Reading6. The Time Value of Money

本文深入探讨了货币的时间价值概念及其对财务管理的重要性,并详细解释了利率的不同解释方式及组成部分,包括实际无风险利率、通货膨胀溢价等。此外,还介绍了单利与复利的区别,以及如何计算现值与未来值。

6.1 利率

6.1.1 货币的时间价值

The cash flow additivity principle refers to the fact that present value of any stream of cash flows equals the sum of the present values of the cash flows.

additivity: 添加;相加性

refer to: 参考;涉及;指的是;适用于

stream: 流

6.1.2 利率的三种解释方式

一、要求回报率(Required Rate of Return)

二、折现率(Discounted Rate)

三、机会成本(Opportunity Cost)

6.1.3 利率的组成

利 率 ( r e q u i r e d   i n t e r e s t   r a t e   o n   a   s e c u r i t y ) = 实 际 无 风 险 利 率 ( r e a l   r i s k − f r e e   r a t e ) + 预 期 通 货 膨 胀 率 ( e x p e c t e d   i n f l a t i o n   r a t e ) + 违 约 风 险 溢 价 ( d e f a u l t   r i s k   p r e m i u m ) + 流 动 性 风 险 溢 价 ( l i q u i d i t y   r i s k   p r e m i u m ) + 期 限 风 险 溢 价 ( m a t u r i t y   r i s k   p r e m i u m ) 利率(required \ interest \ rate \ on \ a \ security) = 实际无风险利率(real \ risk-free \ rate) + 预期通货膨胀率(expected \ inflation \ rate) + 违约风险溢价(default \ risk \ premium) + 流动性风险溢价(liquidity \ risk \ premium) + 期限风险溢价(maturity \ risk \ premium) (required interest rate on a security)=(real riskfree rate)+(expected inflation rate)+(default risk premium)+(liquidity risk premium)+(maturity risk premium)

security: 证券;抵押品

inflation: 膨胀;通货膨胀;

一、实际无风险利率(Real Risk-Free Interest Rate)

二、通货膨胀溢价(Inflation Premium)

在银行查到的利率都是名义利率。
名 义 利 率 ( n o m i n a l   r i s k − f r e e   r a t e ) ≈ 实 际 利 率 ( r e a l   r i s k − f r e e   r a t e ) + 预 期 通 货 膨 胀 率 ( e x p e c t e d   i n f l a t i o n   r a t e ) 名义利率(nominal \ risk-free \ rate) \approx 实际利率(real \ risk-free \ rate) + 预期通货膨胀率(expected \ inflation \ rate) (nominal riskfree rate)(real riskfree rate)+(expected inflation rate)

三、违约风险溢价(Default Risk Premium)

四、流动性风险溢价(Liquidity Premium)

五、期限风险溢价(Maturity Premium)

六、注意

  • Differences between real and nominal interest rate: whether inflation rate is added
  • Differences between risk-free and risky rate: whether risk premium is added

6.1.4 不同计息方式的利率

一、单利与复利(Single Interest vs Compound interest or Interest on interest)

二、报价利率与有效年利率

  1. 报价利率

  2. 有效年利率(Effective Annual Rate or Effective Annual Yield)
    E A R = ( 1 + p e r i o d i c   r a t e ) m – 1 p e r i o d i c   ( e f f e c t i v e )   r a t e = s t a t e d   a n n u a l   r a t e / m m = t h e   n u m b e r   o f   c o m p o u n d i n g   p e r i o d s   p e r   y e a r EAR = (1 + periodic \ rate)^m – 1 \\ periodic \ (effective) \ rate = stated \ annual \ rate/m \\ m = the \ number \ of \ compounding \ periods \ per \ year EAR=(1+periodic rate)m1periodic (effective) rate=stated annual rate/mm=the number of compounding periods per year

periodic rate: 周期性利率

stated annual rate: 名义年利率

6.2 现值(Present value)与未来值(Future value)

6.2.1 现值与未来值的关系

F V = P V ∗ ( 1 + I / Y ) N P V = a m o u n t   o f   m o n e y   i n v e s t e d   t o d a y   ( t h e   p r e s e n t   v a l u e ) I / Y = r a t e   o f   r e t u r n   p e r   c o m p o u n d i n g   p e r i o d N = t o t a l   n u m b e r   o f   c o m p o u n d i n g   p e r i o d s FV = PV * (1 + I/Y)^N \\ PV = amount \ of \ money \ invested \ today \ (the \ present \ value) \\ I/Y = rate \ of \ return \ per \ compounding \ period \\ N = total \ number \ of \ compounding \ periods \\ FV=PV(1+I/Y)NPV=amount of money invested today (the present value)I/Y=rate of return per compounding periodN=total number of compounding periods

P V = F V ∗ [ 1 ( 1 + I / Y ) N ] = F V ( 1 + I / Y ) N F V = a m o u n t   o f   m o n e y   i n   t h e   f u t u r e   ( t h e   f u t u r e   v a l u e ) I / Y = r a t e   o f   r e t u r n   p e r   c o m p o u n d i n g   p e r i o d N = t o t a l   n u m b e r   o f   c o m p o u n d i n g   p e r i o d s PV = FV * [\frac{1}{(1 + I/Y)^N}] = \frac{FV}{(1 + I/Y)^N} \\ FV = amount \ of \ money \ in \ the \ future \ (the \ future \ value) \\ I/Y = rate \ of \ return \ per \ compounding \ period \\ N = total \ number \ of \ compounding \ periods PV=FV[(1+I/Y)N1]=(1+I/Y)NFVFV=amount of money in the future (the future value)I/Y=rate of return per compounding periodN=total number of compounding periods

  • For a given discount rate, the farther in the future the amount to be received, the smaller that amount’s present value.
  • Holding time constant, the larger the discount rate, the smaller the present value of a future amount.
  • The stated rate and the actual (effective) rate of interest are equal only when interest is compounded annually.
  • The greater the compounding frequency, the greater the EAR will be in comparison to the stated rate.

When continuous compounding, for a single cash flow:
F V = P V ∗ e r s N r s : t h e   ( n o m i n a l )   c o n t i n u o u s   c o m p o u n d i n g   i n t e r e s t   r a t e FV = PV * e^{r_sN} \\ r_s: the \ (nominal) \ continuous \ compounding \ interest \ rate FV=PVersNrs:the (nominal) continuous compounding interest rate

E A R = e r s − 1 EAR = e^{r_s} - 1 EAR=ers1

frequency: 频率;频繁

comparison: 比较;对照;

continuous: 连续的,持续的;继续的;连绵不断的

6.2.2 年金

  • An annuity is a stream of equal cash flows that occurs at equal intervals over a given period.

annuity: 年金

interval: 间隔;间距;

一、普通年金(Ordinary Annuity)

  • ordinary annuities: cash flows occur at the end of each compounding period.

二、先付年金(Annuity Due)

  • annuities due: payments or receipts occur at the beginning of each period.
  • With an annuity due, there is one less discounting period since the first cash flow occurs at t = 0 and thus is already its PV.
  • This implies that, all else equal, the PV of an annuity due will be greater than the PV of an ordinary annuity.
  • Two ways to find annuities due:
    • put the calculator in the BGN mode and then input all the relevant variables;
    • multiply the resulting PV by [1 + periodic compounding rate (I/Y)] - This is the same for FV of Annuities Due.

receipts: (企业、银行等)收到的款,进款;收到( receipt的名词复数 );收入;收据;收条

imply: 意味;暗示;隐含

relevant: 相关的;切题的;中肯的;有重大关系的;有意义的,目的明确的

variables: [数] 变量

multiply: 乘

三、延期年金(Deferred Annuity)

  • deferred annuity: payments or receipts start in the future period.

