Comparing Stock Returns Forecasting Methods Using SAS

http://support.sas.com/resources/papers/proceedings12/163-2012.pdf

文章比较了较传统的股票分析方法：移动平均MA，相对强度指标RSI，布连线；处于数据的连续和完整，文章选取1981.1.2-2010.12.31时间内纽交所都进行交易的股票数据，共计355只个股。数据包含了一下变量：日期date,股票的ID，日收益RET,股票调整价格ADJPRC,格式如下如：

355只股票的平均日收益0.0638%,标准差sd=2.2624%.如果预测收益超过阀值就意味着该方法有效。

1.移动平均方法

1日/2日/5日移动平均线为短期均线，50日/150日/200日为长期均线。当短期均线从下向上穿越长期均线，作为买入信号；反之为卖出信号。假设投资者持有或卖出股票严格遵守交易信号进行操作，这种策略为“变长移动平均-VMA”；如果投资者按照固定天数持有或卖出股票，这种策略称为“定长移动平均-FMA”。

data MA;
   set summer.sample;
   MA2 = adjprc;
   MA5 = adjprc;
   MA50 = adjprc;
   MA150 = adjprc;
   MA200 = adjprc;
run;
proc sort data = MA;
   by cusip date;
run;
%macro calave(days);
   %do i = 1 %to &days-1;
       data MA;
          set MA;
          MA&days = MA&days + lag&i(adjprc);
          if &i = &days-1 then MA&days = MA&days/&days;
          if &i = &days-1 then do;
             if &days = 2 and date<mdy(01,05,81) then MA2 = .;
             if &days = 5 and date<mdy(01,08,81) then MA5 = .;
             if &days = 50 and date<mdy(03,13,81) then MA50 = .;
             if &days = 150 and date<mdy(08,05,81) then MA150 = .;
             if &days = 200 and date<mdy(10,15,81) then MA200 = .;
          end;
       run;
   %end;
%mend;
%calave(2)
%calave(5)
%calave(50)
%calave(150)
%calave(200)
data summer.MovingAverage;
   set MA;
run;

下面的代码测试VMA ，该例测试了1日/200日，1日/150日，1日/50日的短线长线策略。

data MAresult;
   set summer.movingaverage;
run;

proc means data = MAresult noprint;
   var ret;
   output out = buyandhold n = BHn mean = BHmean std = BHstd;
run;

data MAresult;
   set MAresult;
   if adjprc=. or MA200=. then status = 0;
   else if adjprc>MA200*1.01 then status = 1; *VMA buy(1,200,0.01);
   else if adjprc<MA200*0.99 then status = -1; *VMA sell(1,200,0.01);
   else status = 0;

   if adjprc=. or MA50=. then status = 0;
   else if adjprc>MA50*1.01 then status = 1; *VMA buy(1,50,0.01);
   else if adjprc<MA50*0.99 then status = -1; *VMA sell(1,50,0.01);
   else status = 0;

   if adjprc=. or MA150=. then status = 0;
   else if adjprc>MA150*1.01 then status = 1; *VMA buy(1,150,0.01);
   else if adjprc<MA150*0.99 then status = -1; *VMA sell(1,150,0.01);
   else status = 0;
run;

proc sort data = MAresult;
   by status;
run;
proc means data = MAresult noprint;
   var ret;
   by status;
   output out = buyandsell n = BSn mean = BSmean std = BSstd;
run;
data VMAfinal; *VMA final result!;
   merge buyandhold buyandsell;
   by _TYPE_;
   drop _FREQ_ _TYPE_;
   if status ~= 0 then
            t =(BSmean-BHmean)/sqrt(BHstd*BHstd/BHn+BHstd*BHstd/BSn);
run;

测试结果如下：

2.相对强弱指标策略:Relative Strength Index
RSI的原理简单来说是以数字计算的方法求出买卖双方的力量对比,譬如有100个人面对一件商品，如果50个人以上要买，竞相抬价，商品价格必涨。相反，如果50个人以上争着卖出，价格自然下跌。强弱指标理论认为，任何市价的大涨或大跌，均在0-100之间变动，根据常态分配，认为RSI值多在30-70之间变动，通常80甚至90时被认为市场已到达超买状态，至此市场价格自然会回落调整。当价格低跌至30以下即被认为是超卖状态，市价将出现反弹回升。具体的公式:

• RS = Ave. Gain / Ave. Loss in prior n days;
• RSI = 100 – 100 / (1+RS)

文章计算了14日RSI，下面的代码系在SAS中定义RSI：

*define RSI in SAS
RS = Ave. Gain / Ave. Loss in prior n days
RSI = 100 – 100 / (1+RS);
data RSI;
   set RSI;
   by cusip;
   ladjprc = lag(adjprc);
   if adjprc>ladjprc then gain = adjprc-ladjprc;
   if adjprc<ladjprc then loss = ladjprc-adjprc;
   if first.cusip then do;
      gain = .;
      loss = .;
   end;

   retain days 0;
   days+1;
   if first.cusip then days = 1; 
   if gain = . then gain = 0;
   if loss = . then loss = 0;

   retain sumgain 0;
   sumgain = sumgain + gain;
   retain sumloss 0;
   sumloss = sumloss + loss;
   if days=15 then do;
      AveGain = (sumgain-gain) / 14;
      AveLoss = (sumloss-loss) / 14;
      RS = AveGain / AveLoss;
      RSI = 100-100/(1+RS);
   end;
   drop sumgain sumloss;
run;

