关键词： 价值投资;量化投资;GARP模型;GARP-PI量化模型;证券市场 量化投资在海外的发展已有30多年，市场规模和份额不断扩大，得到了越来越多投资者的认可。2004年国内机构投资者开始推出量化投资产品，至今已有多家基金公司嘉实、广发、中海、长盛、光大保德信和富国基金先后推出了不同的量化产品，数量投资已经成为投资领域一个重要的研究手段。GARP（Growth at a Reasonable Price）价值成长策略是国内基金普遍应用的数量投资模型，该模型将价值投资和成长投资结合起来选股，通过以相对较低的价格买入具有较高成长性的公司来获得稳定的超额收益。利用这一策略可以同时获得在没有考虑成长潜力下，价值回归带来的投资收益，以及成长潜力释放过程中带来的价值增长。我们应用了该模型并对其进行了A股实证检验。 PI（Prospect Indicator）即景气度指数，在本文中，我们将PI定义为动量效应指标与分析师预测指标相结合的一个总指标，该指标在数量化模型中表示为动量指标评分与预测指标评分的加总，我们试图通过该指数综合考量动量效应给出的买入信号，以及分析师预测给出的买入信号，捕捉那些在时间维度上，过去动量效应强劲，未来预测仍然看好的股票，我们称之为高景气度个股。在GARP模型以及个股景气度指数理论的基础上，本文创造性地提出了GARP-PI（成长价值-个股景气度指数）数量化选股策略模型，模型以上市公司的四个价值指标（市盈率、市净率、市盈率_行业相对、市净率_行业相对）和八个成长指标（收入成长因子、营业利润成长因子、总利润成长因子、净利润成长因子、以及四个指标的各自行业相对），再加上代表个股景气度指数的八个量化指标（由四个动量指标与四个预测指标组成）为标准，为上市公司“打分”，判断其股票是否具有投资价值。 最后，我们尽可能地充分利用披露数据信息，验证GARP-PI（成长价值-个股景气度指数）量化投资模型在国内A股市场的有效性。构建组合，利用回溯性检验测试业绩表现，分析股票的投资价值，给投资决策提供最大限度的支持。
为什么市场在均衡的状态下所有资产的预期收益都落在证券市场线上？ 在一定时期的市场内，即无风险利率和市场平均收益率是相同的情况下，证券市场线是固定的一条线。 因为R=RF+b(RM-RF),即SML是证券组合或者单一证券必要收益率和其风险B值的线性函数。 所有定价正确的证券或者证券组合都能在同一条线上找到。 只有当市场变了，SML的斜率才会发生变化。 但是某些资料上这么写：证券市场线反映了人们回避风险的程度，即直线的倾斜越陡，投资者越回避风险。 是否可以这么理解：所谓的回避风险，即人们在承担相同风险时要求的收益率大了。 如何从CML推导出SML： CML is the Capital market line which show us the relationship between E(Ri) and the security-portfolio(combines the risk free asset and market porfolio) variation. NOT FOR SINGLE SECURITY E(Ri)=Rf+ *Var(portfolio) where Rf is risk free rate, Rm is market portfolio return (Rm-Rf) is the market risk premium. devided by market risk(var) shows the risk premium per var, which gives us the slope of the CML multipling the Var(portfolio) gives the risk premium required for the security portforlio This line is actually tangent the efficient frontier, It shows all the combinations of risk free asset and market(optimal) portfolio. However, SML shows the relationships between the reterns of all securities(not just market portfolio) and their risks. As we all know the market only compensate the systemetic risks which are the risks relating to the market. The nonsystemetic risks can be diversified. Therefore, for a single security the only relevant risk factor is Cov(im) COULD BE USED FOR ALL SECURITIES AND PORTFOLIO E(Ri)=Rf+ *Cov(im) reorganize the formula E(Ri)=Rf+Cov(im)/Vm *(Rm-Rf) where we let Cov(im)/V(m)= beta so we get E(Ri)=Rf+ B* (Rm-Rf) This gives the line which is called security market line (SML) from this SML, we can get the relationship between the E(Ri) and the B(indicates the systemetic risk of the security) (Here,as we know Cov(mm)=Var(m) so when the return B=1,Ri=Rm)
金融风险理论--从统计物理到风险管理特色及评论 在上一个世纪五十、七十年代的两个时间段，有一些智者提出了“风险的处理和效益的优化”两个现代金融学的中心议题。从此，几乎所有数理金融的理论也都围红绕着这两个基本问题而展开。 金融风险理论--从统计物理到风险管理内容简介 本书的重点是金融风险的控制和管理，为此必须要有可管、可控的指标，有了这些指标，就可以对风险定价，给出合理的模式和方法，所以本书的最后一章，广泛讨论了各种期权的定价和风险管理。这是一本视角、方法都很有特点的书，自始至终贯穿着用实际的证券市场的数据来说明、验证相应的分析结论，用股票市场的指数、外汇市场的交易和国债市场的行情作为实例，因此是有数据支持，令人不感到枯燥的分析。各种不同观点的人，从这本书的分析中都会有所收获。 ~Preface 1 Probability theory: basic notions 1.1 Introduction 1.2 Probability distributions 1.3 Typical values and deviations 1.4 Moments and characteristic function 1.5 Divergence of moments-asymptotic behaviour 1.6 Gaussian distribution 1.7 Log- Normal distribution 1.8 Levy distributions and Paretian tails 1.9 Other distributions (*) 1.10 Summary 2 Maximum and addition of random variables 2.1 Maximum of random variables 2.2 Sums of random variables 2.2.1 Convolutions 2.2.2 Additivity of cumulants and of tail amplitudes 2.2.3 Stable distributions and self-similarity 2.3 Central limit theorem 2.3.1 Convergence to a Gaussian 2.3.2 Convergence to a Levy distribution 2.3.3 Large deviations 2.3.4 Steepest descent method and Cram~~r function (*) 2.3.5 The CLT at work on simple cases 2.3.6 Truncated L6vy distributions 2.3.7 Conclusion: survival and vanishing of tails 2.4 From sum to max: progressive dominance of extremes (*) 2.5 Linear correlations and fractional Brownian motion 2.6 Summary 3 Continuous time limit, Ito calculus and path integrals 3. I Divisibility and the continuous time limit 3.1.1 Divisibility 3.1.2 Infinite divisibility 3.1.3 Poisson jump processes 3.2 Functions of the Brownian motion and Ito calculus 3.2.1 Ito's lemma 3.2.2 Novikov's formula 3.2.3 Stratonovich's prescription 3.3 Other techniques 3.3.1 Path integrals 3.3.2 Girsanov's formula and the Martin-Siggia-Rose trick 3.4 Summary 4 Analysis of empirical data 4.1 Estimating probability distributions 4.1.1 Cumulative distribution and densities - rank histogram 4.1.2 Kolmogorov-Smirnov test 4.1.3 Maximum likelihood 4.1.4 Relative likelihood 4.1.5 A general caveat 4.2 Empirical moments: estimation and error 4.2.1 Empirical mean 4.2.2 Empirical variance and MAD 4.2.3 Empirical kurtosis 4.2.4 Error on the volatility 4.3 Correlograms and variograms 4.3.1 Variogram 4.3.2 Correlogram 4.3.3 Hurst exponent 4.3.4 Correlations across different time zones 4.4 Data with heterogeneous volatilities 4.5 Summary 5 Financial products and financial markets 5.1 Introduction 5.2 Financial products 5.2.1 Cash (Interbank market) 5.2.2 Stocks 5.2.3 Stock indices 5.2.4 bonds 5.2.5 Commodities 5.2.6 Derivatives 5.3 Financial markets 5.3.1 Market participants 5.3.2 Market mechanisms 5.3.3 Discreteness 5.3.4 The order book 5.3.5 The bid-ask spread 5.3.6 Transaction costs 5.3.7 Time zones, overnight, seasonalities 5.4 Summary 6 Statistics of real prices: basic results 6.1 Aim of the chapter 6.2 Second-order statistics 6.2.1 Price increments vs. returns 6.2.2 Autocorrelation and power spectrum 6.3 Distribution of returns over different time scales 6.3.1 Presentation of the data 6.3.2 The distribution of returns 6.3.3 Convolutions 6.4 Tails, what tails？ 6.5 Extreme markets 6.6 Discussion 6.7 Summary 7 Non-linear correlations and volatility fluctuations 7.1 Non-linear correlations and dependence 7.1.1 Non identical variables 7.1.2 A stochastic volatility model 7.1.3 GARCH(I,I) 7.1.4 anomalous kurtosis 7.1.5 The case of infinite kurtosis 7.2 Non-linear correlations in financial markets: empirical results 7.2.1 Anomalous decay of the cumulants 7.2.2 Volatility correlations and variogram 7.3 Models and mechanisms 7.3.1 Multifractality and multifractal models (*) 7.3.2 The microstructure of volatility 7.4 Summary 8 Skewness and price-volatility correlations 8.1 Theoretical considerations 8.1.1 Anomalous skewness of sums of random variables 8.1.2 Absolute vs. relative price changes 8.1.3 The additive -multiplicative crossover and the q-transformation 8.2 A retarded model 8.2.1 Definition and basic properties 8.2.2 Skewness in the retarded model 8.3 Price-volatility correlations: empirical evidence 