四、永续年金(Perpetuity Annuity)

  • perpetuity: a perpetual annuity, or a set of level never-ending sequential cash flows, with the first cash flow occurring one period from now (year end).
    P V p e r p e t u i t y = P M T I / Y PV_{perpetuity} = \frac{PMT}{I/Y} PVperpetuity=I/YPMT

sequential: 连续的;相继的;有顺序的

五、不规则现金流的现值与未来值

  • unequal cash flows: To evaluate a cash flow stream that is not equal from period to period - FV
  • unequal cash flows: To evaluate a cash flow stream that is not equal from period to period - PV
Quickstart Note The data files used in the quickstart guide are updated from time to time, which means that the adjusted close changes and with it the close (and the other components). That means that the actual output may be different to what was put in the documentation at the time of writing. Using the platform Let’s run through a series of examples (from almost an empty one to a fully fledged strategy) but not without before roughly explaining 2 basic concepts when working with backtrader Lines Data Feeds, Indicators and Strategies have lines. A line is a succession of points that when joined together form this line. When talking about the markets, a Data Feed has usually the following set of points per day: Open, High, Low, Close, Volume, OpenInterest The series of “Open”s along time is a Line. And therefore a Data Feed has usually 6 lines. If we also consider “DateTime” (which is the actual reference for a single point), we could count 7 lines. Index 0 Approach When accessing the values in a line, the current value is accessed with index: 0 And the “last” output value is accessed with -1. This in line with Python conventions for iterables (and a line can be iterated and is therefore an iterable) where index -1 is used to access the “last” item of the iterable/array. In our case is the last output value what’s getting accessed. As such and being index 0 right after -1, it is used to access the current moment in line. With that in mind and if we imagine a Strategy featuring a Simple Moving average created during initialization: self.sma = SimpleMovingAverage(.....) The easiest and simplest way to access the current value of this moving average: av = self.sma[0] There is no need to know how many bars/minutes/days/months have been processed, because “0” uniquely identifies the current instant. Following pythonic tradition, the “last” output value is accessed using -1: previous_value = self.sma[-1] Of course earlier output values can be accessed with -2, -3, … From 0 to 100: the samples Basic Setup Let’s get running. from __future__ import (absolute_import, division, print_function, unicode_literals) import backtrader as bt if __name__ == '__main__': cerebro = bt.Cerebro() print('Starting Portfolio Value: %.2f' % cerebro.broker.getvalue()) cerebro.run() print('Final Portfolio Value: %.2f' % cerebro.broker.getvalue()) After the execution the output is: Starting Portfolio Value: 10000.00 Final Portfolio Value: 10000.00 In this example: backtrader was imported The Cerebro engine was instantiated The resulting cerebro instance was told to run (loop over data) And the resulting outcome was printed out Although it doesn’t seem much, let’s point out something explicitly shown: The Cerebro engine has created a broker instance in the background The instance already has some cash to start with This behind the scenes broker instantiation is a constant trait in the platform to simplify the life of the user. If no broker is set by the user, a default one is put in place. And 10K monetary units is a usual value with some brokers to begin with. Setting the Cash In the world of finance, for sure only “losers” start with 10k. Let’s change the cash and run the example again. from __future__ import (absolute_import, division, print_function, unicode_literals) import backtrader as bt if __name__ == '__main__': cerebro = bt.Cerebro() cerebro.broker.setcash(100000.0) print('Starting Portfolio Value: %.2f' % cerebro.broker.getvalue()) cerebro.run() print('Final Portfolio Value: %.2f' % cerebro.broker.getvalue()) After the execution the output is: Starting Portfolio Value: 1000000.00 Final Portfolio Value: 1000000.00 Mission accomplished. Let’s move to tempestuous waters. Adding a Data Feed Having cash is fun, but the purpose behind all this is to let an automated strategy multiply the cash without moving a finger by operating on an asset which we see as a Data Feed Ergo … No Data Feed -> No Fun. Let’s add one to the ever growing example. from __future__ import (absolute_import, division, print_function, unicode_literals) import datetime # For datetime objects import os.path # To manage paths import sys # To find out the script name (in argv[0]) # Import the backtrader platform import backtrader as bt if __name__ == '__main__': # Create a cerebro entity cerebro = bt.Cerebro() # Datas are in a subfolder of the samples. Need to find where the script is # because it could have been called from anywhere modpath = os.path.dirname(os.path.abspath(sys.argv[0])) datapath = os.path.join(modpath, '../../datas/orcl-1995-2014.txt') # Create a Data Feed data = bt.feeds.YahooFinanceCSVData( dataname=datapath, # Do not pass values before this date fromdate=datetime.datetime(2000, 1, 1), # Do not pass values after this date todate=datetime.datetime(2000, 12, 31), reverse=False) # Add the Data Feed to Cerebro cerebro.adddata(data) # Set our desired cash start cerebro.broker.setcash(100000.0) # Print out the starting conditions print('Starting Portfolio Value: %.2f' % cerebro.broker.getvalue()) # Run over everything cerebro.run() # Print out the final result print('Final Portfolio Value: %.2f' % cerebro.broker.getvalue()) After the execution the output is: Starting Portfolio Value: 1000000.00 Final Portfolio Value: 1000000.00 The amount of boilerplate has grown slightly, because we added: Finding out where our example script is to be able to locate the sample Data Feed file Having datetime objects to filter on which data from the Data Feed we will be operating Aside from that, the Data Feed is created and added to cerebro. The output has not changed and it would be a miracle if it had. Note Yahoo Online sends the CSV data in date descending order, which is not the standard convention. The reversed=True prameter takes into account that the CSV data in the file has already been reversed and has the standard expected date ascending order. Our First Strategy The cash is in the broker and the Data Feed is there. It seems like risky business is just around the corner. Let’s put a Strategy into the equation and print the “Close” price of each day (bar). DataSeries (the underlying class in Data Feeds) objects have aliases to access the well known OHLC (Open High Low Close) daily values. This should ease up the creation of our printing logic. from __future__ import (absolute_import, division, print_function, unicode_literals) import datetime # For datetime objects import os.path # To manage paths import sys # To find out the script name (in argv[0]) # Import the backtrader platform import backtrader as bt # Create a Stratey class TestStrategy(bt.Strategy): def log(self, txt, dt=None): ''' Logging function for this strategy''' dt = dt or self.datas[0].datetime.date(0) print('%s, %s' % (dt.isoformat(), txt)) def __init__(self): # Keep a reference to the "close" line in the data[0] dataseries self.dataclose = self.datas[0].close def next(self): # Simply log the closing price of the series from the reference self.log('Close, %.2f' % self.dataclose[0]) if __name__ == '__main__': # Create a cerebro entity cerebro = bt.Cerebro() # Add a strategy cerebro.addstrategy(TestStrategy) # Datas are in a subfolder of the samples. Need to find where the script is # because it could have been called from anywhere modpath = os.path.dirname(os.path.abspath(sys.argv[0])) datapath = os.path.join(modpath, '../../datas/orcl-1995-2014.txt') # Create a Data Feed data = bt.feeds.YahooFinanceCSVData( dataname=datapath, # Do not pass values before this date fromdate=datetime.datetime(2000, 1, 1), # Do not pass values before this date todate=datetime.datetime(2000, 12, 31), # Do not pass values after this date reverse=False) # Add the Data Feed to Cerebro cerebro.adddata(data) # Set our desired cash start cerebro.broker.setcash(100000.0) # Print out the starting conditions print('Starting Portfolio Value: %.2f' % cerebro.broker.getvalue()) # Run over everything cerebro.run() # Print out the final result print('Final Portfolio Value: %.2f' % cerebro.broker.getvalue()) After the execution the output is: Starting Portfolio Value: 100000.00 2000-01-03T00:00:00, Close, 27.85 2000-01-04T00:00:00, Close, 25.39 2000-01-05T00:00:00, Close, 24.05 ... ... ... 