Andrew T. Adams & Philip M. Booth 
Investment Mathematics [PDF ebook] 

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Investment Mathematics provides an introductory analysis of investments from a quantitative viewpoint, drawing together many of the tools and techniques required by investment professionals.
Using these techniques, the authors provide simple analyses of a number of securities including fixed interest bonds, equities, index-linked bonds, foreign currency and derivatives. The book concludes with coverage of other applications, including modern portfolio theory, portfolio performance measurement and stochastic investment models.

€56.50
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Tabella dei contenuti

Preface xiii

Acknowledgements xv

Part I Security Analysis 1

1 Compound Interest 3

1.1 Introduction 3

1.2 Accumulated values 3

1.3 Effective and nominal rates of interest 5

1.4 The accumulated value of an annuity-certain 7

1.5 Present values 8

1.6 The present value of an annuity-certain 10

1.7 Investment project analysis 15

1.8 Net present value 15

1.9 Internal rate of return 16

1.10 Discounted payback period 17

1.11 Analysis of decision criteria 19

1.12 Sensitivity analysis 19

Annex 1.1 Exponents 20

Annex 1.2 Geometric series 21

2 Fixed-interest Bonds 25

2.1 Introduction 25

2.2 Types of bond 25

2.3 Accrued interest 26

2.4 Present value of payments 28

2.5 Interest yield 28

2.6 Simple yield to maturity 29

2.7 Gross redemption yield 29

2.8 Net redemption yield 32

2.9 Holding period return 33

2.10 Volatility 33

2.11 Duration 35

2.12 The relationship between duration and volatility 35

2.13 Convexity 36

2.14 Yield curves 36

2.15 The expectations theory 37

2.16 The liquidity preference theory 38

2.17 The market segmentation theory 39

2.18 Inflation risk premium 39

2.19 Par yield curves 39

2.20 Spot and forward interest rates 39

2.21 Spot rates and redemption yields 40

2.22 Strips 41

2.23 Corporate bonds 42

3 Equities and Real Estate 43

3.1 Introduction 43

3.2 Discounted dividend model 43

3.3 Investment ratios 46

3.4 Scrip issues and stock splits 47

3.5 Rights issues 49

3.6 Market efficiency 51

3.7 Real estate 53

3.8 Yield gaps 57

4 Real Returns 59

4.1 Introduction 59

4.2 The calculation of real returns given a constant rate of inflation 59

4.3 Valuation of a series of cash flows given a constant rate of inflation 60

4.4 The relationship between real and nominal yields 62

4.5 Estimation of the rate of inflation 63

4.6 Real returns from equity investments 63

4.7 Estimation of equity values for a given real rate of return 67

4.8 Calculating real returns with varying rates of inflation 68

5 Index-linked Bonds 73

5.1 Introduction 73

5.2 Characteristics of index-linked bonds 73

5.3 Index-linked bonds: simple case 75

5.4 Index-linked bonds: a more general approach 75

5.5 The effect of indexation lags 79

5.6 A further generalisation of the model 80

5.7 Holding period returns 82

5.8 Accrued interest 84

5.9 The real yield gap 84

5.10 Estimating market expectations of inflation 86

5.10.1 Index-linked and conventional bonds: basic relationships 86

5.10.2 Problems with the simple approach to estimating inflation expectations 88

5.10.3 Solving the problem of internal consistency: break-even inflation rates 88

5.10.4 Solving the problem of differing durations 90

5.10.5 Forward and spot inflation expectations 90

6 Foreign Currency Investments 93

6.1 Introduction 93

6.2 Exchange rates 93

6.3 Exchanges rates, inflation rates and interest rates 94

6.4 Covered interest arbitrage 95

6.5 The operation of speculators 96

6.6 Purchasing power parity theory 98

6.7 The international Fisher effect 98

6.8 Interactions between exchange rates, interest rates and inflation 99

6.9 International bond investment 102

6.10 International equity investment 104

6.11 Foreign currency hedging 104

7 Derivative Securities 107

7.1 Introduction 107

7.2 Forward and futures contracts 107

7.2.1 Pricing of forwards and futures 108

7.2.2 Forward pricing on a security paying no income 109

7.2.3 Forward pricing on a security paying a known cash income 110

7.2.4 Forward pricing on assets requiring storage 112

7.2.5 Stock index futures 112

7.2.6 Basis relationships 113

7.2.7 Bond futures 114

7.3 Swap contracts 116

7.3.1 Comparative advantage argument for swaps market 116

7.3.2 Pricing interest rate swap contracts 117

7.3.3 Using swaps in risk management 118

7.4 Option contracts 119

