这篇博文是用Python分析股市数据系列两部中的第二部，内容基于我在阅读第一部分)。在这两篇博文中，我会讨论一些基础知识，包括比如如何用pandas从雅虎财经获得数据， 可视化股市数据，平均数指标的定义，设计移动平均交汇点分析移动平均线的方法，回溯测试和 基准分析法。这篇文章会讨论如何设计用移动平均交汇点分析移动平均线的系统，如何做回溯测试和基准分析，最后留有一些练习题以飨读者。

注意：本文仅代表作者本人的观点。文中的内容不应该被当做经济建议。我不对文中代码负责，取用者自己负责

交易策略

在特定的预期条件达成时一个开放头寸会被关闭。多头头寸表示交易中需要金融商品价格上升才能产生盈利，空头头寸表示交易中需要金融商品价格下降才能产生盈利。在股票交易中，多头头寸是牛市，空头头寸是熊市，反之则不成立。(股票期权交易中这个非常典型)

例如你在预计股价上涨的情况下购入股票，并计划在股票价格上涨高于购入价时抛出，这就是多头头寸。就是说你持有一定的金融产品，如果它们价格上涨，你将会获利，并且没有上限；如果它们价格下降，你会亏损。由于股票价格不会为负，亏损是有限度的。相反的，如果你预计股价会下跌，就从交易公司借贷股票然后卖出，同时期待未来股票价格下降后再低价买入还贷来赚取差额，这就是空头股票。如果股价下跌你会获利。空头头寸的获利额度受股价所限(最佳情况就是股票变得一文不值，你不用花钱就能将它们买回来)，而损失却没有下限，因为你有可能需要花很多钱才能买回股票。所以交换所只会在确定投资者有很好的经济基础的情况下才会让他们空头借贷股票。

所有股民都应该决定他在每一股上可以冒多大的风险。比如有人决定无论什么情况他都不会在某一次交易中投入总额的10%去冒险。同时在交易中，股民要有一个撤出策略，这是让股民退出头寸的各种条件。股民也可以设置一个目标，这是导致股民退出头寸的最小盈利额。同样的，股民也需要有一个他能承受的最大损失额度。当预计损失大于可承受额度时，股民应该退出头寸以避免更大损失(这可以通过设置停止损失委托来避免未来的损失)。

我们要设计一个交易策略，它包含用于快速交易的交易激发信号、决定交易额度的规则和完整的退出策略。我们的目标是设计并评估该交易策略。

假设每次交易金额占总额的比例是固定的(10%)。同时设定在每一次交易中，如果损失超过了20%的交易值，我们就退出头寸。现在我们要决定什么时候进入头寸，什么时候退出以保证盈利。

这里我要演示移动平均交汇点分析移动平均线的方法。我会使用两条移动平均线，一条快速的，另一条是慢速的。我们的策略是：

当快速移动平均线和慢速移动线交汇时开始交易

当快速移动平均线和慢速移动线再次交汇时停止交易

做多是指在快速平均线上升到慢速平均线之上时开始交易，当快速平均线下降到慢速平均线之下时停止交易。卖空正好相反，它是指在快速平均线下降到慢速平均线之下时开始交易，快速平均线上升到慢速平均线之上时停止交易。

现在我们有一整套策略了。在使用它之前我们需要先做一下测试。回溯测试是一个常用的测试方法，它使用历史数据来看策略是否会盈利。例如这张苹果公司的股票价值图，如果20天的移动平均是快速线，50天的移动平均是慢速线，那么我们这个策略不是很挣钱，至少在你一直做多头头寸的时候。

下面让我们来自动化回溯测试的过程。首先我们要识别什么时候20天平均线在50天之下，以及之上。

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apple['20d-50d']=apple['20d']-apple['50d']

apple.tail()

OpenHighLowCloseVolumeAdj Close20d50d200d20d-50d

Date

2016-08-26

107.410004

107.949997

106.309998

106.940002

27766300

106.940002

107.87

101.51

102.73

6.36

2016-08-29

106.620003

107.440002

106.290001

106.820000

24970300

106.820000

107.91

101.74

102.68

6.17

2016-08-30

105.800003

106.500000

105.500000

106.000000

24863900

106.000000

107.98

101.96

102.63

6.02

2016-08-31

105.660004

106.570000

105.639999

106.099998

29662400

106.099998

108.00

102.16

102.60

5.84

2016-09-01

106.139999

106.800003

105.620003

106.730003

26643600

106.730003

108.04

102.39

102.56

5.65

我们将差异的符号称为状态转换。快速移动平均线在慢速移动平均线之上代表牛市状态；相反则为熊市。以下的代码用于识别状态转换。

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# np.where() is a vectorized if-else function, where a condition is checked for each component of a vector, and the first argument passed is used when the condition holds, and the other passed if it does not

apple["Regime"]=np.where(apple['20d-50d']>0,1,0)

# We have 1's for bullish regimes and 0's for everything else. Below I replace bearish regimes's values with -1, and to maintain the rest of the vector, the second argument is apple["Regime"]

apple["Regime"]=np.where(apple['20d-50d']<0,-1,apple["Regime"])

apple.loc['2016-01-01':'2016-08-07',"Regime"].plot(ylim=(-2,2)).axhline(y=0,color="black",lw=2)

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apple["Regime"].plot(ylim=(-2,2)).axhline(y=0,color="black",lw=2)

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apple["Regime"].value_counts()

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1966

-1663

050

Name:Regime,dtype:int64

从上面的曲线可以看到有966天苹果公司的股票是牛市，663天是熊市，有54天没有倾向性。(原文中牛市和熊市说反了，译文中更正；原文数字跟代码结果对不上，译文按照代码结果更正)

交易信号出现在状态转换之时。牛市出现时，买入信号被激活；牛市完结时，卖出信号被激活。同样的，熊市出现时卖出信号被激活，熊市结束时，买入信号被激活。(只有在你空头股票，或者使用一些其他的方法例如用股票期权赌市场的时候这种情况才对你有利)

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# To ensure that all trades close out, I temporarily change the regime of the last row to 0

regime_orig=apple.ix[-1,"Regime"]

apple.ix[-1,"Regime"]=0

apple["Signal"]=np.sign(apple["Regime"]-apple["Regime"].shift(1))

# Restore original regime data

apple.ix[-1,"Regime"]=regime_orig

apple.tail()

OpenHighLowCloseVolumeAdj Close20d50d200d20d-50dRegimeSignal

Date

2016-08-26

107.410004

107.949997

106.309998

106.940002

27766300

106.940002

107.87

101.51

102.73

6.36

1.0

0.0

2016-08-29

106.620003

107.440002

106.290001

106.820000

24970300

106.820000

107.91

101.74

102.68

6.17

1.0

0.0

2016-08-30

105.800003

106.500000

105.500000

106.000000

24863900

106.000000

107.98

101.96

102.63

6.02

1.0

0.0

2016-08-31

105.660004

106.570000

105.639999

106.099998

29662400

106.099998

108.00

102.16

102.60

5.84

1.0

0.0

2016-09-01

106.139999

106.800003

105.620003

106.730003

26643600

106.730003

108.04

102.39

102.56

5.65

1.0

-1.0

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apple["Signal"].plot(ylim=(-2,2))