8.3.1 Leverage effect for stocks and the retarded model 8.3.2 Leverage effect for indices 8.3.3 Return-volume correlations 8.4 The Heston model: a model with volatility fluctuations and skew 8.5 Summary 9 Cross-correlations 9.1 Correlation matrices and principal component analysis 9.1.1 Introduction 9.1.2 Gaussian correlated variables 9.1.3 Empirical correlation matrices 9.2 Non-Gaussian correlated variables 9.2.1 Sums of non Gaussian variables 9.2.2 Non-linear transformation of correlated Gaussian variables 9.2.3 Copulas 9.2.4 Comparison of the two models 9.2.5 Multivariate Student distributions 9.2.6 Multivariate L~~vy variables (*) 9.2.7 Weakly non Gaussian correlated variables (*) 9.3 Factors and clusters 9.3.1 One factor models 9.3.2 Multi-factor models 9.3.3 Partition around medoids 9.3.4 Eigenvector clustering 9.3.5 Maximum spanning tree 9.4 Summary 9.5 Appendix A: central limit theorem for random matrices 9.6 Appendix B: density of eigenvalues for random correlation matrices 10 Risk measures 10.1 Risk measurement and diversification 10.2 Risk and volatility 10.3 Risk of loss, 'value at 10.4 Temporal aspects: drawdown and cumulated loss 10.5 Diversification and utility-satisfaction thresholds 10.6 Summary 11 Extreme correlations and variety 11.1 Extreme event correlations . 11.1.1 Correlations conditioned on large market moves 11.1.2 Real data and surrogate data 11.1.3 Conditioning on large individual stock returns: exceedance correlations 11.1.4 Tail dependence 11.1.5 Tail covariance (*) 11.2 Variety and conditional statistics of the residuals 11.2.1 The variety 11.2.2 The variety in the one-factor model 11.2.3 Conditional variety of the residuals 11.2.4 Conditional skewness of the residuals 11.3 Summary 11.4 Appendix C: some useful results on power-law variables 12 Optimal portfolios 12.1 Portfolios of uncorrelated assets 12.1.1 Uncorrelated Gaussian assets 12.1.2 Uncorrelated 'power-law' assets 12.1.3 Exponential' assets 12.1.4 General case: optimal portfolio and VaR (*) 12.2 Portfolios of correlated assets 12.2.1 Correlated Gaussian fluctuations 12.2.2 Optimal portfolios with non-linear constraints (*) 12.2.3 'Power-law' fluctuations - linear model (*) 12.2.4 'Power-law' fluctuations - Student model (*) 12.3 Optimized trading 12.4 Value-at-risk- general non-linear portfolios (*) 12.4.1 Outline of the method: identifying worst cases 12.4.2 Numerical test of the method 12.5 Summary 13 Futures and options: fundamental concepts 13.1 Introduction 13.1.1 Aim of the chapter 13.1.2 Strategies in uncertain conditions 13.1.3 Trading strategies and efficient markets 13.2 Futures and forwards 13.2.1 Setting the stage 13.2.2 Global financial balance 13.2.3 Riskless hedge 13.2.4 Conclusion: global balance and arbitrage 13.3 Options: definition and valuation 13.3.1 Setting the stage 13.3.2 Orders of magnitude 13.3.3 Quantitative 14 Options: hedging and residual risk 14.1 Introduction 14.2 Optimal hedging strategies 14.2.1 A simple case: static hedging 14.2.2 The general case and 'A' hedging 14.2.3 Global hedging vs. instantaneous hedging 14.3 Residual risk 14.3.1 The Black-Scholes miracle 14.3.2 The 'stop-loss' strategy does not work 14.3.3 Instantaneous residual risk and kurtosis risk 14.3.4 Stochastic volatility models 14.4 