2000-12-26T00:00:00, Close, 29.17 2000-12-27T00:00:00, Close, 28.94 2000-12-28T00:00:00, Close, 29.29 2000-12-29T00:00:00, Close, 27.41 Final Portfolio Value: 100000.00 Someone said the stockmarket was risky business, but it doesn’t seem so. Let’s explain some of the magic: Upon init being called the strategy already has a list of datas that are present in the platform This is a standard Python list and datas can be accessed in the order they were inserted. The first data in the list self.datas[0] is the default data for trading operations and to keep all strategy elements synchronized (it’s the system clock) self.dataclose = self.datas[0].close keeps a reference to the close line. Only one level of indirection is later needed to access the close values. The strategy next method will be called on each bar of the system clock (self.datas[0]). This is true until other things come into play like indicators, which need some bars to start producing an output. More on that later. Adding some Logic to the Strategy Let’s try some crazy idea we had by looking at some charts If the price has been falling 3 sessions in a row … BUY BUY BUY!!! from __future__ import (absolute_import, division, print_function, unicode_literals) import datetime # For datetime objects import os.path # To manage paths import sys # To find out the script name (in argv[0]) # Import the backtrader platform import backtrader as bt # Create a Stratey class TestStrategy(bt.Strategy): def log(self, txt, dt=None): ''' Logging function fot this strategy''' dt = dt or self.datas[0].datetime.date(0) print('%s, %s' % (dt.isoformat(), txt)) def __init__(self): # Keep a reference to the "close" line in the data[0] dataseries self.dataclose = self.datas[0].close def next(self): # Simply log the closing price of the series from the reference self.log('Close, %.2f' % self.dataclose[0]) if self.dataclose[0] < self.dataclose[-1]: # current close less than previous close if self.dataclose[-1] < self.dataclose[-2]: # previous close less than the previous close # BUY, BUY, BUY!!! (with all possible default parameters) self.log('BUY CREATE, %.2f' % self.dataclose[0]) self.buy() if __name__ == '__main__': # Create a cerebro entity cerebro = bt.Cerebro() # Add a strategy cerebro.addstrategy(TestStrategy) # Datas are in a subfolder of the samples. Need to find where the script is # because it could have been called from anywhere modpath = os.path.dirname(os.path.abspath(sys.argv[0])) datapath = os.path.join(modpath, '../../datas/orcl-1995-2014.txt') # Create a Data Feed data = bt.feeds.YahooFinanceCSVData( dataname=datapath, # Do not pass values before this date fromdate=datetime.datetime(2000, 1, 1), # Do not pass values before this date todate=datetime.datetime(2000, 12, 31), # Do not pass values after this date reverse=False) # Add the Data Feed to Cerebro cerebro.adddata(data) # Set our desired cash start cerebro.broker.setcash(100000.0) # Print out the starting conditions print('Starting Portfolio Value: %.2f' % cerebro.broker.getvalue()) # Run over everything cerebro.run() # Print out the final result print('Final Portfolio Value: %.2f' % cerebro.broker.getvalue()) After the execution the output is: Starting Portfolio Value: 100000.00 2000-01-03, Close, 27.85 2000-01-04, Close, 25.39 2000-01-05, Close, 24.05 2000-01-05, BUY CREATE, 24.05 2000-01-06, Close, 22.63 2000-01-06, BUY CREATE, 22.63 2000-01-07, Close, 24.37 ... ... ... 2000-12-20, BUY CREATE, 26.88 2000-12-21, Close, 27.82 2000-12-22, Close, 30.06 2000-12-26, Close, 29.17 2000-12-27, Close, 28.94 2000-12-27, BUY CREATE, 28.94 2000-12-28, Close, 29.29 2000-12-29, Close, 27.41 Final Portfolio Value: 99725.08 Several “BUY” creation orders were issued, our porftolio value was decremented. A couple of important things are clearly missing. The order was created but it is unknown if it was executed, when and at what price. The next example will build upon that by listening to notifications of order status. The curious reader may ask how many shares are being bought, what asset is being bought and how are orders being executed. Where possible (and in this case it is) the platform fills in the gaps: self.datas[0] (the main data aka system clock) is the target asset if no other one is specified The stake is provided behind the scenes by a position sizer which uses a fixed stake, being the default “1. It will be modified in a later example The order is executed “At Market”. The broker (shown in previous examples) executes this using the opening price of the next bar, because that’s the 1st tick after the current under examination bar. The order is executed so far without any commission (more on that later) Do not only buy … but SELL After knowing how to enter the market (long), an “exit concept” is needed and also understanding whether the strategy is in the market. Luckily a Strategy object offers access to a position attribute for the default data feed Methods buy and sell return the created (not yet executed) order Changes in orders’ status will be notified to the strategy via a notify method The “exit concept” will be an easy one: Exit after 5 bars (on the 6th bar) have elapsed for good or for worse Please notice that there is no “time” or “timeframe” implied: number of bars. The bars can represent 1 minute, 1 hour, 1 day, 1 week or any other time period. Although we know the data source is a daily one, the strategy makes no assumption about that. Additionally and to simplify: Do only allow a Buy order if not yet in the market Note The next method gets no “bar index” passed and therefore it seems obscure how to understand when 5 bars may have elapsed, but this has been modeled in pythonic way: call len on an object and it will tell you the length of its lines. Just write down (save in a variable) at which length in an operation took place and see if the current length is 5 bars away. from __future__ import (absolute_import, division, print_function, unicode_literals) import datetime # For datetime objects import os.path # To manage paths import sys # To find out the script name (in argv[0]) # Import the backtrader platform import backtrader as bt # Create a Stratey class TestStrategy(bt.Strategy): def log(self, txt, dt=None): ''' Logging function fot this strategy''' dt = dt or self.datas[0].datetime.date(0) print('%s, %s' % (dt.isoformat(), txt)) def __init__(self): # Keep a reference to the "close" line in the data[0] dataseries self.dataclose = self.datas[0].close # To keep track of pending orders self.order = None