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apple["Signal"].value_counts()

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0.01637

-1.021

1.020

Name:Signal,dtype:int64

我们会买入苹果公司的股票20次，抛出21次 (原文数字跟代码结果不符，译文根据代码结果更正)。如果我们只选了苹果公司的股票，六年内只有21次交易发生。如果每次多头转空头的时候我们都采取行动，我们将会参与21次交易。(请记住交易次数不是越多越好，毕竟交易不是免费的)

你也许注意到了这个系统不是很稳定。快速平均线在慢速平均线之上就激发交易，即使这个状态只是短短一瞬，这样会导致交易马上终止(这样并不好因为现实中每次交易都要付费，这个费用会很快消耗掉收益)。同时所有的牛市瞬间转为熊市，如果你允许同时押熊市和牛市，那就会出现每次交易结束就自动激发另一场押相反方向交易的诡异情况。更好的系统会要求有更多的证据来证明市场的发展方向，但是这里我们不去追究那个细节。

下面我们来看看每次买入卖出时候的股票价格。

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apple.loc[apple["Signal"]==1,"Close"]

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Date

2010-03-16224.449997

2010-06-18274.070011

2010-09-20283.230007

2011-05-12346.569988

2011-07-14357.770004

2011-12-28402.640003

2012-06-25570.770020

2013-05-17433.260010

2013-07-31452.529984

2013-10-16501.110001

2014-03-26539.779991

2014-04-25571.939980

2014-08-1899.160004

2014-10-28106.739998

2015-02-05119.940002

2015-04-28130.559998

2015-10-27114.550003

2016-03-11102.260002

2016-07-0195.889999

2016-07-2597.339996

Name:Close,dtype:float64

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apple.loc[apple["Signal"]==-1,"Close"]

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Date

2010-06-11253.509995

2010-07-22259.020000

2011-03-30348.630009

2011-03-31348.510006

2011-05-27337.409992

2011-11-17377.410000

2012-05-09569.180023

2012-10-17644.610001

2013-06-26398.069992

2013-10-03483.409996

2014-01-28506.499977

2014-04-22531.700020

2014-06-1193.860001

2014-10-1797.669998

2015-01-05106.250000

2015-04-16126.169998

2015-06-25127.500000

2015-12-18106.029999

2016-05-0593.239998

2016-07-0896.680000

2016-09-01106.730003

Name:Close,dtype:float64

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# Create a DataFrame with trades, including the price at the trade and the regime under which the trade is made.

apple_signals=pd.concat([

pd.DataFrame({"Price":apple.loc[apple["Signal"]==1,"Close"],

"Regime":apple.loc[apple["Signal"]==1,"Regime"],

"Signal":"Buy"}),

pd.DataFrame({"Price":apple.loc[apple["Signal"]==-1,"Close"],

"Regime":apple.loc[apple["Signal"]==-1,"Regime"],

"Signal":"Sell"}),

])

apple_signals.sort_index(inplace=True)

apple_signals

PriceRegimeSignal

Date

2010-03-16

224.449997

1.0

Buy

2010-06-11

253.509995

-1.0

Sell

2010-06-18

274.070011

1.0

Buy

2010-07-22

259.020000

-1.0

Sell

2010-09-20

283.230007

1.0

Buy

2011-03-30

348.630009

0.0

Sell

2011-03-31

348.510006

-1.0

Sell

2011-05-12

346.569988

1.0

Buy

2011-05-27

337.409992

-1.0

Sell

2011-07-14

357.770004

1.0

Buy

2011-11-17

377.410000

-1.0

Sell

2011-12-28

402.640003

1.0

Buy

2012-05-09

569.180023

-1.0

Sell

2012-06-25

570.770020

1.0

Buy

2012-10-17

644.610001

-1.0

Sell

2013-05-17

433.260010

1.0

Buy

2013-06-26

398.069992

-1.0

Sell

2013-07-31

452.529984

1.0

Buy

2013-10-03

483.409996

-1.0

Sell

2013-10-16

501.110001

1.0

Buy

2014-01-28

506.499977

-1.0

Sell

2014-03-26

539.779991

1.0

Buy

2014-04-22

531.700020

-1.0

Sell

2014-04-25

571.939980

1.0

Buy

2014-06-11

93.860001

-1.0

Sell

2014-08-18

99.160004

1.0

Buy

2014-10-17

97.669998

-1.0

Sell

2014-10-28

106.739998

1.0

Buy

2015-01-05

106.250000

-1.0

Sell

2015-02-05

119.940002

1.0

Buy

2015-04-16

126.169998

-1.0

Sell

2015-04-28

130.559998

1.0

Buy

2015-06-25

127.500000

-1.0

Sell

2015-10-27

114.550003

1.0

Buy

2015-12-18

106.029999

-1.0

Sell

2016-03-11

102.260002

1.0

Buy

2016-05-05

93.239998

-1.0

Sell

2016-07-01

95.889999

1.0

Buy

2016-07-08

96.680000

-1.0

Sell

2016-07-25

97.339996

1.0

Buy

2016-09-01

106.730003

1.0

Sell

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# Let's see the profitability of long trades

apple_long_profits=pd.DataFrame({

"Price":apple_signals.loc[(apple_signals["Signal"]=="Buy")&

apple_signals["Regime"]==1,"Price"],

"Profit":pd.Series(apple_signals["Price"]-apple_signals["Price"].shift(1)).loc[

apple_signals.loc[(apple_signals["Signal"].shift(1)=="Buy")&(apple_signals["Regime"].shift(1)==1)].index

].tolist(),

"End Date":apple_signals["Price"].loc[

apple_signals.loc[(apple_signals["Signal"].shift(1)=="Buy")&(apple_signals["Regime"].shift(1)==1)].index

