1、证券市场实证研究方法,上海财经大学金融学院韩其恒,教案网址,password: 123456,论文评改标准,共100分平时成绩：20分（1）论文阅读翻译；论文评述（80分）（2）论文背景、文献综述： 15分数学模型：25分模型的求解：25分模型解的意义：15分论文以5000字左右为适宜, 题材不限要求交soft and hard paper,Where & when,接受人：地址：时间：电子版发送到:,主要内容,市场的有效性弱式有效：技术指标，信号处理简介，趋势跟踪法，混沌及小波简介。半强式有效：事件研究法；The Cross-Section of Expected Stock Returns
2、,金融理论的发展历程,Bachelier（1900）：随机游走 Markowitz（1952）：资产组合理论Sharpe（1964）：资本资产定价模型（CAPM） Fama（1967）：有效市场假说（EMH） Black and Scholes（1973）：期权定价模型（Option Pricing Model）Ross（1976）：套利定价理论（APT）,信息,有效市场假说的类型,弱式有效市场：如果所有关于过去价格变化的信息都反映在现行股价上。半强式有效市场：假定所有公开可得的信息反映在股票价格上。强式有效市场：假定所有信息（尤其包括非公开信息）都反映在股价上。,问题并不简单是市场要么严格有
3、效，要么严格无效，而是一个有效的程度问题。问题的关键不是某个市场是否有效，而是多有效。如果价格能够对所有新信息进行相对快速调整，我们就可以说市场是相对有效的。价格与经过仔细分析后的价格不同，这样的市场可以说是相对无效的市场。,相对市场,有效市场的实证检验,一、我国股市的实证检验结果：自从全国性股票市场建立以来，对我国股票市场有效性的讨论和检验从未间断过，遗憾的是，至今仍未能形成统一的令人信服的结论。,二、弱式有效检验,背景：弱式有效检验考察过去价格的时间序列是否能用于预测未来的股价。研究：Fama（1965），股票市场价格行为一文中对30支股票进行了间隔一天的回归分析。结论：过去价格序列确实包
4、含一些有关未来股价行为的信息，但基于过去数据的任何交易方式可能不具价值，即便最小的交易费用也会淹没超额报酬。1. 回归分析,对上证综合指数的回归检验,时间段：12/19/199012/13/199612/13/199608/17/200706/13/200108/17/200701/04/200608/17/2007,结论：回归系数为0.0071 0.1081，因此在0.05的置信水平下，拒绝一次项系数为零的原假设，表明有正相关。,结论：回归系数为-0.0362 0.0411，因此在0.05的置信水平下，不能拒绝一次项系数为零的原假设。,结论：回归系数为-0.0431 0.0588，因此在0.
5、05的置信水平下，不能拒绝一次项系数为零的原假设。,结论：回归系数为-0.1174 0.0830，因此在0.05的置信水平下，不能拒绝一次项系数为零的原假设。,对个股的回归检验,个股：四川长虹（sczh）时间段： 03/11/9412/13/9612/16/9604/30/0306/13/0104/30/03,结论：回归系数为0.0097 0.1163，p值为0.0026，因此在0.05的置信水平下，拒绝一次项系数为零的原假设，表明有正相关。,结论：回归系数为0.0004 0.0659，p值为0.0101，因此在0.05的置信水平下，拒绝一次项系数为零的原假设，表明有正相关。,结论：回归系数为
6、-0.0085 0.0338，p值为0.4747，因此在0.05的置信水平下，不能拒绝一次项系数为零的原假设。,2、随机游走假设的检验方法,Aaron Brown: The Poker Face of Wall Street (John Wiley & Sons, Inc. ,2006 ) Finance professors emphasize a different view. They do not deny that stocks and other securities represent economic fundamentals, but valuation from first
7、 principles is too hard. No one seems to be able to arrive at a more accurate price than the current market price. Therefore it makes sense to treat the stock price as a gamble, a number that can go up or down with some probability. This is called the random walk theory.,Ljung-Box的Q统计量,是通过计算序列自相关系数平
8、方的加权平均来检验序列是否独立，是一种传统直观的方法。Q统计量如下式所示：,其中rj是滞后为j的相关系数，T是样本容量，p为滞后阶数。其原假设为：序列独立。,Autocorrelation Test,弱式有效检验,游程检验：检验时间序列是否独立。,SHCI的0/1转换表，90-01,游程检验,列出观测值计算观测值中值将观测值中大于中值的记为+，小于中值的记为-，等于中值的记为+。正号的个数记为n1，负号的个数记为n2。按照观测值的顺序，将正负号的改变个数加1记为RANS。,当n1或n2大于20时，以下统计量近似服从标准正态分布。,当Z0值小于1.96时，在0.05置信水平上不能拒绝观测值是独立
9、的这一原假设。,clear%importing datar=rand(1,100);alpha=0.05;plot(r)%runsr=r-median(r);for i=1:length(r) if r(i)=0 r(i)=1; else r(i)=0; endendn1=sum(r);n2=length(r)-n1;runs=1;for i=2:length(r) if r(i)=r(i-1) runs=runs+1; endend,%testingz=abs(runs-2*n1*n2/(n1+n2)+1)/sqrt(2*n1*n2*(2*n1*n2-n1-n2)/(n1+n2)2*(n1+
10、n2-1);c=norminv(1-alpha/2);if zc h=1,else h=0,end,100 random samples of uniform distributionrand(100,1),Z=0.4020,1000 random samples from AR(1) process rt+1= rt+t, =0.5, r1=0.5,Runs test: z=11.4532,3-month riskfree rate,Runs test: z=7.5292,Runs test: z=4.2734,Runs test: z=1.8407,Runs test: z=1.3379,
11、Runs test: z=0.5394,RUNS=1913，Z0=4.1426。因此在0.05置信水平上拒绝SHCI收益率序列是独立的这一原假设。,技术指标实证检验,研究背景,实证对象：上证综指（SHCI）指标：MA、EMA、MACD、TRIX、BIAS、PSY、W%R、RSI、KDJ佣金：0.35%买卖规则,时间段：01/02/1997;06/13/2001;01/04/2006,1. 算术移动平均线（MA）,高明的趋势波段交易师 美Alan S. Farley,移动平均线的设定20天：短期趋势50天：中期趋势200天：长期趋势最流行的观点认为：200日移动平均线是股票牛市和熊市划分的参考标