def notify_order(self, order): if order.status in [order.Submitted, order.Accepted]: # Buy/Sell order submitted/accepted to/by broker - Nothing to do return # Check if an order has been completed # Attention: broker could reject order if not enough cash if order.status in [order.Completed]: if order.isbuy(): self.log('BUY EXECUTED, %.2f' % order.executed.price) elif order.issell(): self.log('SELL EXECUTED, %.2f' % order.executed.price) self.bar_executed = len(self) elif order.status in [order.Canceled, order.Margin, order.Rejected]: self.log('Order Canceled/Margin/Rejected') # Write down: no pending order self.order = None def next(self): # Simply log the closing price of the series from the reference self.log('Close, %.2f' % self.dataclose[0]) # Check if an order is pending ... if yes, we cannot send a 2nd one if self.order: return # Check if we are in the market if not self.position: # Not yet ... we MIGHT BUY if ... if self.dataclose[0] < self.dataclose[-1]: # current close less than previous close if self.dataclose[-1] < self.dataclose[-2]: # previous close less than the previous close # BUY, BUY, BUY!!! (with default parameters) self.log('BUY CREATE, %.2f' % self.dataclose[0]) # Keep track of the created order to avoid a 2nd order self.order = self.buy() else: # Already in the market ... we might sell if len(self) >= (self.bar_executed + 5): # SELL, SELL, SELL!!! (with all possible default parameters) self.log('SELL CREATE, %.2f' % self.dataclose[0]) # Keep track of the created order to avoid a 2nd order self.order = self.sell() if __name__ == '__main__': # Create a cerebro entity cerebro = bt.Cerebro() # Add a strategy cerebro.addstrategy(TestStrategy) # Datas are in a subfolder of the samples. Need to find where the script is # because it could have been called from anywhere modpath = os.path.dirname(os.path.abspath(sys.argv[0])) datapath = os.path.join(modpath, '../../datas/orcl-1995-2014.txt') # Create a Data Feed data = bt.feeds.YahooFinanceCSVData( dataname=datapath, # Do not pass values before this date fromdate=datetime.datetime(2000, 1, 1), # Do not pass values before this date todate=datetime.datetime(2000, 12, 31), # Do not pass values after this date reverse=False) # Add the Data Feed to Cerebro cerebro.adddata(data) # Set our desired cash start cerebro.broker.setcash(100000.0) # Print out the starting conditions print('Starting Portfolio Value: %.2f' % cerebro.broker.getvalue()) # Run over everything cerebro.run() # Print out the final result print('Final Portfolio Value: %.2f' % cerebro.broker.getvalue()) After the execution the output is: Starting Portfolio Value: 100000.00 2000-01-03T00:00:00, Close, 27.85 2000-01-04T00:00:00, Close, 25.39 2000-01-05T00:00:00, Close, 24.05 2000-01-05T00:00:00, BUY CREATE, 24.05 2000-01-06T00:00:00, BUY EXECUTED, 23.61 2000-01-06T00:00:00, Close, 22.63 2000-01-07T00:00:00, Close, 24.37 2000-01-10T00:00:00, Close, 27.29 2000-01-11T00:00:00, Close, 26.49 2000-01-12T00:00:00, Close, 24.90 2000-01-13T00:00:00, Close, 24.77 2000-01-13T00:00:00, SELL CREATE, 24.77 2000-01-14T00:00:00, SELL EXECUTED, 25.70 2000-01-14T00:00:00, Close, 25.18 ... ... ... 2000-12-15T00:00:00, SELL CREATE, 26.93 2000-12-18T00:00:00, SELL EXECUTED, 28.29 2000-12-18T00:00:00, Close, 30.18 2000-12-19T00:00:00, Close, 28.88 2000-12-20T00:00:00, Close, 26.88 2000-12-20T00:00:00, BUY CREATE, 26.88 2000-12-21T00:00:00, BUY EXECUTED, 26.23 2000-12-21T00:00:00, Close, 27.82 2000-12-22T00:00:00, Close, 30.06 2000-12-26T00:00:00, Close, 29.17 2000-12-27T00:00:00, Close, 28.94 2000-12-28T00:00:00, Close, 29.29 2000-12-29T00:00:00, Close, 27.41 2000-12-29T00:00:00, SELL CREATE, 27.41 Final Portfolio Value: 100018.53 Blistering Barnacles!!! The system made money … something must be wrong The broker says: Show me the money! And the money is called “commission”. Let’s add a reasonable 0.1% commision rate per operation (both for buying and selling … yes the broker is avid …) A single line will suffice for it: # 0.1% ... divide by 100 to remove the % cerebro.broker.setcommission(commission=0.001) Being experienced with the platform we want to see the profit or loss after a buy/sell cycle, with and without commission. from __future__ import (absolute_import, division, print_function, unicode_literals) import datetime # For datetime objects import os.path # To manage paths import sys # To find out the script name (in argv[0]) # Import the backtrader platform import backtrader as bt # Create a Stratey class TestStrategy(bt.Strategy): def log(self, txt, dt=None): ''' Logging function fot this strategy''' dt = dt or self.datas[0].datetime.date(0) print('%s, %s' % (dt.isoformat(), txt)) def __init__(self): # Keep a reference to the "close" line in the data[0] dataseries self.dataclose = self.datas[0].close # To keep track of pending orders and buy price/commission self.order = None self.buyprice = None self.buycomm = None def notify_order(self, order): if order.status in [order.Submitted, order.Accepted]: # Buy/Sell order submitted/accepted to/by broker - Nothing to do return # Check if an order has been completed # Attention: broker could reject order if not enough cash if order.status in [order.Completed]: if order.isbuy(): self.log( 'BUY EXECUTED, Price: %.2f, Cost: %.2f, Comm %.2f' % (order.executed.price, order.executed.value, order.executed.comm)) self.buyprice = order.executed.price self.buycomm = order.executed.comm else: # Sell self.log('SELL EXECUTED, Price: %.2f, Cost: %.2f, Comm %.2f' % (order.executed.price, order.executed.value, order.executed.comm)) self.bar_executed = len(self) elif order.status in [order.Canceled, order.Margin, order.Rejected]: self.log('Order Canceled/Margin/Rejected') self.order = None def notify_trade(self, trade): if not trade.isclosed: return self.log('OPERATION PROFIT, GROSS %.2f, NET %.2f' % (trade.pnl, trade.pnlcomm)) def next(self): # Simply log the closing price of the series from the reference self.log('Close, %.2f' % self.dataclose[0]) # Check if an order is pending ... if yes, we cannot send a 2nd one if self.order: return # Check if we are in the market if not self.position: # Not yet ... we MIGHT BUY if ... if self.dataclose[0] < self.dataclose[-1]: # current close less than previous close if self.dataclose[-1] < self.dataclose[-2]: # previous close less than the previous close # BUY, BUY, BUY!!! (with default parameters) self.log('BUY CREATE, %.2f' % self.dataclose[0]) # Keep track of the created order to avoid a 2nd order self.order = self.buy() else: # Already in the market ... we might sell if len(self) >= (self.bar_executed + 5): # SELL, SELL, SELL!!! (with all possible default parameters) self.log('SELL CREATE, %.2f' % self.dataclose[0]) # Keep track of the created order to avoid a 2nd order self.order = self.sell() if __name__ == '__main__': # Create a cerebro entity cerebro = bt.Cerebro() # Add a strategy cerebro.addstrategy(TestStrategy) # Datas are in a subfolder of the samples. Need to find where the script is # because it could have been called from anywhere modpath = os.path.dirname(os.path.abspath(sys.argv[0])) datapath = os.path.join(modpath, '../../datas/orcl-1995-2014.txt') # Create a Data Feed data = bt.feeds.YahooFinanceCSVData( dataname=datapath, # Do not pass values before this date fromdate=datetime.datetime(2000, 1, 1), # Do not pass values before this date todate=datetime.datetime(2000, 12, 31), # Do not pass values after this date reverse=False) # Add the Data Feed to Cerebro cerebro.adddata(data) # Set our desired cash start cerebro.broker.setcash(100000.0) # Set the commission - 0.1% ... divide by 100 to remove the % cerebro.broker.setcommission(commission=0.001) # Print out the starting conditions print('Starting Portfolio Value: %.2f' % cerebro.broker.getvalue()) # Run over everything cerebro.run() # Print out the final result print('Final Portfolio Value: %.2f' % cerebro.broker.getvalue()) After the execution the output is: Starting Portfolio Value: 100000.00 2000-01-03T00:00:00, Close, 27.85 2000-01-04T00:00:00, Close, 25.39 2000-01-05T00:00:00, Close, 24.05 2000-01-05T00:00:00, BUY CREATE, 24.05 2000-01-06T00:00:00, BUY EXECUTED, Price: 23.61, Cost: 23.61, Commission 0.02 2000-01-06T00:00:00, Close, 22.63 2000-01-07T00:00:00, Close, 24.37 2000-01-10T00:00:00, Close, 27.29 2000-01-11T00:00:00, Close, 26.49 2000-01-12T00:00:00, Close, 24.90 2000-01-13T00:00:00, Close, 24.77 2000-01-13T00:00:00, SELL CREATE, 24.77 2000-01-14T00:00:00, SELL EXECUTED, Price: 25.70, Cost: 25.70, Commission 0.03 2000-01-14T00:00:00, OPERATION PROFIT, GROSS 2.09, NET 2.04 2000-01-14T00:00:00, Close, 25.18 ... ... ... 