].index

})

apple_long_profits

End DatePriceProfit

Date

2010-03-16

2010-06-11

224.449997

29.059998

2010-06-18

2010-07-22

274.070011

-15.050011

2010-09-20

2011-03-30

283.230007

65.400002

2011-05-12

2011-05-27

346.569988

-9.159996

2011-07-14

2011-11-17

357.770004

19.639996

2011-12-28

2012-05-09

402.640003

166.540020

2012-06-25

2012-10-17

570.770020

73.839981

2013-05-17

2013-06-26

433.260010

-35.190018

2013-07-31

2013-10-03

452.529984

30.880012

2013-10-16

2014-01-28

501.110001

5.389976

2014-03-26

2014-04-22

539.779991

-8.079971

2014-04-25

2014-06-11

571.939980

-478.079979

2014-08-18

2014-10-17

99.160004

-1.490006

2014-10-28

2015-01-05

106.739998

-0.489998

2015-02-05

2015-04-16

119.940002

6.229996

2015-04-28

2015-06-25

130.559998

-3.059998

2015-10-27

2015-12-18

114.550003

-8.520004

2016-03-11

2016-05-05

102.260002

-9.020004

2016-07-01

2016-07-08

95.889999

0.790001

2016-07-25

2016-09-01

97.339996

9.390007

从上表可以看出2013年5月17日那天苹果公司股票价格大跌，我们的系统会表现很差。但是那个价格下降不是因为苹果遇到了什么大危机，而仅仅是一次分股。由于分红不如分股那么显著，这也许会影响系统行为。

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# Let's see the result over the whole period for which we have Apple data

pandas_candlestick_ohlc(apple,stick=45,otherseries=["20d","50d","200d"])

我们不希望我们的交易系统的表现受到分红和分股的影响。一个解决方案是利用历史的分红分股数据来设计交易系统，这些数据可以真实地反映股市的行为从而帮助我们找到最佳解决方案，但是这个方法要更复杂一些。另一个方案就是根据分红和分股来调整股票的价格。

雅虎财经只提供调整之后的股票闭市价格，不过这些对于我们调整开市，高价和低价已经足够了。调整闭市股价是这样实现的：

让我们回到开始，先调整股票价格，然后再来评价我们的交易系统。

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defohlc_adj(dat):

"""

:param dat: pandas DataFrame with stock data, including "Open", "High", "Low", "Close", and "Adj Close", with "Adj Close" containing adjusted closing prices

:return: pandas DataFrame with adjusted stock data

This function adjusts stock data for splits, dividends, etc., returning a data frame with

"Open", "High", "Low" and "Close" columns. The input DataFrame is similar to that returned

by pandas Yahoo! Finance API.

"""

returnpd.DataFrame({"Open":dat["Open"]*dat["Adj Close"]/dat["Close"],

"High":dat["High"]*dat["Adj Close"]/dat["Close"],

"Low":dat["Low"]*dat["Adj Close"]/dat["Close"],

"Close":dat["Adj Close"]})

apple_adj=ohlc_adj(apple)

# This next code repeats all the earlier analysis we did on the adjusted data

apple_adj["20d"]=np.round(apple_adj["Close"].rolling(window=20,center=False).mean(),2)

apple_adj["50d"]=np.round(apple_adj["Close"].rolling(window=50,center=False).mean(),2)

apple_adj["200d"]=np.round(apple_adj["Close"].rolling(window=200,center=False).mean(),2)

apple_adj['20d-50d']=apple_adj['20d']-apple_adj['50d']

# np.where() is a vectorized if-else function, where a condition is checked for each component of a vector, and the first argument passed is used when the condition holds, and the other passed if it does not

apple_adj["Regime"]=np.where(apple_adj['20d-50d']>0,1,0)

# We have 1's for bullish regimes and 0's for everything else. Below I replace bearish regimes's values with -1, and to maintain the rest of the vector, the second argument is apple["Regime"]

apple_adj["Regime"]=np.where(apple_adj['20d-50d']<0,-1,apple_adj["Regime"])

# To ensure that all trades close out, I temporarily change the regime of the last row to 0

regime_orig=apple_adj.ix[-1,"Regime"]

apple_adj.ix[-1,"Regime"]=0

apple_adj["Signal"]=np.sign(apple_adj["Regime"]-apple_adj["Regime"].shift(1))

# Restore original regime data

apple_adj.ix[-1,"Regime"]=regime_orig

# Create a DataFrame with trades, including the price at the trade and the regime under which the trade is made.

apple_adj_signals=pd.concat([

pd.DataFrame({"Price":apple_adj.loc[apple_adj["Signal"]==1,"Close"],

"Regime":apple_adj.loc[apple_adj["Signal"]==1,"Regime"],

"Signal":"Buy"}),

pd.DataFrame({"Price":apple_adj.loc[apple_adj["Signal"]==-1,"Close"],

"Regime":apple_adj.loc[apple_adj["Signal"]==-1,"Regime"],

"Signal":"Sell"}),

])

apple_adj_signals.sort_index(inplace=True)

apple_adj_long_profits=pd.DataFrame({

"Price":apple_adj_signals.loc[(apple_adj_signals["Signal"]=="Buy")&

apple_adj_signals["Regime"]==1,"Price"],

"Profit":pd.Series(apple_adj_signals["Price"]-apple_adj_signals["Price"].shift(1)).loc[

apple_adj_signals.loc[(apple_adj_signals["Signal"].shift(1)=="Buy")&(apple_adj_signals["Regime"].shift(1)==1)].index

].tolist(),

"End Date":apple_adj_signals["Price"].loc[

apple_adj_signals.loc[(apple_adj_signals["Signal"].shift(1)=="Buy")&(apple_adj_signals["Regime"].shift(1)==1)].index

].index

})

pandas_candlestick_ohlc(apple_adj,stick=45,otherseries=["20d","50d","200d"])

Python

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apple_adj_long_profits

End DatePriceProfit

Date

2010-03-16

2010-06-10

29.355667

3.408371

2010-06-18

2010-07-22

35.845436

-1.968381

2010-09-20

2011-03-30

37.043466

8.553623

2011-05-12

2011-05-27

45.327660

-1.198030

2011-07-14

2011-11-17

46.792503

2.568702

2011-12-28

2012-05-09

52.661020

21.781659

2012-06-25

2012-10-17

74.650634

10.019459

2013-05-17

2013-06-26

57.882798

-4.701326

2013-07-31

2013-10-04

60.457234

4.500835

2013-10-16

2014-01-28

67.389473

1.122523

2014-03-11

2014-03-17

72.948554

-1.272298

2014-03-24

2014-04-22

73.370393

-1.019203

2014-04-25

2014-10-17

77.826851

16.191371

2014-10-28

2015-01-05

102.749105

-0.028185

2015-02-05

2015-04-16

116.413846

6.046838

2015-04-28

2015-06-26

126.721620

-3.184117

2015-10-27

2015-12-18

112.152083

-7.897288

2016-03-10

2016-05-05

100.015950

-7.278331

2016-06-23

2016-06-27

95.582210

-4.038123

2016-06-30

2016-07-11

95.084904

1.372569

2016-07-25

2016-09-01

96.815526

9.914477

可以看到根据分红和分股调整之后的价格图变得很不一样了。之后的分析我们都会用到这个调整之后的数据。

假设我们在股市有一百万，让我们来看看根据下面的条件，我们的系统会如何反应：

每次用总额的10%来进行交易

退出头寸如果亏损达到了交易额的20%

模拟的时候要记住：

每次交易有100支股票

我们的避损规则是当股票价格下降到一定数值时就抛出。我们需要检查这段时间内的低价是否低到可以出发避损规则。现实中除非我们买入看空期权，我们无法保证我们能以设定低值价格卖出股票。这里为了简洁我们将设定值作为卖出值。