%macro calRSI();
   %do i=16 %to 7570;
       data RSI;
          set RSI;
          lAveGain = lag1(AveGain);
          lAveLoss = lag1(AveLoss);
          if days = &i then do;
             AveGain = (lAveGain*13+gain)/14;
             AveLoss = (lAveLoss*13+loss)/14;
             RS = AveGain / AveLoss;
             RSI = 100-100/(1+RS);
          end;
   %end;
%mend;
%calRSI;
data summer.RSIresult;
   set RSI;
run;

下面的代码测试了“变长RSI”（Variable-Length RSI,VRSI),定义超买信号为RSI>80，RSI<60时投资者弱卖；RSI<20为超卖信号，RSI>40强卖信号。

data VRSIB;
   set RSIresult;
   by cusip;
   drop status;
   retain period 0;
   if first.cusip then period = 0;
   if RSI<20 then period = 1; *RSI<20 buy and until RIS>40;
   if RSI>40 then period = 0;
      RealPeriod = lag(period);
   if RealPeriod = 0 then delete;
run;

data VRSIS;
   set RSIresult;
   by cusip;
   drop status;
   retain period 0;
   if first.cusip then period = 0;
   if RSI>80 then period = 1; *RSI>80 sell and until RIS<60;
   if RSI<60 then period = 0;
      RealPeriod = lag(period);
   if RealPeriod = 0 then delete;
run;
proc means data = VRSIB;
   var ret;
run;
proc means data = VRSIS;
   var ret;
run;

结果如下：

 

3.布连线策略BOLLINGER BANDS STRATEGY (BOLL)

BOLL指标的计算公式 ：

　　中轨线=N日的移动平均线

　　上轨线=中轨线+两倍的标准差

　　下轨线=中轨线－两倍的标准差

BOLL指标的计算过程

　　（1）计算MA ：　　MA=N日内的收盘价之和÷N

　　（2）计算标准差MD：MD=平方根N日的（C－MA）的两次方之和除以N

　　（3）计算MB、UP、DN线 ：MB=（N－1）日的MA，UP=MB+2×MD，DN=MB－2×MD

文章，以20日作为移动平均日期，2（4）倍标准差作为上下轨与中轨距离。股价在大于上轨为卖出信号，股价低于下轨为买入信号。作者下面的代码测试了“变长的布林线策略”。

/*The following program illustrates how we define the Bollinger Bands Strategy in SAS*/
data BB;
   set summer.sample;
   MA20 = 0;
run;
proc sort data = BB;
   by cusip date;
run;
%macro calave(days);
   %do i = 1 %to &days;
       data BB;
          set BB;
            MA&days = MA&days + lag&i(adjprc);
            if &i = &days then MA&days = MA&days/&days;
            if &i = &days then do;
               if &days = 20 and date<mdy(02,05,81) then MA20 = .;
            end;
       run;
   %end;
%mend;
%calave(20)
%macro sd;
   proc delete data=all;
   run;
   %do firstobs = 1 %to (2684248-20);
       %let lastobs = %eval( &firstobs + 19);
       proc means data=BB(firstobs=&firstobs obs=&lastobs) noprint;
            var adjprc;
            output out=tempfile stddev=sd20;
       run;
      
       proc append base=all data=tempfile;
       run;
   %end;
%mend sd;
%sd;
data summer.BBand;
   set all;
run;

下面的代码测试了布林线策略：

/*The following program evaluates the variable and fixed Bollinger Bands: Program 3B:*/
data BB;
   set summer.finalBB;
       upperband = MA20+2*sd20;
       lowerband = MA20-2*sd20;
       upperband1 = MA20+1*sd20;
       lowerband1 = MA20-1*sd20;
       if adjprc>upperband then status = -1;
       else if adjprc<lowerband then status = 1;
       else status = 0;
run;
data VBBB;
   set BB;
   by cusip;
   drop status;
   retain period 0;
   if first.cusip then period = 0;
   if adjprc<lowerband then period = 1;
   if adjprc>lowerband1 then period = 0;
      RealPeriod = lag(period);
   if RealPeriod = 0 or RealPeriod = . then delete;
run;
data VBBS;
   set BB;
   by cusip;
   drop status;
   retain period 0;
   if first.cusip then period = 0;
   if adjprc>upperband then period = 1;
   if adjprc<upperband1 then period = 0;
      RealPeriod = lag(period);
   if RealPeriod = 0 or RealPeriod = . then delete;
run;
proc means data=VBBB;
   var ret;
run;
proc means data=VBBS;
   var ret;
run;

测试结果如下：