1、Econometrics for Finance 金融計量經濟學講授：薛明皋 電話：E-mail: 1課程目標課程目標:了解和掌握廣泛應用于金融領域的現代經濟計量的技術和方法.金融學的快速發展使它已成為一門相對獨立的學科。金融學“是一門具有高度實踐性的科學”，“金融理論與實證分析之間關系的密切程度是其他社會學科無法相比的”.金融經濟學家進行推斷的基本方法是金融計量經濟學，即以模型為基礎的統計推斷。2教材Introductory Econometrics for Finance Chris BrooksCambridge University Press 20083作者簡介Chris Brook

2、s was formerly Professor of Finance at the ISMA Centre, University of Reading, where he also obtained his PhD and BA in Economics and Econometrics. His areas of research interest include econometric modeling and forecasting, risk measurement, asset management, and property finance. He has published

3、over sixty articles in leading academic and practitioner journals, including the Journal of Business, the Journal of Banking and Finance, Journal of Empirical Finance, Oxford Bulletin and Economic Journal. Chris is Associate Editor of several journals, including the International Journal of Forecast

4、ing. 4本書的特點內容廣泛：包含了與金融領域相關的各種經濟計量方法難度適中：不要求具備很多的數學知識預備知識數學：微積分和線性代數基礎，統計學基礎金融：公司金融、金融市場、投資等方面的基礎知識注重應用：提供相關軟件的使用和金融方面的應用實例5其它參考教材經濟計量學方面的教科書；羅伯特 S. 平狄克 等計量經濟模型與經濟預測，機械工業出版社J.M.伍德里奇,計量經濟學導論現代觀點，人民大學出版社時間序列分析方面的教科書；G.E.Box 等時間序列分析預測與控制，中國統計出版社有關金融市場學、公司金融等方面的教科書；T.C.Mills，1999, The Econometric Modelli

5、ng of Financial Time Series，金融時間序列的經濟計量學模型，經濟科學出版社，2002年。J.Y.Campbell et al.,1997, The Econometrics of Financial Market；金融市場計量經濟學，上海財經大學出版社，2003年。專門介紹和論述股票市場、衍生證券、固定收入證券等方面的實證分析方法和理論前沿。6Chapter 1Introduction1Learning OutcomesIn this chapter, you will learn how to Distinguish between different types

6、of data Describe the steps involved in building an econometric model Calculate asset price returns Construct a workfile, import data and accomplish simple tasks in EViews81.1 What is Econometrics?Literal meaning is “measurement in economics”. 對經濟現象和經濟關系的數量/計量分析以經濟理論和經濟數據為依據,應用數學和統計學的方法，通過建立數學模型來研究經濟

7、現象及其變化規律的一門經濟學科。（有多種定義）Definition of financial econometrics:The application of statistical and mathematical techniques to study problems in finance.9the value of financial econometricsTesting theories in financeDetermining asset prices or returnsTesting hypotheses concerning the relationships betwee

8、n variables Examining the effect on financial markets of changes in economic conditionsForecasting future values of financial variables and for financial decision-making. 10Examples of some problems that may be solved by an Econometrician1.Testing whether financial markets are weak-form informationa

9、lly efficient.2.Testing whether the CAPM or APT represent superior models for the determination of returns on risky assets.3.Measuring and forecasting the volatility of bond returns.4.Explaining the determinants of bond credit ratings used by the ratings agencies.5.Modelling long-term relationships

10、between prices and exchange rates 11Examples of some problems that may be solved by an Econometrician 6 Determining the optimal hedge ratio for a spot position in oil7 Testing technical trading rules to determine which makes the most money8 Testing the hypothesis that earnings or dividend announceme

11、nts have no effect on stock prices.9 Testing whether spot or futures markets react more rapidly to news.10 Forecasting the correlation between the returns to the stock indices of two countries.12Financial data often differ from macroeconomic data.1 In economics, there are some problems: (a) small sa