每次交易都会付给中介一定的佣金。这里我们没有考虑这个。

下面的代码演示了如何实现回溯测试：

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# We need to get the low of the price during each trade.

tradeperiods=pd.DataFrame({"Start":apple_adj_long_profits.index,

"End":apple_adj_long_profits["End Date"]})

apple_adj_long_profits["Low"]=tradeperiods.apply(lambdax:min(apple_adj.loc[x["Start"]:x["End"],"Low"]),axis=1)

apple_adj_long_profits

End DatePriceProfitLow

Date

2010-03-16

2010-06-10

29.355667

3.408371

26.059775

2010-06-18

2010-07-22

35.845436

-1.968381

31.337127

2010-09-20

2011-03-30

37.043466

8.553623

35.967068

2011-05-12

2011-05-27

45.327660

-1.198030

43.084626

2011-07-14

2011-11-17

46.792503

2.568702

46.171251

2011-12-28

2012-05-09

52.661020

21.781659

52.382438

2012-06-25

2012-10-17

74.650634

10.019459

73.975759

2013-05-17

2013-06-26

57.882798

-4.701326

52.859502

2013-07-31

2013-10-04

60.457234

4.500835

60.043080

2013-10-16

2014-01-28

67.389473

1.122523

67.136651

2014-03-11

2014-03-17

72.948554

-1.272298

71.167335

2014-03-24

2014-04-22

73.370393

-1.019203

69.579335

2014-04-25

2014-10-17

77.826851

16.191371

76.740971

2014-10-28

2015-01-05

102.749105

-0.028185

101.411076

2015-02-05

2015-04-16

116.413846

6.046838

114.948237

2015-04-28

2015-06-26

126.721620

-3.184117

119.733299

2015-10-27

2015-12-18

112.152083

-7.897288

104.038477

2016-03-10

2016-05-05

100.015950

-7.278331

91.345994

2016-06-23

2016-06-27

95.582210

-4.038123

91.006996

2016-06-30

2016-07-11

95.084904

1.372569

93.791913

2016-07-25

2016-09-01

96.815526

9.914477

95.900485

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# Now we have all the information needed to simulate this strategy in apple_adj_long_profits

cash=1000000

apple_backtest=pd.DataFrame({"Start Port. Value":[],

"End Port. Value":[],

"End Date":[],

"Shares":[],

"Share Price":[],

"Trade Value":[],

"Profit per Share":[],

"Total Profit":[],

"Stop-Loss Triggered":[]})

port_value=.1# Max proportion of portfolio bet on any trade

batch=100# Number of shares bought per batch

stoploss=.2# % of trade loss that would trigger a stoploss

forindex,row inapple_adj_long_profits.iterrows():

batches=np.floor(cash*port_value)//np.ceil(batch*row["Price"])# Maximum number of batches of stocks invested in

trade_val=batches*batch*row["Price"]# How much money is put on the line with each trade

ifrow["Low"]

share_profit=np.round((1-stoploss)*row["Price"],2)

stop_trig=True

else:

share_profit=row["Profit"]

stop_trig=False

profit=share_profit*batches*batch# Compute profits

# Add a row to the backtest data frame containing the results of the trade

apple_backtest=apple_backtest.append(pd.DataFrame({

"Start Port. Value":cash,

"End Port. Value":cash+profit,

"End Date":row["End Date"],

"Shares":batch*batches,

"Share Price":row["Price"],

"Trade Value":trade_val,

"Profit per Share":share_profit,

"Total Profit":profit,

"Stop-Loss Triggered":stop_trig

},index=[index]))

cash=max(0,cash+profit)

apple_backtest

End DateEnd Port. ValueProfit per ShareShare PriceSharesStart Port. ValueStop-Loss TriggeredTotal ProfitTrade Value

2010-03-16

2010-06-10

1.011588e+06

3.408371

29.355667

3400.0

1.000000e+06

0.0

11588.4614

99809.2678

2010-06-18

2010-07-22

1.006077e+06

-1.968381

35.845436

2800.0

1.011588e+06

0.0

-5511.4668

100367.2208

2010-09-20

2011-03-30

1.029172e+06

8.553623

37.043466

2700.0

1.006077e+06

0.0

23094.7821

100017.3582

2011-05-12

2011-05-27

1.026536e+06

-1.198030

45.327660

2200.0

1.029172e+06

0.0

-2635.6660

99720.8520

2011-07-14

2011-11-17

1.031930e+06

2.568702

46.792503

2100.0

1.026536e+06

0.0

5394.2742

98264.2563

2011-12-28

2012-05-09

1.073316e+06

21.781659

52.661020

1900.0

1.031930e+06

0.0

41385.1521

100055.9380

2012-06-25

2012-10-17

1.087343e+06

10.019459

74.650634

1400.0

1.073316e+06

0.0

14027.2426

104510.8876

2013-05-17

2013-06-26

1.078880e+06

-4.701326

57.882798

1800.0

1.087343e+06

0.0

-8462.3868

104189.0364

2013-07-31

2013-10-04

1.086532e+06

4.500835

60.457234

1700.0

1.078880e+06

0.0

7651.4195

102777.2978

2013-10-16

2014-01-28

1.088328e+06

1.122523

67.389473

1600.0

1.086532e+06

0.0

1796.0368

107823.1568

2014-03-11

2014-03-17

1.086547e+06

-1.272298

72.948554

1400.0

1.088328e+06

0.0

-1781.2172

102127.9756

2014-03-24

2014-04-22

1.085120e+06

-1.019203

73.370393

1400.0

1.086547e+06

0.0

-1426.8842

102718.5502

2014-04-25

2014-10-17

1.106169e+06

16.191371

77.826851

1300.0

1.085120e+06

0.0

21048.7823

101174.9063

2014-10-28

2015-01-05

1.106140e+06

-0.028185

102.749105

1000.0

1.106169e+06

0.0

-28.1850

102749.1050

2015-02-05

2015-04-16

1.111582e+06

6.046838

116.413846

900.0

1.106140e+06

0.0

5442.1542

104772.4614

2015-04-28

2015-06-26

1.109035e+06

-3.184117

126.721620

800.0

1.111582e+06

0.0

-2547.2936

101377.2960

2015-10-27

2015-12-18

1.101928e+06

-7.897288

112.152083

900.0

1.109035e+06

0.0

-7107.5592

100936.8747

2016-03-10

2016-05-05

1.093921e+06

-7.278331

100.015950

1100.0

1.101928e+06

0.0

-8006.1641

110017.5450

2016-06-23

2016-06-27

1.089480e+06

-4.038123

95.582210

1100.0

1.093921e+06

0.0

-4441.9353

105140.4310

2016-06-30

2016-07-11

1.090989e+06

1.372569

95.084904

1100.0

1.089480e+06

0.0

1509.8259

104593.3944

2016-07-25

2016-09-01

1.101895e+06

9.914477

96.815526

1100.0

1.090989e+06

0.0

10905.9247

106497.0786

Python

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apple_backtest["End Port. Value"].plot()

