Quantitative Methods for Finance and Investments

by Teall, John; Hasan, Iftekhar

• ISBN13: 9780631223399
• ISBN10: 0631223398
• Edition: 1st
• Format: Paperback
• Copyright: 2002-03-12
• Publisher: Wiley-Blackwell

Summary

Quantitative Methods for Finance and Investments ensures that readers will gain a reasonable degree of comfort and proficiency in applying elementary mathematics to financial analysis in a variety of areas. All of the methodology in this book is geared toward the development, implementation, and analysis of financial models to solve problems encountered by both finance students and practitioners. The book: bull; bull;analyzes theoretical and practitioner-oriented models long with the mathematics required to construct them bull;presents the most essential mathematical techniques and their applications to financial analysis bull;provides dozens of practical applications, examples, and end-of-chapter exercises with detailed solutions bull; bull;demonstrates key spreadsheet applications of the mathematical models in chapter appendices bull;emphasizes practical applications of modeling technique.

Author Biography

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.

Table of Contents

Preface	xii
Acknowledgments	xiv
Introduction and Overview	1	(6)
The importance of mathematics in finance	1	(1)
Mathematical and computer modeling in finance	2	(1)
Money, securities, and markets	3	(2)
Time value, risk, arbitrage, and pricing	5	(1)
The organization of this book	6	(1)
A Review of Elementary Mathematics: Functions and Operations	7	(18)
Introduction	7	(1)
Variables, equations, and inequalities	7	(1)
Exponents	8	(2)
Application 2.1: Interest and future value	9	(1)
The order of arithmetic operations and the rules of algebra	10	(1)
Application 2.2: Initial deposit amounts	11	(1)
The number e	11	(1)
Logarithms	12	(2)
Application 2.3: The time needed to double your money	13	(1)
Subscripts	14	(1)
Summations	14	(2)
Application 2.4: Mean values	15	(1)
Double summations	16	(1)
Products	17	(2)
Application 2.5: Geometric means	17	(1)
Application 2.6: The term structure of interest rates	18	(1)
Factorial products	19	(1)
Application 2.7: Deriving the number e	19	(1)
Permutations and combinations	20	(5)
Exercises	21	(2)
Appendix 2.A An introduction to the Excel™ spreadsheet	23	(2)
A Review of Elementary Mathematics: Algebra and Solving Equations	25	(26)
Algebraic manipulations	25	(4)
Application 3.1: Purchase power parity	27	(1)
Application 3.2: Finding break-even production levels	28	(1)
Application 3.3: Solving for spot and forward interest rates	29	(1)
The quadratic formula	29	(3)
Application 3.4: Finding break-even production levels	30	(1)
Application 3.5: Finding the perfectly hedged portfolio	31	(1)
Solving systems of equations that contain multiple variables	32	(6)
Application 3.6: Pricing factors	35	(1)
Application 3.7: External financing needs	35	(3)
Geometric expansions	38	(3)
Application 3.8: Money multipliers	40	(1)
Functions and graphs	41	(10)
Application 3.9: Utility of wealth	43	(1)
Exercises	44	(4)
Appendix 3.A Solving systems of equations on a spreadsheet	48	(3)
The Time Value of Money	51	(28)
Introduction and future value	51	(1)
Simple interest	51	(1)
Compound interest	52	(1)
Fractional period compounding of interest	53	(3)
Application 4.1: APY and bank account comparisons	55	(1)
Continuous compounding of interest	56	(1)
Annuity future values	57	(3)
Application 4.2: Planning for retirement	59	(1)
Discounting and present value	60	(1)
The present value of a series of cash flows	61	(1)
Annuity present values	62	(3)
Application 4.3: Planning for retirement, part II	64	(1)
Application 4.4: Valuing a bond	64	(1)
Amortization	65	(2)
Application 4.5: Determining the mortgage payment	66	(1)
Perpetuity models	67	(1)
Single-stage growth models	68	(4)