12、准。,Long=10：ret(B ret(10)=88.25%,short(i)long(i),Long=50：ret(B ret(50)=18.58%,short(i)long(i-1),Long=50：ret(B ret(50)=20.86%,fee=0,2. 指数平滑移动平均线(EMA),short(i)0 if length(buy)=length(sell) sell(k)=n; endelse sell(k)=n;end,资金曲线,function profit,index=funprofit(p,open,buy,sell,allowed)%profitfee=0.0035;k=
13、length(buy);n=length(p);flag=1;for i=1:k profit(buy(i):sell(i)-1)=p(buy(i):sell(i)-1)/open(buy(i)*flag*(1-fee); profit(sell(i)=open(sell(i)/open(buy(i)*flag*(1-fee); flag=profit(sell(i); if allowed=0 if ik profit(sell(i)+1:buy(i+1)-1)=flag*ones(1,buy(i+1)-sell(i)-1); elseif sell(i)n profit(sell(i)+1
14、:n)=flag*ones(1,n-sell(i); end else,if ik profit(sell(i)+1:buy(i+1)-1)=2*p(sell(i)-p(sell(i)+1:buy(i+1)-1); profit(buy(i+1)=2*open(sell(i)-open(buy(i+1); profit(sell(i)+1:buy(i+1)=flag*profit(sell(i)+1:buy(i+1)/open(sell(i)*(1-fee)2; flag=profit(buy(i+1); elseif sell(i)n profit(sell(i)+1:n)=2*p(sell
15、(i)-p(sell(i)+1:n); profit(n)=2*open(sell(i)-open(n); profit(sell(i)+1:n)=flag*profit(sell(i)+1:n)/open(sell(i)*(1-fee)2; end endendindex=p/p(1)*(1-fee)2;,信号处理(Signal Processing),单位脉冲函数,任何一个序列均可表示成,线性时不变系统,线性时不变系统,有限脉冲响应(FIR)：这些单位脉冲响应只有有限个非零样本无限脉冲响应(IIR)频率响应,b=1/2,1/2，freqz(b,1),b=1/2,1/2，grpdelay(b
16、,1),n=20; x=sin(2*pi*1:n/3);,b=ones(1,20)/20, freqz(b,1),n=150;x=0.1*1:n+sin(2*pi*1:n/50+pi/4)+sin(2*pi*1:n/20+pi/4);,Momentum: b=1,-1,freqz(b,1),n=150;x=0.1*1:n+sin(2*pi*1:n/50+pi/4)+sin(2*pi*1:n/5+pi/4);,EMA(5): b=2/6,a=1,-4/6,freqz(b,a),MESAMaximum Entropy Spectral AnalysisBy John Parker Burg,MES
17、As claim,Technical analysis of the market is successful because the market is not always efficient. Discernible events that occur in chart patterns, such as double tops and Elliott waves, enable trading to be guided by technical analysis. Cycles are one of these discernible events that occur and ide
18、ntifiable by direct measurement. Identification of cycles does not take a lifetime experience or an expert system. Cycles can be measured directly, either by a simple system such as measuring the distance between successive lows or by a sophisticated computer program such as MESA.,However,The fact t
19、hat cycles exist does not imply that they exist all the time. Cycles come and go. External events sometimes dominate and obscure existing cycles. Experience shows that cycles useful for trading are present only about 15 to 30 percent of the time. This corresponds remarkably with J. M. Hursts stateme
20、nt that “23% of all price motion is oscillatory in nature and semi-predictable.” It is analogous to the problem of the trend follower who finds that the market “trend” only a small percentage of the time.,Conclusion,Arguments that cycles exist in the market arise not only from fundamental considerat
21、ions or direct measurement but also on philosophical grounds related to physical phenomena. The natural response to any physical disturbance is harmonic motion. If you pluck a guitar string, the string vibrates with cycles you can hear. By analogy, we have every right to expect that the market will
22、response to disturbances with cyclic motion. This expectation is reinforced with random walk theory that suggests there are times the market prices can be described by the diffusion equation and other times when the market prices can be described by the telegraphers equations.The challenge for techn
