backtrader策略库：基于z-score的配对策略

配对交易，其基本原理就是找出两只走势相关的股票。这两只股票的价格差距从长期来看在一个固定的水平内波动，如果价差暂时性的超过或低于这个水平，就买多价格偏低的股票，卖空价格偏高的股票。等到价差恢复正常水平时，进行平仓操作，赚取这一过程中价差变化所产生的利润。

配对策略本质上也是多股操作，可以采用我们教程中的多股组合操作的技术。

假设我们找到两支走势高度相关的股票601128.SH 常熟银行 X 和601166.SH 兴业银行 Y，通过OLS回归得到两者价格的关系为：Y – 1.5575*X = 6.1175

我们令 Z = Y – 1.5575*X，则Z应该在均值6.1175上下波动，Z过大，则说明Y超过X过多，此时可以卖Y买X；Z过小（负数），则说明Y低于X过多，应该买Y卖X。

那么怎么衡量Z过大还是过小呢？我们可以计算一个z−score 值，z−score =（Z – 均值）/标准差，它表示时间序列Z偏离了其均值多少倍的标准差。比如z−score>1则认为Y过大，z−score<-1则认为Y过小。以下是代码样本。

import backtrader as bt
import backtrader.feeds as btfeeds
import backtrader.indicators as btind


class PairTradingStrategy(bt.Strategy):
    params = dict(
        period=10,
        qty1=0,
        qty2=0,
        printout=False,
        upper=1,
        lower=-1,
        up_medium=0.5,
        low_medium=-0.5,
        status=0,
    )

    def log(self, txt, dt=None):
        if self.p.printout:
            dt = dt or self.data.datetime[0]
            dt = bt.num2date(dt)

    def notify_order(self, order):
        if order.status in [bt.Order.Submitted, bt.Order.Accepted]:
            return  # Await further notifications

        if order.status == order.Completed:
            if order.isbuy():
                buytxt = 'BUY COMPLETE, %.2f' % order.executed.price
                self.log(buytxt, order.executed.dt)
            else:
                selltxt = 'SELL COMPLETE, %.2f' % order.executed.price
                self.log(selltxt, order.executed.dt)

        elif order.status in [order.Expired, order.Canceled, order.Margin]:
            self.log('%s ,' % order.Status[order.status])
            pass  # Simply log

        # Allow new orders
        self.orderid = None

    def __init__(self):
        # To control operation entries
        self.orderid = None
        self.qty1 = self.p.qty1
        self.qty2 = self.p.qty2
        self.upper_limit = self.p.upper
        self.lower_limit = self.p.lower
        self.up_medium = self.p.up_medium
        self.low_medium = self.p.low_medium
        self.status = self.p.status

        # Signals performed with PD.OLS :
        self.transform = btind.OLS_TransformationN(self.data0, self.data1,
                                                   period=self.p.period)
        self.zscore = self.transform.zscore

    def next(self):

        if self.orderid:
            return  # if an order is active, no new orders are allowed


        if (self.zscore[0] > self.upper_limit) and (self.status != 1):
            self.status = 1
            self.order_target_percent(self.data1,0) # data1 = y
            self.order_target_percent(self.data0,1) # data0 = x

        elif (self.zscore[0] < self.lower_limit) and (self.status != 2):
            self.order_target_percent(self.data0,0) # data0 = x
            self.order_target_percent(self.data1,1) # data1 = y
            self.status = 2 


    def stop(self):
        print('==================================================')
        print('Starting Value - %.2f' % self.broker.startingcash)
        print('Ending   Value - %.2f' % self.broker.getvalue())
        print('==================================================')