12、mples problem (b) measurement error (c) data revisions2 In finance, higher frequency data Furthermore, the analysis of financial data also brings with it a number of new problems. For example, (a) financial data have” noisy”; (b) almost always not normally distribution. 1.2 Is financial econometrics

13、 different from economic econometrics?13 1.3 Types of Data There are 3 types of data :1. Time series data2. Cross-sectional data3. Panel data, a combination of 1. & 2.The data may be quantitative (e.g. exchange rates, stock prices), or qualitative.Examples of time series dataSeriesFrequencyGDP or un

14、employmentyear, quarterly or monthlygovernment budget deficitannuallymoney supplyweeklyvalue of a stock market indexas transactions occur 14Types of Data Problems that Could be Tackled Using a Time Series Data- How the value of a countrys stock index has varied with that countrys macroeconomic polic

15、y.- How a companys stock price has varied when it announced the value of its dividend payment.- The effect on stock price of an increase in countrys interest rateCross-sectional data(橫截面數據) are data on one or more variables collected at a single point in time, e.g.- Cross-section of stock returns on

16、 the New York Stock Exchange- A sample of bond credit ratings for UK banks15Types of Data and Notation Problems that Could be Tackled Using a Cross-Sectional Data- The relationship between company size and the return to investing in its shares- The relationship between a countrys GDP level and the p

17、robability that the government will default on its sovereign debt.（主權債務）Panel Data （平行數據，面板數據）has the dimensions of both time series and cross-sections, e.g. the daily prices of a number of blue chip stocks over two years.It is common to denote each observation by the letter t and the total number o

18、f observations by T for time series data, and to denote each observation by the letter i and the total number of observations by N for cross-sectional data.16It is preferable not to work directly with asset prices, so we usually convert the raw prices into a series of returns. * There are two ways t

19、o do this: Simple returns or continuously compounded returnswhere, Rt denotes the return at time t pt denotes the asset price at time t ln denotes the natural logarithmWe also ignore any dividend payments, or alternatively assume that the price series have been already adjusted to account for them.1

20、.4 Returns in Financial Modelling17There are a number of reasons for Log Returns:1. They have the nice property that they can be interpreted as continuously compounded returns（連續復合收益）。此時，收益的復合頻率無關緊要，不同資產間的收益很容易加以比較2. 多期連續復合收益就是單期復合收益的連續簡單加總。e.g. if we want a weekly return and we have calculated dail

21、y log returns:r1 = ln p1/p0 = ln p1 - ln p0 r2 = ln p2/p1 = ln p2 - ln p1 r3 = ln p3/p2 = ln p3 - ln p2r4 = ln p4/p3 = ln p4 - ln p3r5 = ln p5/p4 = ln p5 - ln p4 ln p5 - ln p0 = ln p5/p0Log Returns18A Disadvantage of using Log ReturnsThere is a disadvantage of using the log-returns. The simple retur

22、n on a portfolio of assets is a weighted average of the simple returns on the individual assets:But this does not work for the continuously compounded returns.In the limit. 191.5 Steps involved in the formulation of econometric models 1a Economic or Financial Theory (Previous Studies)1b Formulation

23、of an Estimable Theoretical Model 2. Collection of Data 3. Model Estimation 4. Is the Model Statistically Adequate? No Yes Reformulate Model 5. Interpret Model 6. Use for Analysis 20補充例子以著名的凱恩斯消費理論為例說明上述步驟（1）步驟:理論或假說的陳述：凱恩斯說：基本的心理定律是，平均而言，人們傾向于消費隨著他們收入的增加而增加，但比不上收入增加的那么多。簡言之，凱恩斯設想，邊際消費傾向（MPC），即收入每變化