我们的财产总额六年增加了10%。考虑到每次交易额只有总额的10%，这个成绩不算差。

同时我们也注意到这个策略并没有引发停止损失委托。这意味着我们可以不需要它么？这个难说。毕竟这个激发事件完全取决于我们的设定值。

停止损失委托是被自动激活的，它并不会考虑股市整体走势。也就是说不论是股市真正的走低还是暂时的波动都会激发停止损失委托。而后者是我们需要注意的因为在现实中，由价格波动激发停止损失委托不仅让你支出一笔交易费用，同时还无法保证最终的卖出价格是你设定的价格。

下面的链接分别支持和反对使用停止损失委托，但是之后的内容我不会要求我们的回溯测试系统使用它。这样可以简化系统，但不是很符合实际(我相信工业系统应该有停止损失委托)。

现实中我们不会只用总额的10%去押一支股票而是投资多种股票。在给定的时间可以跟不同公司同时交易，而且大部分财产应该在股票上，而不是现金。现在我们开始投资多支股票 (原文是stops，感觉是typo，译文按照stocks翻译)，并且在两条移动平均线交叉的时候退市(不使用止损)。我们需要改变回溯测试的代码。我们会用一个pandas的DataFrame来存储所有股票的买卖，上一层的循环也需要记录更多的信息。

下面的函数用于产生买卖订单，以及另一回溯测试函数。

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defma_crossover_orders(stocks,fast,slow):

"""

:param stocks: A list of tuples, the first argument in each tuple being a string containing the ticker symbol of each stock (or however you want the stock represented, so long as it's unique), and the second being a pandas DataFrame containing the stocks, with a "Close" column and indexing by date (like the data frames returned by the Yahoo! Finance API)

:param fast: Integer for the number of days used in the fast moving average

:param slow: Integer for the number of days used in the slow moving average

:return: pandas DataFrame containing stock orders

This function takes a list of stocks and determines when each stock would be bought or sold depending on a moving average crossover strategy, returning a data frame with information about when the stocks in the portfolio are bought or sold according to the strategy

"""

fast_str=str(fast)+'d'

slow_str=str(slow)+'d'

ma_diff_str=fast_str+'-'+slow_str

trades=pd.DataFrame({"Price":[],"Regime":[],"Signal":[]})

fors instocks:

# Get the moving averages, both fast and slow, along with the difference in the moving averages

s[1][fast_str]=np.round(s[1]["Close"].rolling(window=fast,center=False).mean(),2)

s[1][slow_str]=np.round(s[1]["Close"].rolling(window=slow,center=False).mean(),2)

s[1][ma_diff_str]=s[1][fast_str]-s[1][slow_str]

# np.where() is a vectorized if-else function, where a condition is checked for each component of a vector, and the first argument passed is used when the condition holds, and the other passed if it does not

s[1]["Regime"]=np.where(s[1][ma_diff_str]>0,1,0)

# We have 1's for bullish regimes and 0's for everything else. Below I replace bearish regimes's values with -1, and to maintain the rest of the vector, the second argument is apple["Regime"]

s[1]["Regime"]=np.where(s[1][ma_diff_str]<0,-1,s[1]["Regime"])

# To ensure that all trades close out, I temporarily change the regime of the last row to 0

regime_orig=s[1].ix[-1,"Regime"]

s[1].ix[-1,"Regime"]=0

s[1]["Signal"]=np.sign(s[1]["Regime"]-s[1]["Regime"].shift(1))

# Restore original regime data

s[1].ix[-1,"Regime"]=regime_orig

# Get signals

signals=pd.concat([

pd.DataFrame({"Price":s[1].loc[s[1]["Signal"]==1,"Close"],

"Regime":s[1].loc[s[1]["Signal"]==1,"Regime"],

"Signal":"Buy"}),

pd.DataFrame({"Price":s[1].loc[s[1]["Signal"]==-1,"Close"],

"Regime":s[1].loc[s[1]["Signal"]==-1,"Regime"],

"Signal":"Sell"}),

])

signals.index=pd.MultiIndex.from_product([signals.index,[s[0]]],names=["Date","Symbol"])

trades=trades.append(signals)

trades.sort_index(inplace=True)

trades.index=pd.MultiIndex.from_tuples(trades.index,names=["Date","Symbol"])

returntrades

defbacktest(signals,cash,port_value=.1,batch=100):

"""

:param signals: pandas DataFrame containing buy and sell signals with stock prices and symbols, like that returned by ma_crossover_orders

:param cash: integer for starting cash value

:param port_value: maximum proportion of portfolio to risk on any single trade

:param batch: Trading batch sizes

:return: pandas DataFrame with backtesting results

This function backtests strategies, with the signals generated by the strategies being passed in the signals DataFrame. A fictitious portfolio is simulated and the returns generated by this portfolio are reported.

"""

SYMBOL=1# Constant for which element in index represents symbol

portfolio=dict()# Will contain how many stocks are in the portfolio for a given symbol

port_prices=dict()# Tracks old trade prices for determining profits

# Dataframe that will contain backtesting report

results=pd.DataFrame({"Start Cash":[],

"End Cash":[],

"Portfolio Value":[],

"Type":[],

"Shares":[],

"Share Price":[],

"Trade Value":[],

"Profit per Share":[],

"Total Profit":[]})

forindex,row insignals.iterrows():

# These first few lines are done for any trade

shares=portfolio.setdefault(index[SYMBOL],0)

trade_val=0

batches=0

cash_change=row["Price"]*shares# Shares could potentially be a positive or negative number (cash_change will be added in the end; negative shares indicate a short)

portfolio[index[SYMBOL]]=0# For a given symbol, a position is effectively cleared

old_price=port_prices.setdefault(index[SYMBOL],row["Price"])

portfolio_val=0

forkey,val inportfolio.items():

portfolio_val+=val*port_prices[key]

ifrow["Signal"]=="Buy"androw["Regime"]==1:# Entering a long position

batches=np.floor((portfolio_val+cash)*port_value)//np.ceil(batch*row["Price"])# Maximum number of batches of stocks invested in

trade_val=batches*batch*row["Price"]# How much money is put on the line with each trade

cash_change-=trade_val# We are buying shares so cash will go down

portfolio[index[SYMBOL]]=batches*batch# Recording how many shares are currently invested in the stock

port_prices[index[SYMBOL]]=row["Price"]# Record price

old_price=row["Price"]

elifrow["Signal"]=="Sell"androw["Regime"]==-1:# Entering a short

pass

# Do nothing; can we provide a method for shorting the market?

#else:

#raise ValueError("I don't know what to do with signal " + row["Signal"])

pprofit=row["Price"]-old_price# Compute profit per share; old_price is set in such a way that entering a position results in a profit of zero

# Update report

results=results.append(pd.DataFrame({

"Start Cash":cash,

"End Cash":cash+cash_change,

"Portfolio Value":cash+cash_change+portfolio_val+trade_val,

"Type":row["Signal"],

"Shares":batch*batches,

"Share Price":row["Price"],

"Trade Value":abs(cash_change),

"Profit per Share":pprofit,

"Total Profit":batches*batch*pprofit

},index=[index]))

cash+=cash_change# Final change to cash balance

results.sort_index(inplace=True)

results.index=pd.MultiIndex.from_tuples(results.index,names=["Date","Symbol"])

returnresults

# Get more stocks

microsoft=web.DataReader("MSFT","yahoo",start,end)

google=web.DataReader("GOOG","yahoo",start,end)

facebook=web.DataReader("FB","yahoo",start,end)

twitter=web.DataReader("TWTR","yahoo",start,end)

netflix=web.DataReader("NFLX","yahoo",start,end)

amazon=web.DataReader("AMZN","yahoo",start,end)

yahoo=web.DataReader("YHOO","yahoo",start,end)

sony=web.DataReader("SNY","yahoo",start,end)

nintendo=web.DataReader("NTDOY","yahoo",start,end)

ibm=web.DataReader("IBM","yahoo",start,end)

hp=web.DataReader("HPQ","yahoo",start,end)

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signals=ma_crossover_orders([("AAPL",ohlc_adj(apple)),

("MSFT",ohlc_adj(microsoft)),

("GOOG",ohlc_adj(google)),

("FB",ohlc_adj(facebook)),

("TWTR",ohlc_adj(twitter)),

("NFLX",ohlc_adj(netflix)),

("AMZN",ohlc_adj(amazon)),

("YHOO",ohlc_adj(yahoo)),

("SNY",ohlc_adj(yahoo)),

("NTDOY",ohlc_adj(nintendo)),

("IBM",ohlc_adj(ibm)),

("HPQ",ohlc_adj(hp))],

fast=20,slow=50)

signals

PriceRegimeSignal

DateSymbol

2010-03-16AAPL

29.355667

1.0

Buy

AMZN

131.789993

1.0

Buy

GOOG

282.318173

-1.0

Sell

HPQ

20.722316

1.0

Buy

IBM

110.563240

1.0

Buy

MSFT

24.677580

-1.0

Sell

NFLX

10.090000

1.0

Buy

NTDOY

37.099998

1.0

Buy

SNY

16.360001

-1.0

Sell

YHOO

16.360001

-1.0

Sell

2010-03-17SNY

16.500000

1.0

Buy

YHOO

16.500000

1.0

Buy

2010-03-22GOOG

278.472004

1.0

Buy

2010-03-23MSFT

25.106096

1.0

Buy

2010-05-03GOOG

265.035411

-1.0

Sell

2010-05-10HPQ

19.435830

-1.0

Sell

2010-05-14NTDOY

35.799999

-1.0

Sell

2010-05-17SNY

16.270000

-1.0

Sell

YHOO

16.270000

-1.0

Sell

2010-05-19AMZN

124.589996

-1.0

Sell

MSFT

23.835187

-1.0

Sell

2010-05-21IBM

108.322991

-1.0

Sell

2010-06-10AAPL

32.764038

0.0

Sell

2010-06-11AAPL

33.156405

-1.0

Sell

2010-06-18AAPL

35.845436

1.0

Buy

2010-06-28IBM

111.397697

1.0

Buy

2010-07-01IBM

105.861499

-1.0

Sell

2010-07-06IBM

106.630175

1.0

Buy

2010-07-09NTDOY

36.950001

1.0

Buy

2010-07-20IBM

109.298956

-1.0

Sell

……

…

…

…

2016-06-23AAPL

95.582210

1.0

Buy

TWTR

17.040001

1.0

Buy

2016-06-27AAPL

91.544087

-1.0

Sell

FB

108.970001

-1.0

Sell

2016-06-28SNY

36.040001

-1.0

Sell

YHOO

36.040001

-1.0

Sell

2016-06-30AAPL

95.084904

1.0

Buy

NFLX

91.480003

0.0

Sell

2016-07-01NFLX

96.669998

-1.0

Sell

SNY

37.990002

1.0

Buy

YHOO

37.990002

1.0

Buy

2016-07-11AAPL

96.457473

-1.0

Sell

NTDOY

27.700001

1.0

Buy

2016-07-14MSFT

53.407133

1.0

Buy

2016-07-25AAPL

96.815526

1.0

Buy

FB

121.629997

1.0

Buy

2016-07-26GOOG

738.419983

1.0

Buy

2016-08-18NFLX

96.160004

1.0

Buy

2016-09-01AAPL

106.730003

1.0

Sell

2016-09-02AMZN

772.440002

1.0

Sell

FB

126.510002

1.0

Sell

GOOG

771.460022

1.0

Sell

HPQ

14.490000

1.0

Sell

IBM

159.550003

1.0

Sell

MSFT

57.669998

1.0

Sell

NFLX

97.379997

1.0

Sell

NTDOY

28.840000

1.0

Sell

SNY

43.279999

1.0

Sell

TWTR

19.549999

1.0

Sell

YHOO

43.279999

1.0

Sell

475 rows × 3 columns

Python

1

2

bk=backtest(signals,1000000)

bk

End CashPortfolio ValueProfit per ShareShare PriceSharesStart CashTotal ProfitTrade ValueType