7.4.1 Payoff diagrams for options 120

7.4.2 Intrinsic value and time value 121

7.4.3 Factors affecting option prices 122

Part II Statistics for Investment 125

8 Describing Investment Data 127

8.1 Introduction 127

8.2 Data sources 127

8.3 Sampling and data types 128

8.4 Data presentation 129

8.4.1 Frequency tables 129

8.4.2 Cumulative frequency tables 131

8.4.3 Bar charts 131

8.4.4 Histograms 132

8.4.5 Stem and leaf plots 135

8.4.6 Pie charts 136

8.4.7 Time series graphs 140

8.4.8 Cumulative frequency graphs 141

8.4.9 Scatter diagrams 141

8.4.10 The misrepresentation of data 143

8.5 Descriptive statistics 145

8.5.1 Arithmetic mean 145

8.5.2 Median 147

8.5.3 Mode 147

8.5.4 Link between the mean, median and mode 147

8.5.5 Weighted average 148

8.5.6 Geometric mean 149

8.5.7 Range 149

8.5.8 Inter-quartile range 150

8.5.9 Mean deviation (from the mean) 150

8.5.10 Sample variance 151

8.5.11 Sample standard deviation 151

8.5.12 Coefficient of variation 151

9 Modelling Investment Returns 153

9.1 Introduction 153

9.2 Probability 153

9.2.1 Relative frequency definition of probability 153

9.2.2 Subjective probability 154

9.2.3 The addition rule 154

9.2.4 Mutually exclusive events 154

9.2.5 Conditional probability 155

9.2.6 Independent events 155

9.2.7 Complementary events 156

9.2.8 Bayes’ theorem 156

9.3 Probability distributions 158

9.3.1 Cumulative distribution function (c.d.f.) 159

9.3.2 The mean and variance of probability distributions 160

9.3.3 Expected values of probability distributions 160

9.3.4 Properties of the expected value 161

9.3.5 The general linear transformation 162

9.3.6 Variance 162

9.3.7 Covariance 163

9.3.8 Moments of random variables 163

9.3.9 Probability density function (p.d.f.) 163

9.4 The binomial distribution 165

9.5 The normal distribution 166

9.5.1 The standard normal distribution 167

9.6 The normal approximation to the binomial 169

9.6.1 Binomial proportions 171

9.7 The lognormal distribution 171

9.8 The concept of probability applied to investment returns 172

9.9 Some useful probability results 173

9.10 Accumulation of investments using a stochastic approach: one time period 175

9.11 Accumulation of single investments with independent rates of return 177

9.12 The accumulation of annual investments with independent rates of return 179

Annex 9.1 Properties of the expected value 185

Annex 9.2 Properties of the variance 186

10 Estimating Parameters and Hypothesis Testing 187

10.1 Introduction 187

10.2 Unbiased estimators 187

10.3 Confidence interval for the mean 188

10.4 Levels of confidence 191

10.5 Small samples 191

10.6 Confidence interval for a proportion 193

10.7 Classical hypothesis testing 194

10.8 Type I and Type II errors 196

10.9 Power 196

10.10 Operating characteristic 197

10.11 Hypothesis test for a proportion 198

10.12 Some problems with classical hypothesis testing 199

10.13 An alternative to classical hypothesis testing: the use of p-values 200

10.14 Statistical and practical significance 201

Annex 10.1 Standard error of the sample mean 202

11 Measuring and Testing Comovements in Returns 203

11.1 Introduction 203

11.2 Correlation 203

11.3 Measuring linear association 203

11.4 Pearson’s product moment correlation coefficient 205

11.5 Covariance and the population correlation coefficient 207

11.6 Spearman’s rank correlation coefficient 207

11.7 Pearson’s versus Spearman’s 208

11.8 Non-linear association 209

11.9 Outliers 210

11.10 Significance test for r 211

11.11 Significance test for Spearman’s rank correlation coefficient 213

11.12 Simple linear regression 213

11.13 The least-squares regression line 214

11.14 The Least-squares Regression Line of X on Y 217

11.15 Prediction intervals for the conditional mean 220

11.16 The coefficient of determination 222

11.17 Residuals 224

11.18 Multiple regression 226

11.19 A warning 226

Part III Applications 227

12 Modern Portfolio Theory and Asset Pricing 229

12.1 Introduction 229

12.2 Expected return and risk for a portfolio of two investments 229

12.3 Expected return and risk for a portfolio of many investments 234

12.4 The efficient frontier 235

12.5 Indifference curves and the optimum portfolio 236

12.6 Practical application of the Markowitz model 237

12.7 The Market Model 237

12.8 Estimation of expected returns and risks 240

12.9 Portfolio selection models incorporating liabilities 240

12.10 Modern portfolio theory and international diversification 243