2000-12-15T00:00:00, SELL CREATE, 26.93 2000-12-18T00:00:00, SELL EXECUTED, Price: 28.29, Cost: 28.29, Commission 0.03 2000-12-18T00:00:00, OPERATION PROFIT, GROSS -0.06, NET -0.12 2000-12-18T00:00:00, Close, 30.18 2000-12-19T00:00:00, Close, 28.88 2000-12-20T00:00:00, Close, 26.88 2000-12-20T00:00:00, BUY CREATE, 26.88 2000-12-21T00:00:00, BUY EXECUTED, Price: 26.23, Cost: 26.23, Commission 0.03 2000-12-21T00:00:00, Close, 27.82 2000-12-22T00:00:00, Close, 30.06 2000-12-26T00:00:00, Close, 29.17 2000-12-27T00:00:00, Close, 28.94 2000-12-28T00:00:00, Close, 29.29 2000-12-29T00:00:00, Close, 27.41 2000-12-29T00:00:00, SELL CREATE, 27.41 Final Portfolio Value: 100016.98 God Save the Queen!!! The system still made money. Before moving on, let’s notice something by filtering the “OPERATION PROFIT” lines: 2000-01-14T00:00:00, OPERATION PROFIT, GROSS 2.09, NET 2.04 2000-02-07T00:00:00, OPERATION PROFIT, GROSS 3.68, NET 3.63 2000-02-28T00:00:00, OPERATION PROFIT, GROSS 4.48, NET 4.42 2000-03-13T00:00:00, OPERATION PROFIT, GROSS 3.48, NET 3.41 2000-03-22T00:00:00, OPERATION PROFIT, GROSS -0.41, NET -0.49 2000-04-07T00:00:00, OPERATION PROFIT, GROSS 2.45, NET 2.37 2000-04-20T00:00:00, OPERATION PROFIT, GROSS -1.95, NET -2.02 2000-05-02T00:00:00, OPERATION PROFIT, GROSS 5.46, NET 5.39 2000-05-11T00:00:00, OPERATION PROFIT, GROSS -3.74, NET -3.81 2000-05-30T00:00:00, OPERATION PROFIT, GROSS -1.46, NET -1.53 2000-07-05T00:00:00, OPERATION PROFIT, GROSS -1.62, NET -1.69 2000-07-14T00:00:00, OPERATION PROFIT, GROSS 2.08, NET 2.01 2000-07-28T00:00:00, OPERATION PROFIT, GROSS 0.14, NET 0.07 2000-08-08T00:00:00, OPERATION PROFIT, GROSS 4.36, NET 4.29 2000-08-21T00:00:00, OPERATION PROFIT, GROSS 1.03, NET 0.95 2000-09-15T00:00:00, OPERATION PROFIT, GROSS -4.26, NET -4.34 2000-09-27T00:00:00, OPERATION PROFIT, GROSS 1.29, NET 1.22 2000-10-13T00:00:00, OPERATION PROFIT, GROSS -2.98, NET -3.04 2000-10-26T00:00:00, OPERATION PROFIT, GROSS 3.01, NET 2.95 2000-11-06T00:00:00, OPERATION PROFIT, GROSS -3.59, NET -3.65 2000-11-16T00:00:00, OPERATION PROFIT, GROSS 1.28, NET 1.23 2000-12-01T00:00:00, OPERATION PROFIT, GROSS 2.59, NET 2.54 2000-12-18T00:00:00, OPERATION PROFIT, GROSS -0.06, NET -0.12 Adding up the “NET” profits the final figure is: 15.83 But the system said the following at the end: 2000-12-29T00:00:00, SELL CREATE, 27.41 Final Portfolio Value: 100016.98 And obviously 15.83 is not 16.98. There is no error whatsoever. The “NET” profit of 15.83 is already cash in the bag. Unfortunately (or fortunately to better understand the platform) there is an open position on the last day of the Data Feed. Even if a SELL operation has been sent … IT HAS NOT YET BEEN EXECUTED. The “Final Portfolio Value” calculated by the broker takes into account the “Close” price on 2000-12-29. The actual execution price would have been set on the next trading day which happened to be 2001-01-02. Extending the Data Feed” to take into account this day the output is: 2001-01-02T00:00:00, SELL EXECUTED, Price: 27.87, Cost: 27.87, Commission 0.03 2001-01-02T00:00:00, OPERATION PROFIT, GROSS 1.64, NET 1.59 2001-01-02T00:00:00, Close, 24.87 2001-01-02T00:00:00, BUY CREATE, 24.87 Final Portfolio Value: 100017.41 Now adding the previous NET profit to the completed operation’s net profit: 15.83 + 1.59 = 17.42 Which (discarding rounding errors in the “print” statements) is the extra Portfolio above the initial 100000 monetary units the strategy started with. Customizing the Strategy: Parameters It would a bit unpractical to hardcode some of the values in the strategy and have no chance to change them easily. Parameters come in handy to help. Definition of parameters is easy and looks like: params = (('myparam', 27), ('exitbars', 5),) Being this a standard Python tuple with some tuples inside it, the following may look more appealling to some: params = ( ('myparam', 27), ('exitbars', 5), ) With either formatting parametrization of the strategy is allowed when adding the strategy to the Cerebro engine: # Add a strategy cerebro.addstrategy(TestStrategy, myparam=20, exitbars=7) Note The setsizing method below is deprecated. This content is kept here for anyone looking at old samples of the sources. The sources have been update to use: cerebro.addsizer(bt.sizers.FixedSize, stake=10)`` Please read the section about sizers Using the parameters in the strategy is easy, as they are stored in a “params” attribute. If we for example want to set the stake fix, we can pass the stake parameter to the position sizer like this durint init: # Set the sizer stake from the params self.sizer.setsizing(self.params.stake) We could have also called buy and sell with a stake parameter and self.params.stake as the value. The logic to exit gets modified: # Already in the market ... we might sell if len(self) >= (self.bar_executed + self.params.exitbars): With all this in mind the example evolves to look like: from __future__ import (absolute_import, division, print_function, unicode_literals) import datetime # For datetime objects import os.path # To manage paths import sys # To find out the script name (in argv[0]) # Import the backtrader platform import backtrader as bt # Create a Stratey class TestStrategy(bt.Strategy): params = ( ('exitbars', 5), ) def log(self, txt, dt=None): ''' Logging function fot this strategy''' dt = dt or self.datas[0].datetime.date(0) print('%s, %s' % (dt.isoformat(), txt)) def __init__(self): # Keep a reference to the "close" line in the data[0] dataseries self.dataclose = self.datas[0].close # To keep track of pending orders and buy price/commission self.order = None self.buyprice = None self.buycomm = None def notify_order(self, order): if order.status in [order.Submitted, order.Accepted]: # Buy/Sell order submitted/accepted to/by broker - Nothing to do return # Check if an order has been completed # Attention: broker could reject order if not enough cash if order.status in [order.Completed]: if order.isbuy(): self.log( 'BUY EXECUTED, Price: %.2f, Cost: %.2f, Comm %.2f' % (order.executed.price, order.executed.value, order.executed.comm)) self.buyprice = order.executed.price self.buycomm = order.executed.comm else: # Sell self.log('SELL EXECUTED, Price: %.2f, Cost: %.2f, Comm %.2f' % (order.executed.price, order.executed.value, order.executed.comm)) self.bar_executed = len(self) elif order.status in [order.Canceled, order.Margin, order.Rejected]: self.log('Order Canceled/Margin/Rejected') self.order = None def notify_trade(self, trade): if not trade.isclosed: return self.log('OPERATION PROFIT, GROSS %.2f, NET %.2f' % (trade.pnl, trade.pnlcomm)) def next(self): # Simply log the