DateSymbol

2010-03-16AAPL

9.001907e+05

1.000000e+06

0.000000

29.355667

3400.0

1.000000e+06

0.0

99809.2678

Buy

AMZN

8.079377e+05

1.000000e+06

0.000000

131.789993

700.0

9.001907e+05

0.0

92252.9951

Buy

GOOG

8.079377e+05

1.000000e+06

0.000000

282.318173

0.0

8.079377e+05

0.0

0.0000

Sell

HPQ

7.084706e+05

1.000000e+06

0.000000

20.722316

4800.0

8.079377e+05

0.0

99467.1168

Buy

IBM

6.089637e+05

1.000000e+06

0.000000

110.563240

900.0

7.084706e+05

0.0

99506.9160

Buy

MSFT

6.089637e+05

1.000000e+06

0.000000

24.677580

0.0

6.089637e+05

0.0

0.0000

Sell

NFLX

5.090727e+05

1.000000e+06

0.000000

10.090000

9900.0

6.089637e+05

0.0

99891.0000

Buy

NTDOY

4.126127e+05

1.000000e+06

0.000000

37.099998

2600.0

5.090727e+05

0.0

96459.9948

Buy

SNY

4.126127e+05

1.000000e+06

0.000000

16.360001

0.0

4.126127e+05

0.0

0.0000

Sell

YHOO

4.126127e+05

1.000000e+06

0.000000

16.360001

0.0

4.126127e+05

0.0

0.0000

Sell

2010-03-17SNY

3.136127e+05

1.000000e+06

0.000000

16.500000

6000.0

4.126127e+05

0.0

99000.0000

Buy

YHOO

2.146127e+05

1.000000e+06

0.000000

16.500000

6000.0

3.136127e+05

0.0

99000.0000

Buy

2010-03-22GOOG

1.310711e+05

1.000000e+06

0.000000

278.472004

300.0

2.146127e+05

0.0

83541.6012

Buy

2010-03-23MSFT

3.315733e+04

1.000000e+06

0.000000

25.106096

3900.0

1.310711e+05

0.0

97913.7744

Buy

2010-05-03GOOG

1.126680e+05

9.959690e+05

-13.436593

265.035411

0.0

3.315733e+04

-0.0

79510.6233

Sell

2010-05-10HPQ

2.059599e+05

9.897939e+05

-1.286486

19.435830

0.0

1.126680e+05

-0.0

93291.9840

Sell

2010-05-14NTDOY

2.990399e+05

9.864139e+05

-1.299999

35.799999

0.0

2.059599e+05

-0.0

93079.9974

Sell

2010-05-17SNY

3.966599e+05

9.850339e+05

-0.230000

16.270000

0.0

2.990399e+05

-0.0

97620.0000

Sell

YHOO

4.942799e+05

9.836539e+05

-0.230000

16.270000

0.0

3.966599e+05

-0.0

97620.0000

Sell

2010-05-19AMZN

5.814929e+05

9.786139e+05

-7.199997

124.589996

0.0

4.942799e+05

-0.0

87212.9972

Sell

MSFT

6.744502e+05

9.736573e+05

-1.270909

23.835187

0.0

5.814929e+05

-0.0

92957.2293

Sell

2010-05-21IBM

7.719409e+05

9.716411e+05

-2.240249

108.322991

0.0

6.744502e+05

-0.0

97490.6919

Sell

2010-06-10AAPL

8.833386e+05

9.832296e+05

3.408371

32.764038

0.0

7.719409e+05

0.0

111397.7292

Sell

2010-06-11AAPL

8.833386e+05

9.832296e+05

3.800738

33.156405

0.0

8.833386e+05

0.0

0.0000

Sell

2010-06-18AAPL

7.865559e+05

9.832296e+05

0.000000

35.845436

2700.0

8.833386e+05

0.0

96782.6772

Buy

2010-06-28IBM

6.974378e+05

9.832296e+05

0.000000

111.397697

800.0

7.865559e+05

0.0

89118.1576

Buy

2010-07-01IBM

7.821270e+05

9.788006e+05

-5.536198

105.861499

0.0

6.974378e+05

-0.0

84689.1992

Sell

2010-07-06IBM

6.861598e+05

9.788006e+05

0.000000

106.630175

900.0

7.821270e+05

0.0

95967.1575

Buy

2010-07-09NTDOY

5.900898e+05

9.788006e+05

0.000000

36.950001

2600.0

6.861598e+05

0.0

96070.0026

Buy

2010-07-20IBM

6.884589e+05

9.812025e+05

2.668781

109.298956

0.0

5.900898e+05

0.0

98369.0604

Sell

……

…

…

…

…

…

…

…

…

…

2016-06-23AAPL

3.951693e+05

1.863808e+06

0.000000

95.582210

1900.0

5.767755e+05

0.0

181606.1990

Buy

TWTR

2.094333e+05

1.863808e+06

0.000000

17.040001

10900.0

3.951693e+05

0.0

185736.0109

Buy

2016-06-27AAPL

3.833670e+05

1.856135e+06

-4.038123

91.544087

0.0

2.094333e+05

-0.0

173933.7653

Sell

FB

5.795130e+05

1.862921e+06

3.770004

108.970001

0.0

3.833670e+05

0.0

196146.0018

Sell

2016-06-28SNY

7.885450e+05

1.880959e+06

3.110001

36.040001

0.0

5.795130e+05

0.0

209032.0058

Sell

YHOO

9.975770e+05

1.898997e+06

3.110001

36.040001

0.0

7.885450e+05

0.0

209032.0058

Sell

2016-06-30AAPL

8.169157e+05

1.898997e+06

0.000000

95.084904

1900.0

9.975770e+05

0.0

180661.3176

Buy

NFLX

9.907277e+05

1.893981e+06

-2.640000

91.480003

0.0

8.169157e+05

-0.0

173812.0057

Sell

2016-07-01NFLX

9.907277e+05

1.893981e+06

2.549995

96.669998

0.0

9.907277e+05

0.0

0.0000

Sell

SNY

8.045767e+05

1.893981e+06

0.000000

37.990002

4900.0

9.907277e+05

0.0

186151.0098

Buy

YHOO

6.184257e+05

1.893981e+06

0.000000

37.990002

4900.0

8.045767e+05

0.0

186151.0098

Buy

2016-07-11AAPL

8.016949e+05

1.896589e+06

1.372569

96.457473

0.0

6.184257e+05

0.0

183269.1987

Sell

NTDOY

6.133349e+05

1.896589e+06

0.000000

27.700001

6800.0

8.016949e+05

0.0

188360.0068

Buy

2016-07-14MSFT

4.264099e+05

1.896589e+06

0.000000

53.407133

3500.0

6.133349e+05

0.0