23、ical traders is to recognize when the short term cycles are present and to trade them in a logical and consistent manner so there cycles can contribute profitably to the bottom line.,Maximum Entropy Spectral Analysis,Assumption：stationary time series with mean 0.Best model：it is known for a gaussian
24、 process, the optimum predicator is a linear predictor, i.e., AR model,Problems with direct estimation of autocorrelation function,(1.0, 1.1, 1.0), R(0)=1.07, R(1)=1.1Non-negative definiteFourier Transformation: Newton; FourierFast Fourier Transformation: assume that the N point sample repeats itsel
25、f periodically.,Power spectral density,Norbert Wiener: in 1930, gave precise statistical definitions pf autocorrelation and power spectral density for stationary random processes.,Maximum entropy,MESA Software: today, MESA is acknowledged as the single best method of measuring market cycles.,Informa
26、tion theory: Maximum entropy time series is governed by a gaussian joint probability function and that the entropy is proportional to the integral of the logarithm of the spectrum.Upper bound is achieved if the time series is a gaussian process.,clear%input datan=100;%x=sin(2*pi*1:n/12)+sin(2*pi*1:n
27、/20+pi/3);x=randn(1,n);,clear%input datan=200;x=sin(2*pi*1:n/12)+sin(2*pi*1:n/20+pi/3);x =x+randn(1,n);,Lowpass filter,clearn=3;rp=0.1;rs=30;wn=0.22;b,a = ellip(n,rp,rs,wn);freqz(b,a)pausegrpdelay(b,a),detrending,clearb=0.95,-0.95;a=1,-0.9;freqz(b,a)pausegrpdelay(b,a),n=50;p=0.5*1:n+2*sin(2*pi*1:n/1
28、5)+2*sin(2*pi*1:n/5+pi/3);,filter+detrending,clearn=3;rp=0.1;rs=30;wn=0.22;b1,a1 = ellip(n,rp,rs,wn);b2=0.95,-0.95;a2=1,-0.9;b=conv(b1,b2);a=conv(a1,a2);,Trend FollowingHow great traders make millions in up or down markets,Michael W. Covel, FT Press, ,Assumption,The ability of Trend Following strate
29、gies to succeed depends on two obvious but important assumptions about markets. First, it assumes that price trends occur regularly in markets. Secondly, it assumes that trading systems can be created to profit from these trends. The basic trading strategy that all trend followers try to systematize
30、 is to “cut losses” and “let profits run”.,What is their factor?,Trend followers generate phenomenal returns because their decisions are ultimately based on one piece of core information: price. In an increasingly uncertain and, these days, downright unfriendly world, it is extremely efficient and e
31、ffective if our decision-making is based on this single, simple, reliable truth.What is most important factor: price; What is second most important factor: price;What is third most important factor: price;,Where profit comes from?,John W. Henry: We rely on the fact that other investors are convinced
32、 that they can predict the future, and I believe thats where our profits come from. I believe its that simple.Remember that only 30-40 percent of trades are typically profitable for trend followers. Since trend followers never knows which trend will be their big winners, they accumulate small losses
33、 trying to find it.,Who lose,There are two kinds of people who lose money: those who know nothing and those who know everything. “With two Nobel prize wimmers in the house, Long-Term Capital clearly fits the second case.”,Different traders,Investor v. trader: they are not investing in anything. They
34、 are trading. It is an important distinction.Fundamental v. technicalTechnical: predictive v. reactiveDiscretionary v. mechanical.Using “common sense” is not a good way to judge or trade markets.Is mechanical trading system boring? I dont trade for excitement; I trade to win.,Ed Seykota: “there is n