closing price of the series from the reference self.log('Close, %.2f' % self.dataclose[0]) # Check if an order is pending ... if yes, we cannot send a 2nd one if self.order: return # Check if we are in the market if not self.position: # Not yet ... we MIGHT BUY if ... if self.dataclose[0] < self.dataclose[-1]: # current close less than previous close if self.dataclose[-1] < self.dataclose[-2]: # previous close less than the previous close # BUY, BUY, BUY!!! (with default parameters) self.log('BUY CREATE, %.2f' % self.dataclose[0]) # Keep track of the created order to avoid a 2nd order self.order = self.buy() else: # Already in the market ... we might sell if len(self) >= (self.bar_executed + self.params.exitbars): # SELL, SELL, SELL!!! (with all possible default parameters) self.log('SELL CREATE, %.2f' % self.dataclose[0]) # Keep track of the created order to avoid a 2nd order self.order = self.sell() if __name__ == '__main__': # Create a cerebro entity cerebro = bt.Cerebro() # Add a strategy cerebro.addstrategy(TestStrategy) # Datas are in a subfolder of the samples. Need to find where the script is # because it could have been called from anywhere modpath = os.path.dirname(os.path.abspath(sys.argv[0])) datapath = os.path.join(modpath, '../../datas/orcl-1995-2014.txt') # Create a Data Feed data = bt.feeds.YahooFinanceCSVData( dataname=datapath, # Do not pass values before this date fromdate=datetime.datetime(2000, 1, 1), # Do not pass values before this date todate=datetime.datetime(2000, 12, 31), # Do not pass values after this date reverse=False) # Add the Data Feed to Cerebro cerebro.adddata(data) # Set our desired cash start cerebro.broker.setcash(100000.0) # Add a FixedSize sizer according to the stake cerebro.addsizer(bt.sizers.FixedSize, stake=10) # Set the commission - 0.1% ... divide by 100 to remove the % cerebro.broker.setcommission(commission=0.001) # Print out the starting conditions print('Starting Portfolio Value: %.2f' % cerebro.broker.getvalue()) # Run over everything cerebro.run() # Print out the final result print('Final Portfolio Value: %.2f' % cerebro.broker.getvalue()) After the execution the output is: Starting Portfolio Value: 100000.00 2000-01-03T00:00:00, Close, 27.85 2000-01-04T00:00:00, Close, 25.39 2000-01-05T00:00:00, Close, 24.05 2000-01-05T00:00:00, BUY CREATE, 24.05 2000-01-06T00:00:00, BUY EXECUTED, Size 10, Price: 23.61, Cost: 236.10, Commission 0.24 2000-01-06T00:00:00, Close, 22.63 ... ... ... 2000-12-20T00:00:00, BUY CREATE, 26.88 2000-12-21T00:00:00, BUY EXECUTED, Size 10, Price: 26.23, Cost: 262.30, Commission 0.26 2000-12-21T00:00:00, Close, 27.82 2000-12-22T00:00:00, Close, 30.06 2000-12-26T00:00:00, Close, 29.17 2000-12-27T00:00:00, Close, 28.94 2000-12-28T00:00:00, Close, 29.29 2000-12-29T00:00:00, Close, 27.41 2000-12-29T00:00:00, SELL CREATE, 27.41 Final Portfolio Value: 100169.80 In order to see the difference, the print outputs have also been extended to show the execution size. Having multiplied the stake by 10, the obvious has happened: the profit and loss has been multiplied by 10. Instead of 16.98, the surplus is now 169.80 Adding an indicator Having heard of indicators, the next thing anyone would add to the strategy is one of them. For sure they must be much better than a simple “3 lower closes” strategy. Inspired in one of the examples from PyAlgoTrade a strategy using a Simple Moving Average. Buy “AtMarket” if the close is greater than the Average If in the market, sell if the close is smaller than the Average Only 1 active operation is allowed in the market Most of the existing code can be kept in place. Let’s add the average during init and keep a reference to it: self.sma = bt.indicators.MovingAverageSimple(self.datas[0], period=self.params.maperiod) And of course the logic to enter and exit the market will rely on the Average values. Look in the code for the logic. Note The starting cash will be 1000 monetary units to be in line with the PyAlgoTrade example and no commission will be applied from __future__ import (absolute_import, division, print_function, unicode_literals) import datetime # For datetime objects import os.path # To manage paths import sys # To find out the script name (in argv[0]) # Import the backtrader platform import backtrader as bt # Create a Stratey class TestStrategy(bt.Strategy): params = ( ('maperiod', 15), ) def log(self, txt, dt=None): ''' Logging function fot this strategy''' dt = dt or self.datas[0].datetime.date(0) print('%s, %s' % (dt.isoformat(), txt)) def __init__(self): # Keep a reference to the "close" line in the data[0] dataseries self.dataclose = self.datas[0].close # To keep track of pending orders and buy price/commission self.order = None self.buyprice = None self.buycomm = None # Add a MovingAverageSimple indicator self.sma = bt.indicators.SimpleMovingAverage( self.datas[0], period=self.params.maperiod) def notify_order(self, order): if order.status in [order.Submitted, order.Accepted]: # Buy/Sell order submitted/accepted to/by broker - Nothing to do return # Check if an order has been completed # Attention: broker could reject order if not enough cash if order.status in [order.Completed]: if order.isbuy(): self.log( 'BUY EXECUTED, Price: %.2f, Cost: %.2f, Comm %.2f' % (order.executed.price, order.executed.value, order.executed.comm)) self.buyprice = order.executed.price self.buycomm = order.executed.comm else: # Sell self.log('SELL EXECUTED, Price: %.2f, Cost: %.2f, Comm %.2f' % (order.executed.price, order.executed.value, order.executed.comm)) self.bar_executed = len(self) elif order.status in [order.Canceled, order.Margin, order.Rejected]: self.log('Order Canceled/Margin/Rejected') self.order = None def notify_trade(self, trade): if not trade.isclosed: return self.log('OPERATION PROFIT, GROSS %.2f, NET %.2f' % (trade.pnl, trade.pnlcomm)) def next(self): # Simply log the closing price of the series from the reference self.log('Close, %.2f' % self.dataclose[0]) # Check if an order is pending ... if yes, we cannot send a 2nd one if self.order: return # Check if we are in the market if not self.position: # Not yet ... we MIGHT BUY if ... if self.dataclose[0] > self.sma[0]: # BUY, BUY, BUY!!! (with all possible default parameters) self.log('BUY CREATE, %.2f' % self.dataclose[0]) # Keep track of the created order to avoid a 2nd order self.order = self.buy() else: if self.dataclose[0] < self.sma[0]: # SELL, SELL, SELL!!! (with all possible default parameters) self.log('SELL CREATE, %.2f' % self.dataclose[0]) # Keep track of the created order to avoid a 2nd order self.order = self.sell() if __name__ == '__main__': # Create a cerebro entity cerebro = bt.Cerebro() # Add a strategy cerebro.addstrategy(TestStrategy) # Datas are in a subfolder of the samples. Need to find where the script is # because it could have been called from anywhere modpath = os.path.dirname(os.path.abspath(sys.argv[0])) datapath = os.path.join(modpath, '../../datas/orcl-1995-2014.txt') # Create a Data Feed data = bt.feeds.YahooFinanceCSVData( dataname=datapath, # Do not pass values before this date fromdate=datetime.datetime(2000, 1, 1), # Do not pass values before this date todate=datetime.datetime(2000, 12, 31), # Do not pass values after this date reverse=False) # Add the Data Feed to Cerebro cerebro.adddata(data) # Set our desired cash start cerebro.broker.setcash(1000.0) # Add a FixedSize sizer according to the stake cerebro.addsizer(bt.sizers.FixedSize, stake=10) # Set the commission cerebro.broker.setcommission(commission=0.0) # Print out the starting conditions print('Starting Portfolio Value: %.2f' % cerebro.broker.getvalue()) # Run