24、一個單位的消費變化率，大于零而小于1。（2）步驟: 消費數學模型的設定雖然凱恩斯假設了消費與收入之間有一正向的相關關系，但他并沒有明確指出這兩者之間的準確的函數關系。為簡單起見，數理經濟學家也許建議采用如下的凱恩斯消費函數形式：2122（）步驟：計量經濟學模型考慮經濟變量之間的非準確關系，計量經濟學家會把確定性的消費函數修改如下：其中u被稱為干擾或誤差項，是一個隨機變量，它有良好定義的概率性質，干擾項u可用來代表所有未經指明的對消費有所影響的哪些因素。23可把消費函數的計量經濟模型描繪成像圖1.2那樣24（4）步驟：獲得數據年YX19802447.13776.319812476.93843.1

25、19822503.73760.319832619.43906.619842746.14148.519852865.84279.819862969.14404.519873052.24539.919883162.44718.619893223.34838.019903260.44877.519913240.84821.0Y（個人消費支出）和X（國內總產值）數據，1980-1991，均以10億1987年美元為單位資料來源：Economic Report of the President總統經濟報告，1993，Table B-2，p.350。25（5）步驟：計量經濟模型的估計既然有了數據，下一步的工

26、作就是估計消費函數中的參數，參數的估計將對消費函數賦予經驗內容。利用回歸分析的統計技術獲得估計值。26（6）步驟：假設檢驗如前所說，凱恩斯曾預期MPC是正的，但小于1.在我們的例子中，我們求得MPC約為0.72.但在把這一發現看作是對凱恩斯消費理論的認可之前，還要追問這一估計值是否充分地低于1，以使我們不再懷疑這個估計值僅是一次偶然的機會得來，或者懷疑我們用的數據太特殊了，換言之，0.72是不是在統計意義（statistically）上小于1？如果是，就可用來支持凱恩斯理論。27（7）步驟：預報或預測為了說明起見，假定實際GDP在1994年的預期未來值是60萬美元，問1994年的預期消費支出是

27、多少？如果我們認為在1994年消費函數仍然有效，這個答案就是：所估計的模型還有另一用途。假若政策改變，投資有所下降，其對經濟的影響將如何？宏觀經濟理論告訴我們，投資支出每改變1元，收入的改變由收入乘數（M）給出。28（8）步驟：利用模型進行控制或制定政策假若我們已估計出凱恩斯消費函數，而且政府認為4萬億美元的（消費）支出水平即可維持當前約6.5%的失業率（1994年4月美國勞工統計局做出的估計），問什么收入水平將保證消費支出的這一目標值？4000=-231.8+0.7194X X=5882（近似值）就是說，給定約為0.72的一個MPC，58820（億）美元的收入水平。上述計算提示我們，一個已估

28、計出來的模型可服務于控制或政策的目的。通過適當的財政與貨幣政策的配合，政府可操縱控制度量（control Variable）X以產生目標變量（target variable）Y的指望水平。29小結上述步驟剖析了經典計量經濟學的建模方法經濟理論理論的數學模型理論的計量經濟模型數據計量經濟模型的估計假設檢驗預報或預測利用模型進行控制或制定政策301. Does the paper involve the development of a theoretical model or is it merely a technique looking for an application so that

29、the motivation for the whole exercise is poor?2. Is the data of “good quality”? Is it from a reliable source? Is the size of the sample sufficiently large for the model estimation?3. Have the techniques been validly applied? Have tests been conducted for possible violations of any assumptions made i

30、n the estimation of the model?1.6 Points to Consider when reading a published paper314. Have the results been interpreted sensibly? Is the strength of the results exaggerated? Do the results relate to the questions posed by the authors?5. Are the conclusions drawn appropriate given the results, or h

31、as the importance of the results of the paper been overstated? Points to Consider when reading empirical finance papers321.7 Econometric packages for modelling financial datawhat packages are available?EVIEWS (menu-driven); RATS (command-driven)GAUSS; LIMDEP; MATLAB; SAS: SHAZAM; SPSS ; TSP* RATS *EVIEWS33Accomplishing simple tasks using EViews1. Creating a work importing data2. Verifying the data3. Transformations(new variable “A, B, G”, old variable “Z”)A=Z/2 B=Z*2 C=Z2 D=