35、o best systems any more than there is a best car. There might however a best car for you.”,Is there a best system?,A robust trading system, one that is not curve-fit, must ideally trade all markets at all times in all conditions.Systems that rely too much on past data and past occurrences are likely
36、 to fail in the future.,Curve-fitting,Holding period,The average holding periods ranges from two weeks to one year.,The five questions for a trading system,How does the system determine what market to buy or sell at any time?How does the system determine how much of a market to buy or sell at any ti
37、me?How does the system determine when you get buy or sell a market?How does the system determine when you get out of a losing position?How does the system determine when you get out of a winning position?,Assets: portfolio,Dun Capital Management37 percent non-US interest rate25 percent US interest r
38、ate16 percent major currencies17 percent stock indices5 percent energiesTotal 100 percent,Stability test,Suitable to all marketsRobust test and Monte Carlo simulationStop-loss: less than 2%; the exposure of of each position to 10% of our current equity.,Average True Range (ATR)真实波动幅度均值,A measure of
39、volatility introduced by Welles Wilder in his book: New Concepts in Technical Trading Systems. The True Range indicator is the greatest of the following: -current high less the current low. -the absolute value of the current high less the previous close. -the absolute value of the current low less t
40、he previous close. The Average True Range is a moving average (generally 14-days) of the True Ranges Wilder originally developed the ATR for commodities but the indicator can also be used for stocks and indexes. Simply put, a stock experiencing a high level of volatility will have a higher ATR, and
41、a low volatility stock will have a lower ATR.,System SMA 100-50,Set a stop loss of four times the ATR of 10 days.Although it is possible to design a system in Wealth Lab Developer using the best parameter for each market, we believe this would lead us into curve-fitting-trap.,SMA 100-50,SMA 100-50,S
42、ystem SMA 20-10 (weekly data),Set a stop loss of four times the ATR of 10 weeks.,SMA 20-10,SMA+stoploss,Donchian Channel,The Donchian Channel indictor wae created by Richard Donchian.The higher band: the highest high of the past n days.The lower band: the lowest low of the past n days.Assumption: a
43、crossover of these psychologically important lines is the result of a change in the markets opinion, and thus a continuation of the initial movement could possibly expected.,N=100,Varying length,N=50,N=50,01/02/1997-06/13/2001,Examples,混沌简介Introduction to Chaos,Why technical？,Why is there structure
44、in financial markets? Why people does the data cluster in predictable pattern? The short answer is simple. Financial markets are the product of human activity, and humans are irrational, trend-following, herd-driven creatures who react and overreact. I believe in the inefficient market theory, based on human foibles and the herd behavior of people acting in groups. Traders share common knowledge and biases. We all read the same newspapers. We share common emotions, like fear and greed. We obey universal rules of human psychology and act in herds.,