Hedging errors. A variational point of view 14.5 Other measures of risk-hedging and VaR (*) 14.6 Conclusion of the chapter 14.7 Summary 14.8 Appendix D 15 Options: the role of drift and correlations 15.1 Influence of drift on optimally hedged option 15.1.1 A perturbative expansion 15.1.2 'Risk neutral' probability and martingale s 15.2 Drift risk and delta-hedged options 15.2.1 Hedging the drift risk 15.2.2 The price of delta-hedged options 15.2.3 A general option pricing formula 15.3 Pricing and hedging in the presence of temporal correlations (*) 15.3.1 A general model of correlations 15.3.2 Derivative pricing with small correlations 15.3.3 The case of delta-hedging 15.4 Conclusion 15.4.1 Is the price of an option unique？ 15.4.2 Should one always optimally hedge？ 15.5 Summary 15.6 Appendix E 16 Options: the Black and Scholes model 16.1 Ito calculus and the Black-Scholes equation 16.1.1 The Gaussian Bachelier model 16.1.2 Solution and Martingale 16.1.3 Time value and the cost of hedging 16.1.4 The Log-normal Black-Scholes model 16.1.5 General pricing and hedging in a Brownian world 16.1.6 The GREEKS 16.2 Drift and hedge in the Gaussian model (*) 16.2.1 Constant drift 16.2.2 Price dependent drift and the Omstein-Uhlenbeck paradox 16.3 The binomial model 16.4 Summary 17 Options: some more specific 17.1.3 Discrete dividends 17.1.4 Transaction costs 17.2 Other types of options 17.2.1 'Put-call' parity 17.2.2 'Digital' options 17.2.3 'Asian' options 17.2.4 'American' options 17.2.5 'Barrier' options (*) 17.2.6 Other types of options 17.3 The 'Greeks' and risk control 17.4 Risk diversification (*) 17.5 Summary 18 Options: minimum variance Monte-Carlo 18.1 Plain Monte-Carlo 18.1.1 Motivation and basic principle 18.1.2 Pricing the forward exactly 18.1.3 Calculating the Greeks 18.1.4 Drawbacks of the method 18.2 An 'hedged' Monte-Carlo method 18.2.1 Basic principle of the method 18.2.2 A linear parameterization of the price and hedge 18.2.3 The Black-Scholes limit 18.3 Non Gaussian models and purely historical option pricing 18.4 Discussion and extensions. Calibration 18.5 Summary 18.6 Appendix F: generating some random variables 19 The yield curve 19.1 Introduction 19.2 The bond market 19.3 Hedging bonds with other bonds 19.3.1 The general problem 19.3.2 The continuous time Ganssian limit 19.4 The equation for bond pricing 19.4.1 A general solution 19.4.2 The Vasicek model 19.4.3 Forward rates 19.4.4 More general models 19.5 Empirical study of the forward rate curve 19.5.1 Data and notations 19.5.2 Quantities of interest and data analysis 19.6 Theoretical considerations (*) 19.6.1 Comparison with the Vasicek model 19.6.2 Market price of risk 19.6.3 Risk-premium and the law 19.7 Summary 19.8 Appendix G: optimal portfolio of bonds 20 Simple mechanisms for anomalous price statistics 20.1 Introduction 20.2 Simple models for herding and mimicry 20.2.1 Herding and percolation 20.2.2 Avalanches of opinion changes 20.3 Models of feedback effects on price fluctuations 20.3.1 Risk-aversion induced crashes 20.3.2 A simple model with volatility correlations and tails 20.3.3 Mechanisms for long ranged volatility correlations 20.4 The Minority Game 20.5 Summary Index of most important symbols Index~
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