Application 4.6: Stock valuation models	70	(2)
Multiple-stage growth models	72	(7)
Exercises	73	(4)
Appendix 4.A Time value spreadsheet applications	77	(2)
Return, Risk, and Co-movement	79	(24)
Return on investment	79	(3)
Application 5.1: Fund performance	81	(1)
Geometric mean return on investment	82	(2)
Application 5.2: Fund performance, part II	83	(1)
Internal rate of return	84	(3)
Bond yields	87	(1)
An introduction to risk	88	(1)
Expected return	88	(1)
Variance and standard deviation	89	(2)
Historical variance and standard deviation	91	(2)
Covariance	93	(1)
The coefficient of correlation and the coefficient of determination	94	(9)
Exercises	95	(4)
Appendix 5.A Return and risk spreadsheet applications	99	(4)
Elementary Portfolio Mathematics	103	(12)
An introduction to portfolio analysis	103	(1)
Portfolio return	103	(1)
Portfolio variance	104	(2)
Diversification and efficiency	106	(4)
The market portfolio and beta	110	(1)
Deriving the portfolio variance expression	111	(4)
Exercises	113	(2)
Elements of Matrix Mathematics	115	(30)
An introduction to matrices	115	(2)
Application 7.1: Portfolio mathematics	116	(1)
Matrix arithmetic	117	(6)
Application 7.2: Portfolio mathematics, part II	120	(1)
Application 7.3: Put-call parity	121	(2)
Inverting matrices	123	(2)
Solving systems of equations	125	(8)
Application 7.4: External funding requirements	126	(1)
Application 7.5: Coupon bonds and deriving yield curves	127	(3)
Application 7.6: Arbitrage with riskless bonds	130	(1)
Application 7.7: Fixed income portfolio dedication	131	(1)
Application 7.8: Binomial option pricing	132	(1)
Spanning the state space	133	(12)
Application 7.9: Using options to span the state space	136	(1)
Exercises	137	(5)
Appendix 7.A Matrix mathematics on a spreadsheet	142	(3)
Differential Calculus	145	(35)
Functions and limits	145	(2)
Application 8.1: The natural log	146	(1)
Slopes, derivatives, maxima, and minima	147	(2)
Derivatives of polynomials	149	(8)
Application 8.2: Marginal utility	151	(2)
Application 8.3: Duration and immunization	153	(3)
Application 8.4: Portfolio risk and diversification	156	(1)
Partial and total derivatives	157	(1)
The chain rule, product rule, and quotient rule	158	(7)
Application 8.5: Plotting the Capital Market Line	159	(6)
Logarithmic and exponential functions	165	(1)
Taylor series expansions	166	(2)
Application 8.6: Convexity and immunization	167	(1)
The method of Lagrange multipliers	168	(12)
Application 8.7: Optimal portfolio selection	170	(2)
Exercises	172	(4)
Appendix 8.A Derivatives of polynomials	176	(1)
Appendix 8.B A table of rules for finding derivatives	177	(1)
Appendix 8.C Portfolio risk minimization on a spreadsheet	178	(2)
Integral Calculus	180	(23)
Antidifferentiation and the indefinite integral	180	(1)
Riemann sums	181	(4)
Definite integrals and areas	185	(6)
Application 9.1: Cumulative densities	186	(2)
Application 9.2: Expected value and variance	188	(1)
Application 9.3: Valuing continuous dividend payments	189	(2)
Application 9.4: Expected option values	191	(1)
Differntial equations	191	(12)
Application 9.5: Security returns in continuous time	193	(1)
Application 9.6: Annuities and growing annuities	194	(1)
Exercises	195	(3)
Appendix 9.A Rules for finding integrals	198	(1)
Appendix 9.B Riemann sums on a spreadsheet	199	(4)
Elements of Options Mathematics	203	(19)
An introduction to stock options	203	(2)
Binomial option pricing: one time period	205	(2)
Binomial option pricing: multiple time periods	207	(3)
The Black-Scholes option pricing model	210	(2)
Puts and valuation	212	(1)
Black-Scholes model sensitivities	213	(2)
Estimating implied volatilities	215	(7)
Exercises	219	(3)
References	222	(2)
Appendix A Solutions to Exercises	224	(42)
Appendix B The z-Table	266	(1)
Appendix C Notation	267	(3)
Appendix D Glossary	270	(4)
Index	274