Investment Mathematics (Andrew 版) 英国各大院校金融投资课本
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Investment Mathematics (Andrew 版) 英国各大院校金融投资研究生课本.包含
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
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
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