186924.9655

Buy

2016-07-25AAPL

2.424604e+05

1.896589e+06

0.000000

96.815526

1900.0

4.264099e+05

0.0

183949.4994

Buy

FB

6.001543e+04

1.896589e+06

0.000000

121.629997

1500.0

2.424604e+05

0.0

182444.9955

Buy

2016-07-26GOOG

-8.766857e+04

1.896589e+06

0.000000

738.419983

200.0

6.001543e+04

0.0

147683.9966

Buy

2016-08-18NFLX

-2.703726e+05

1.896589e+06

0.000000

96.160004

1900.0

-8.766857e+04

0.0

182704.0076

Buy

2016-09-01AAPL

-6.758557e+04

1.915427e+06

9.914477

106.730003

0.0

-2.703726e+05

0.0

202787.0057

Sell

2016-09-02AMZN

1.641464e+05

1.979327e+06

213.000000

772.440002

0.0

-6.758557e+04

0.0

231732.0006

Sell

FB

3.539114e+05

1.986647e+06

4.880005

126.510002

0.0

1.641464e+05

0.0

189765.0030

Sell

GOOG

5.082034e+05

1.993255e+06

33.040039

771.460022

0.0

3.539114e+05

0.0

154292.0044

Sell

HPQ

7.081654e+05

2.006030e+06

0.925746

14.490000

0.0

5.082034e+05

0.0

199962.0000

Sell

IBM

8.996254e+05

2.015652e+06

8.018727

159.550003

0.0

7.081654e+05

0.0

191460.0036

Sell

MSFT

1.101470e+06

2.030572e+06

4.262865

57.669998

0.0

8.996254e+05

0.0

201844.9930

Sell

NFLX

1.286492e+06

2.032890e+06

1.219993

97.379997

0.0

1.101470e+06

0.0

185021.9943

Sell

NTDOY

1.482604e+06

2.040642e+06

1.139999

28.840000

0.0

1.286492e+06

0.0

196112.0000

Sell

SNY

1.694676e+06

2.066563e+06

5.289997

43.279999

0.0

1.482604e+06

0.0

212071.9951

Sell

TWTR

1.907771e+06

2.093922e+06

2.509998

19.549999

0.0

1.694676e+06

0.0

213094.9891

Sell

YHOO

2.119843e+06

2.119843e+06

5.289997

43.279999

0.0

1.907771e+06

0.0

212071.9951

Sell

475 rows × 9 columns

Python

1

bk["Portfolio Value"].groupby(level=0).apply(lambdax:x[-1]).plot()

更为现实的投资组合可以投资任何12支股票而达到100%的收益。这个看上去不错，但是我们可以做得更好。

基准分析法

基准分析法可以分析交易策略效率的好坏。所谓基准分析，就是将策略和其他(著名)策略进行比较从而评价该策略的表现好坏。

每次你评价交易系统的时候，都要跟买入持有策略(SPY)进行比较。除了一些信托基金和少数投资经理没有使用它，该策略在大多时候都是无敌的。有效市场假说强调没有人能战胜股票市场，所以每个人都应该购入指数基金，因为它能反应整个市场的构成。SPY是一个交易型开放式指数基金(一种可以像股票一样交易的信托基金)，它的价格有效反映了S&P 500中的股票价格。买入并持有SPY，说明你可以有效地匹配市场回报率而不是战胜它。

下面是SPY的数据，让我们看看简单买入持有SPY能得到的回报：

Python

1

2

spyder=web.DataReader("SPY","yahoo",start,end)

spyder.iloc[[0,-1],:]

OpenHighLowCloseVolumeAdj Close

Date

2010-01-04

112.370003

113.389999

111.510002

113.330002

118944600

99.292299

2016-09-01

217.369995

217.729996

216.029999

217.389999

93859000

217.389999

Python

1

2

3

4

batches=1000000//np.ceil(100*spyder.ix[0,"Adj Close"])# Maximum number of batches of stocks invested in

trade_val=batches*batch*spyder.ix[0,"Adj Close"]# How much money is used to buy SPY

final_val=batches*batch*spyder.ix[-1,"Adj Close"]+(1000000-trade_val)# Final value of the portfolio

final_val

Python

1

2180977.0

Python

1

2

3

4

5

# We see that the buy-and-hold strategy beats the strategy we developed earlier. I would also like to see a plot.

ax_bench=(spyder["Adj Close"]/spyder.ix[0,"Adj Close"]).plot(label="SPY")

ax_bench=(bk["Portfolio Value"].groupby(level=0).apply(lambdax:x[-1])/1000000).plot(ax=ax_bench,label="Portfolio")

ax_bench.legend(ax_bench.get_lines(),[l.get_label()forl inax_bench.get_lines()],loc='best')

ax_bench

买入持有SPY比我们当前的交易系统好——我们的系统还没有考虑不菲的交易费用。考虑到机会成本和该策略的消耗，我们不应该用它。

怎样才能改进我们的系统呢？对于初学者来尽量多样化是一个选择。目前我们所有的股票都来自技术公司，这意味着技术型公司的不景气会反映在我们的投资组合上。我们应该设计一个可以利用空头头寸和熊市的系统，这样不管市场如何变动，我们都可以盈利。我们也可以寻求更好的方法预测股票的最高期望价格。但是不论如何我们都需要做得比SPY更好，不然由于我们的系统会自带机会成本，是没用的。

其他的基准策略也是存在的。如果我们的系统比“买入持有SPY”更好，我们可以进一步跟其他的系统比较，例如：

(我最初在这里接触到这些策略)基本准则仍然是：不要使用一个复杂的，包含大量交易的系统如果它赢不了一个简单的交易不频繁的指数基金模型。(事实上这个标准挺难实现的)

最后要强调的是，假设你的交易系统在回溯测试中打败了所有的基准系统，也不意味着它能够准确地预测未来。因为回溯测试容易过拟合，它不能用于预测未来。

结论

虽然讲座最后的结论不是那么乐观，但记住有效市场理论也有缺陷。我个人的观点是当交易更多依赖于算法的时候，就更难战胜市场。有一个说法是：信托基金都不太可能战胜市场，你的系统能战胜市场仅仅是一个可能性而已。(当然信托基金表现很差的原因是收费太高，而指数基金不存在这个问题。)

本讲座只简单地说明了一种基于移动平均的交易策略。还有许多别的交易策略这里并没有提到。而且我们也没有深入探讨空头股票和货币交易。特别是股票期权有很多东西可以讲，它也提供了不同的方法来预测股票的走向。你可以在Derivatives Analytics with Python: Data Analysis, Models, Simulation, Calibration and Hedging书中读到更多的相关内容。(犹他大学的图书馆有这本书)

另一个资源是O’Reilly出的Python for Finance，犹他大学的图书馆里也有。

记住在股票里面亏钱是很正常的，同样股市也能提供其他方法无法提供的高回报，每一个投资策略都应该是经过深思熟虑的。这个讲座旨在抛砖引玉，希望同学们自己进一步探讨这个话题。

作业

问题1

建立一个基于移动平均的交易系统(不需要止损条件)。选择15支2010年1月1日之前上市的股票，利用回溯测试检验你的 系统，并且SPY基准作比较，你的系统能战胜市场吗？

问题2

在现实中每一笔交易都要支付一笔佣金。弄明白如何计算佣金，然后修改你的backtes()函数，使之能够计算不同的佣金模式(固定费用，按比例收费等等)。

我们现在的移动平均交汇点分析系统在两条平均线交叉的时候触发交易。修改系统令其更准确：

当你完成修改之后，重复问题1，使用一个真实的佣金策略(从交易所查)来模拟你的系统，同时要求移动平均差异达到一定的移动标准差再激发交易。

问题3

我们的交易系统无法处理空头股票。空头买卖的复杂性在于损失是没有下限的(多头头寸的最大损失等于购入股票的总价格)。学习如何处理空头头寸，然后修改backtest()使其能够处理空头交易。思考要如何实现空头交易，包括允许多少空头交易？在进行其他交易的时候如何处理空头交易？提示：空头交易的量在函数中可以用一个负数来表示。

完成之后重复问题1，也可以同时考虑问题2中提到的因素。