over everything cerebro.run() # Print out the final result print('Final Portfolio Value: %.2f' % cerebro.broker.getvalue()) Now, before skipping to the next section LOOK CAREFULLY to the first date which is shown in the log: It’ no longer 2000-01-03, the first trading day in the year 2K. It’s 2000-01-24 … Who has stolen my cheese? The missing days are not missing. The platform has adapted to the new circumstances: An indicator (SimpleMovingAverage) has been added to the Strategy. This indicator needs X bars to produce an output: in the example: 15 2000-01-24 is the day in which the 15th bar occurs The backtrader platform assumes that the Strategy has the indicator in place for a good reason, to use it in the decision making process. And it makes no sense to try to make decisions if the indicator is not yet ready and producing values. next will be 1st called when all indicators have already reached the minimum needed period to produce a value In the example there is a single indicator, but the strategy could have any number of them. After the execution the output is: Starting Portfolio Value: 1000.00 2000-01-24T00:00:00, Close, 25.55 2000-01-25T00:00:00, Close, 26.61 2000-01-25T00:00:00, BUY CREATE, 26.61 2000-01-26T00:00:00, BUY EXECUTED, Size 10, Price: 26.76, Cost: 267.60, Commission 0.00 2000-01-26T00:00:00, Close, 25.96 2000-01-27T00:00:00, Close, 24.43 2000-01-27T00:00:00, SELL CREATE, 24.43 2000-01-28T00:00:00, SELL EXECUTED, Size 10, Price: 24.28, Cost: 242.80, Commission 0.00 2000-01-28T00:00:00, OPERATION PROFIT, GROSS -24.80, NET -24.80 2000-01-28T00:00:00, Close, 22.34 2000-01-31T00:00:00, Close, 23.55 2000-02-01T00:00:00, Close, 25.46 2000-02-02T00:00:00, Close, 25.61 2000-02-02T00:00:00, BUY CREATE, 25.61 2000-02-03T00:00:00, BUY EXECUTED, Size 10, Price: 26.11, Cost: 261.10, Commission 0.00 ... ... ... 2000-12-20T00:00:00, SELL CREATE, 26.88 2000-12-21T00:00:00, SELL EXECUTED, Size 10, Price: 26.23, Cost: 262.30, Commission 0.00 2000-12-21T00:00:00, OPERATION PROFIT, GROSS -20.60, NET -20.60 2000-12-21T00:00:00, Close, 27.82 2000-12-21T00:00:00, BUY CREATE, 27.82 2000-12-22T00:00:00, BUY EXECUTED, Size 10, Price: 28.65, Cost: 286.50, Commission 0.00 2000-12-22T00:00:00, Close, 30.06 2000-12-26T00:00:00, Close, 29.17 2000-12-27T00:00:00, Close, 28.94 2000-12-28T00:00:00, Close, 29.29 2000-12-29T00:00:00, Close, 27.41 2000-12-29T00:00:00, SELL CREATE, 27.41 Final Portfolio Value: 973.90 In the name of the King!!! A winning system turned into a losing one … and that with no commission. It may well be that simply adding an indicator is not the universal panacea. Note The same logic and data with PyAlgoTrade yields a slightly different result (slightly off). Looking at the entire printout reveals that some operations are not exactly the same. Being the culprit again the usual suspect: rounding. PyAlgoTrade does not round the datafeed values when applying the divided “adjusted close” to the data feed values. The Yahoo Data Feed provided by backtrader rounds the values down to 2 decimals after applying the adjusted close. Upon printing the values everything seems the same, but it’s obvious that sometimes that 5th place decimal plays a role. Rounding down to 2 decimals seems more realistic, because Market Exchanges do only allow a number of decimals per asset (being that 2 decimals usually for stocks) Note The Yahoo Data Feed (starting with version 1.8.11.99 allows to specify if rounding has to happen and how many decimals) Visual Inspection: Plotting A printout or log of the actual whereabouts of the system at each bar-instant is good but humans tend to be visual and therefore it seems right to offer a view of the same whereabouts as chart. Note To plot you need to have matplotlib installed Once again defaults for plotting are there to assist the platform user. Plotting is incredibly a 1 line operation: cerebro.plot() Being the location for sure after cerebro.run() has been called. In order to display the automatic plotting capabilities and a couple of easy customizations, the following will be done: A 2nd MovingAverage (Exponential) will be added. The defaults will plot it (just like the 1st) with the data. A 3rd MovingAverage (Weighted) will be added. Customized to plot in an own plot (even if not sensible) A Stochastic (Slow) will be added. No change to the defaults. A MACD will be added. No change to the defaults. A RSI will be added. No change to the defaults. A MovingAverage (Simple) will be applied to the RSI. No change to the defaults (it will be plotted with the RSI) An AverageTrueRange will be added. Changed defaults to avoid it being plotted. The entire set of additions to the init method of the Strategy: # Indicators for the plotting show bt.indicators.ExponentialMovingAverage(self.datas[0], period=25) bt.indicators.WeightedMovingAverage(self.datas[0], period=25).subplot = True bt.indicators.StochasticSlow(self.datas[0]) bt.indicators.MACDHisto(self.datas[0]) rsi = bt.indicators.RSI(self.datas[0]) bt.indicators.SmoothedMovingAverage(rsi, period=10) bt.indicators.ATR(self.datas[0]).plot = False Note Even if indicators are not explicitly added to a member variable of the strategy (like self.sma = MovingAverageSimple…), they will autoregister with the strategy and will influence the minimum period for next and will be part of the plotting. In the example only RSI is added to a temporary variable rsi with the only intention to create a MovingAverageSmoothed on it. The example now: from __future__ import (absolute_import, division, print_function, unicode_literals) import datetime # For datetime objects import os.path # To manage paths import sys # To find out the script name (in argv[0]) # Import the backtrader platform import backtrader as bt # Create a Stratey class TestStrategy(bt.Strategy): params = ( ('maperiod', 15), ) def log(self, txt, dt=None): ''' Logging function fot this strategy''' dt = dt or self.datas[0].datetime.date(0) print('%s, %s' % (dt.isoformat(), txt)) def __init__(self): # Keep a reference to the "close" line in the data[0] dataseries self.dataclose = self.datas[0].close # To keep track of pending orders and buy price/commission self.order = None self.buyprice = None self.buycomm = None # Add a MovingAverageSimple indicator self.sma = bt.indicators.SimpleMovingAverage( self.datas[0], period=self.params.maperiod) # Indicators for the plotting show bt.indicators.ExponentialMovingAverage(self.datas[0], period=25) bt.indicators.WeightedMovingAverage(self.datas[0], period=25, subplot=True) bt.indicators.StochasticSlow(self.datas[0]) bt.indicators.MACDHisto(self.datas[0]) rsi = bt.indicators.RSI(self.datas[0]) bt.indicators.SmoothedMovingAverage(rsi, period=10) bt.indicators.ATR(self.datas[0], plot=False) def notify_order(self, order): if order.status in [order.Submitted, order.Accepted]: # Buy/Sell order submitted/accepted to/by broker - Nothing to do return # Check if an order has been completed # Attention: broker could reject order if not enough cash if order.status in [order.Completed]: if order.isbuy(): self.log( 'BUY EXECUTED, Price: %.2f, Cost: %.2f, Comm %.2f' % (order.executed.price, order.executed.value, order.executed.comm)) self.buyprice = order.executed.price self.buycomm = order.executed.comm else: # Sell self.log('SELL EXECUTED, Price: %.2f, Cost: %.2f, Comm %.2f' % (order.executed.price, order.executed.value, order.executed.comm)) self.bar_executed = len(self) elif order.status in [order.Canceled, order.Margin, order.Rejected]: self.log('Order Canceled/Margin/Rejected') # Write down: no pending order self.order = None def notify_trade(self, trade): if