12.11 The Capital Asset Pricing Model 245

12.12 International CAPM 254

12.13 Arbitrage Pricing Theory 257

12.14 Downside measures of risk 262

12.15 Markowitz semi-variance 264

12.16 Mean semi-variance efficient frontiers 265

Annex 12.1 Using Excel to calculate efficient frontiers 266

13 Market Indices 271

13.1 Introduction 271

13.2 Equity indices 271

13.3 Bond indices 279

13.4 Ex-dividend adjustment 280

13.5 Calculating total return indices within a calendar year 281

13.6 Net and gross indices 282

13.7 Commercial real estate indices 283

13.7.1 US real estate indices 283

14 Portfolio Performance Measurement 285

14.1 Introduction 285

14.2 Money-weighted rate of return 285

14.3 Time-weighted rate of return 287

14.4 Linked internal rate of return 291

14.5 Notional funds 292

14.6 Consideration of risk 294

14.7 Information ratios 298

14.8 Survivorship bias 299

14.9 Transitions 301

15 Bond Analysis 303

15.1 Introduction 303

15.2 Volatility 303

15.3 Duration 304

15.4 The relationship between volatility and duration 305

15.5 Factors affecting volatility and duration 308

15.6 Convexity 309

15.7 Non-government bonds 314

15.8 Some applications of the concepts of volatility and duration 315

15.9 The theory of immunisation 317

15.10 Some practical issues with immunisation and matching 320

16 Option Pricing Models 323

16.1 Introduction 323

16.2 Stock options 323

16.3 The riskless hedge 324

16.4 Risk neutrality 325

16.5 A more general binomial model 329

16.6 The value of p 330

16.7 Estimating the parameters u, and n 331

16.8 The Black–Scholes model 333

16.9 Call options 334

16.10 Computational considerations 338

16.11 Put options 339

16.12 Volatility 342

16.13 Estimation of volatility from historical data 342

16.14 Implied volatility 343

16.15 Put=call parity 344

16.16 Adjustments for known dividends 347

16.17 Put=call parity with known dividends 349

16.18 American-style options 350

16.19 Option trading strategies 351

16.20 Stock index options 357

16.21 Bond options 357

16.22 Futures options 358

16.23 Currency options 358

16.24 Exotic options 359

Annex 16.1 The heuristic derivation of the Black–Scholes model 359

17 Stochastic Investment Models 365

17.1 Introduction 365

17.2 Persistence in economic series 367

17.3 Autocorrelation 371

17.4 The random walk model 374

17.5 Autoregressive models 376

17.6 ARIMA models 380

17.7 ARCH models 381

17.8 Asset-liability modelling 384

17.9 The Wilkie model 385

17.10 A note on calibration 388

17.11 Interest rate modelling 388

17.12 Value at risk 391

Compound Interest Tables 399

Student’s t Distribution: Critical Points 408

Areas in the Right-hand Tail of the Normal Distribution 409

Index 411

Circa l’autore

ANDREW ADAMS is Senior Lecturer in Finance and Director of the Centre for Financial Markets Research at the University of Edinburgh. He has studied financial markets for over thirty years, as a practitioner in the City of London and as an academic. His research interests focus mainly on investment trust pricing and risk.
PHILIP BOOTH is Professor of Insurance and Risk Management at the Sir John Cass Business School, City of London and Editorial and Programme Director at the Institute of Economic Affairs. He is a former special adviser at the Bank of England and previously held the Chair in Real Estate Finance and Investment at the Sir John Cass Business School. He has a long experience of teaching and researching in the fields of investment and social insurance and is author or co-author of a number of books and papers in these fields. Philip Booth is a Fellow of the Institute of Actuaries and of the Royal Statistical Society.
DAVID BOWIE is a Partner and head of quantitative analysis in the Investment Practice of Hymans Robertson Consultants & Actuaries. His focus is on the development and application of asset/liability modelling and the use of capital market theory in providing investment advice to pension funds and other institutional investors.
DELLA FREETH is Reader in Education for Health Care Practice at St Bartholomew School of Nursing and Midwifery, City University, where she conducts quantitative and qualitative research.

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Lingua Inglese ● Formato PDF ● ISBN 9780470859186 ● Dimensione 3.5 MB ● Casa editrice John Wiley & Sons ● Paese GB ● Pubblicato 2003 ● Edizione 1 ● Scaricabile 24 mesi ● Moneta EUR ● ID 2324802 ● Protezione dalla copia Adobe DRM
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