done consulting work for many of the world's leading financial institutions. Iftekhar Hasan is Professor of Finance at the New Jersey Institute of Technology. He has published numerous articles in academic journals and has been associated with several universities and regulatory organizations in Europe. He is the co-editor of Research in Banking and Finance.

• PrefaceAcknowledgments1 Introduction and Overview 11.1 The importance of mathematics in finance 11.2 Mathematical and computer modeling in finance 21.3 Money, securities, and markets 31.4 Time value, risk, arbitrage, and pricing 51.5 The organization of this book 62 A Review of Elementary Mathematics: Functions and Operations 72.1 Introduction 72.2 Variables, equations, and inequalities 72.3 Exponents 8Application 2.1: Interest and future value 92.4 The order of arithmetic operations and the rules of algebra 10Application 2.2: Initial deposit amounts 112.5 The number e 112.6 Logarithms 12Application 2.3: The time needed to double your money 132.7 Subscripts 142.8 Summations 14Application 2.4: Mean values 152.9 Double summations 162.10 Products 17Application 2.5: Geometric means 17Application 2.6: The term structure of interest rates 182.11 Factorial products 19Application 2.7: Deriving the number e 192.12 Permutations and combinations 20Exercises 21Appendix 2.A An introduction to the Excel™ spreadsheet 233 A Review of Elementary Mathematics: Algebra and Solving Equations 253.1 Algebraic manipulations 25Application 3.1: Purchase power parity 27Application 3.2: Finding break-even production levels 28Application 3.3: Solving for spot and forward interest rates 293.2 The quadratic formula 29Application 3.4: Finding break-even production levels 30Application 3.5: Finding the perfectly hedged portfolio 313.3 Solving systems of equations that contain multiple variables 32Application 3.6: Pricing factors 35Application 3.7: External financing needs 353.4 Geometric expansions 38Application 3.8: Money multipliers 403.5 Functions and graphs 41Application 3.9: Utility of wealth 43Exercises 44Appendix 3.A Solving systems of equations on a spreadsheet 484 The Time Value of Money 514.1 Introduction and future value 514.2 Simple interest 514.3 Compound interest 524.4 Fractional period compounding of interest 53Application 4.1: APY and bank account comparisons 554.5 Continuous compounding of interest 564.6 Annuity future values 57Application 4.2: Planning for retirement 594.7 Discounting and present value 604.8 The present value of a series of cash flows 614.9 Annuity present values 62Application 4.3: Planning for Retirement, Part Ii 64Application 4.4: Valuing a bond 644.10 Amortization 65Application 4.5: Determining the mortgage payment 664.11 Perpetuity models 674.12 Single-stage growth models 68Application 4.6: Stock valuation models 704.13 Multiple-stage growth models 72Exercises 73Appendix 4.A Time value spreadsheet applications 775 Return, Risk, and Co-movement 795.1 Return on investment 79Application 5.1: Fund performance 815.2 Geometric mean return on investment 82Application 5.2: Fund Performance, Part Ii 835.3 Internal rate of return 845.4 Bond yields 875.5 An introduction to risk 885.6 Expected return 885.7 Variance and standard deviation 895.8 Historical variance and standard deviation 915.9 Covariance 935.10 The coefficient of correlation and the coefficient of determination 94Exercises 95Appendix 5.A Return and risk spreadsheet applications 996 Elementary Portfolio Mathematics 1036.1 An introduction to portfolio analysis 1036.2 Portfolio return 1036.3 Portfolio variance 1046.4 Diversification and efficiency 1066.5 The market portfolio and beta 1106.6 Deriving the portfolio variance expression 111Exercises 1137 Elements of Matrix Mathematics 1157.1 An introduction to matrices 115Application 7.1: Portfolio mathematics 1167.2 Matrix arithmetic 117Application 7.2: Portfolio Mathematics, Part Ii 120Application 7.3: Put–call parity 1217.3 Inverting matrices 1237.4 Solving systems of equations 125Application 7.4: External funding requirements 126Application 7.5: Coupon bonds and deriving yield curves 127Application 7.6: Arbitrage with riskless bonds 130Application 7.7: Fixed income portfolio dedication 131Application 7.8: Binomial option pricing 1327.5 Spanning the state space 133Application 7.9: Using options to span the state space 136Exercises 137Appendix 7.A Matrix mathematics on a spreadsheet 1428 Differential Calculus 1458.1 Functions and limits 145Application 8.1: The natural log 1468.2 Slopes, derivatives, maxima, and minima 1478.3 Derivatives of polynomials 149Application 8.2: Marginal utility 151Application 8.3: Duration and immunization 153Application 8.4: Portfolio risk and diversification 1568.4 Partial and total derivatives 1578.5 The chain rule, product rule, and quotient rule 158Application 8.5: Plotting the Capital Market Line 1598.6 Logarithmic and exponential functions 1658.7 Taylor series expansions 166Application 8.6: Convexity and immunization 167Exercises 172Appendix 8.A Derivatives of polynomials 176Appendix 8.B A table of rules for finding derivatives 177Appendix 8.C Portfolio risk minimization on a spreadsheet 1789 Integral Calculus 1809.1 Antidifferentiation and the indefinite integral 1809.2 Riemann sums 1819.3 Definite integrals and areas 185Application 9.1: Cumulative densities 186Application 9.2: Expected value and variance 188Application 9.3: Valuing continuous dividend payments 189Application 9.4: Expected option values 1919.4 Differential equations 191Application 9.5: Security returns in continuous time 193Application 9.6: Annuities and growing annuities 194Exercises 195Appendix 9.A Rules for finding integrals 198Appendix 9.B Riemann sums on a spreadsheet 19910 Elements of Options Mathematics 20310.1 An introduction to stock options 20310.2 Binomial option pricing: one time period 20510.3 Binomial option pricing: multiple time periods 20710.4 The Black–Scholes option pricing model 21010.5 Puts and valuation 21210.6 Black–Scholes model sensitivities 21310.7 Estimating implied volatilities 215Exercises 219References 222Appendix A Solutions to Exercises 224Appendix B The z-Table 266Appendix C Notation 267Appendix D Glossary 270Index 274

"This excellent text patiently guides the reader through a wide array of mathematics, ranging from elementary matrix algebra to differential and integral calculus. The quantitative methods are illustrated with a rich and captivating assortment of applications to the analysis of portfolios, derivatives, exchange, fixed income instruments, and equities. Undergraduate and MBA-level students who have read this book will feel comfortable with the mathematics in their finance courses and their professors can focus on teaching finance as it should be taught." Kose John, Stern School of Business, New York University <1--end-->"This volume provides a comprehensive review of mathematics which will prove invaluable for students of finance. It is a reference book for the nonmathematician and a clear and concise text that will help fill the gaps in students' knowledge. Although the topic is quantitative methods, the organization, emphasis, applications, and numerous examples are all geared to the student of finance. Having Teall and Hasan on your bookshelf provides an essential safety net for students, teachers, and practitioners." Paul Wachtel, Stern School of Business, New York University