not trade.isclosed: return self.log('OPERATION PROFIT, GROSS %.2f, NET %.2f' % (trade.pnl, trade.pnlcomm)) def next(self): # Simply log the closing price of the series from the reference self.log('Close, %.2f' % self.dataclose[0]) # Check if an order is pending ... if yes, we cannot send a 2nd one if self.order: return # Check if we are in the market if not self.position: # Not yet ... we MIGHT BUY if ... if self.dataclose[0] > self.sma[0]: # BUY, BUY, BUY!!! (with all possible default parameters) self.log('BUY CREATE, %.2f' % self.dataclose[0]) # Keep track of the created order to avoid a 2nd order self.order = self.buy() else: if self.dataclose[0] < self.sma[0]: # SELL, SELL, SELL!!! (with all possible default parameters) self.log('SELL CREATE, %.2f' % self.dataclose[0]) # Keep track of the created order to avoid a 2nd order self.order = self.sell() if __name__ == '__main__': # Create a cerebro entity cerebro = bt.Cerebro() # Add a strategy cerebro.addstrategy(TestStrategy) # Datas are in a subfolder of the samples. Need to find where the script is # because it could have been called from anywhere modpath = os.path.dirname(os.path.abspath(sys.argv[0])) datapath = os.path.join(modpath, '../../datas/orcl-1995-2014.txt') # Create a Data Feed data = bt.feeds.YahooFinanceCSVData( dataname=datapath, # Do not pass values before this date fromdate=datetime.datetime(2000, 1, 1), # Do not pass values before this date todate=datetime.datetime(2000, 12, 31), # Do not pass values after this date reverse=False) # Add the Data Feed to Cerebro cerebro.adddata(data) # Set our desired cash start cerebro.broker.setcash(1000.0) # Add a FixedSize sizer according to the stake cerebro.addsizer(bt.sizers.FixedSize, stake=10) # Set the commission cerebro.broker.setcommission(commission=0.0) # Print out the starting conditions print('Starting Portfolio Value: %.2f' % cerebro.broker.getvalue()) # Run over everything cerebro.run() # Print out the final result print('Final Portfolio Value: %.2f' % cerebro.broker.getvalue()) # Plot the result cerebro.plot() After the execution the output is: Starting Portfolio Value: 1000.00 2000-02-18T00:00:00, Close, 27.61 2000-02-22T00:00:00, Close, 27.97 2000-02-22T00:00:00, BUY CREATE, 27.97 2000-02-23T00:00:00, BUY EXECUTED, Size 10, Price: 28.38, Cost: 283.80, Commission 0.00 2000-02-23T00:00:00, Close, 29.73 ... ... ... 2000-12-21T00:00:00, BUY CREATE, 27.82 2000-12-22T00:00:00, BUY EXECUTED, Size 10, Price: 28.65, Cost: 286.50, Commission 0.00 2000-12-22T00:00:00, Close, 30.06 2000-12-26T00:00:00, Close, 29.17 2000-12-27T00:00:00, Close, 28.94 2000-12-28T00:00:00, Close, 29.29 2000-12-29T00:00:00, Close, 27.41 2000-12-29T00:00:00, SELL CREATE, 27.41 Final Portfolio Value: 981.00 The final result has changed even if the logic hasn’t. This is true but the logic has not been applied to the same number of bars. Note As explained before, the platform will first call next when all indicators are ready to produce a value. In this plotting example (very clear in the chart) the MACD is the last indicator to be fully ready (all 3 lines producing an output). The 1st BUY order is no longer scheduled during Jan 2000 but close to the end of Feb 2000. The chart: image Let’s Optimize Many trading books say each market and each traded stock (or commodity or ..) have different rythms. That there is no such thing as a one size fits all. Before the plotting sample, when the strategy started using an indicator the period default value was 15 bars. It’s a strategy parameter and this can be used in an optimization to change the value of the parameter and see which one better fits the market. Note There is plenty of literature about Optimization and associated pros and cons. But the advice will always point in the same direction: do not overoptimize. If a trading idea is not sound, optimizing may end producing a positive result which is only valid for the backtested dataset. The sample is modified to optimize the period of the Simple Moving Average. For the sake of clarity any output with regards to Buy/Sell orders has been removed The example now: from __future__ import (absolute_import, division, print_function, unicode_literals) import datetime # For datetime objects import os.path # To manage paths import sys # To find out the script name (in argv[0]) # Import the backtrader platform import backtrader as bt # Create a Stratey class TestStrategy(bt.Strategy): params = ( ('maperiod', 15), ('printlog', False), ) def log(self, txt, dt=None, doprint=False): ''' Logging function fot this strategy''' if self.params.printlog or doprint: dt = dt or self.datas[0].datetime.date(0) print('%s, %s' % (dt.isoformat(), txt)) def __init__(self): # Keep a reference to the "close" line in the data[0] dataseries self.dataclose = self.datas[0].close # To keep track of pending orders and buy price/commission self.order = None self.buyprice = None self.buycomm = None # Add a MovingAverageSimple indicator self.sma = bt.indicators.SimpleMovingAverage( self.datas[0], period=self.params.maperiod) def notify_order(self, order): if order.status in [order.Submitted, order.Accepted]: # Buy/Sell order submitted/accepted to/by broker - Nothing to do return # Check if an order has been completed # Attention: broker could reject order if not enough cash if order.status in [order.Completed]: if order.isbuy(): self.log( 'BUY EXECUTED, Price: %.2f, Cost: %.2f, Comm %.2f' % (order.executed.price, order.executed.value, order.executed.comm)) self.buyprice = order.executed.price self.buycomm = order.executed.comm else: # Sell self.log('SELL EXECUTED, Price: %.2f, Cost: %.2f, Comm %.2f' % (order.executed.price, order.executed.value, order.executed.comm)) self.bar_executed = len(self) elif order.status in [order.Canceled, order.Margin, order.Rejected]: self.log('Order Canceled/Margin/Rejected') # Write down: no pending order self.order = None def notify_trade(self, trade): if not trade.isclosed: return self.log('OPERATION PROFIT, GROSS %.2f, NET %.2f' % (trade.pnl, trade.pnlcomm)) def next(self): # Simply log the closing price of the series from the reference self.log('Close, %.2f' % self.dataclose[0]) # Check if an order is pending ... if yes, we cannot send a 2nd one if self.order: return # Check if we are in the market if not self.position: # Not yet ... we MIGHT BUY if ... if self.dataclose[0] > self.sma[0]: # BUY, BUY, BUY!!! (with all possible default parameters) self.log('BUY CREATE, %.2f' % self.dataclose[0]) # Keep track of the created order to avoid a 2nd order self.order = self.buy() else: if self.dataclose[0] < self.sma[0]: # SELL, SELL, SELL!!! (with all possible default parameters) self.log('SELL CREATE, %.2f' % self.dataclose[0]) # Keep track of the created order to avoid a 2nd order self.order = self.sell() def stop(self): self.log('(MA Period %2d) Ending Value %.2f' % (self.params.maperiod, self.broker.getvalue()), doprint=True) if __name__ == '__main__': # Create a cerebro entity cerebro = bt.Cerebro() # Add a strategy strats = cerebro.optstrategy( TestStrategy, maperiod=range(10, 31)) # Datas are in a subfolder of the samples. Need to find where the script is # because it could have been called from anywhere modpath = os.path.dirname(os.path.abspath(sys.argv[0])) datapath = os.path.join(modpath, '../../datas/orcl-1995-2014.txt') # Create a Data Feed data = bt.feeds.YahooFinanceCSVData( dataname=datapath, # Do not pass values before this date fromdate=datetime.datetime(2000, 1, 1), # Do not pass values before this date todate=datetime.datetime(2000, 12, 31), # Do not pass values after this date reverse=False) # Add the Data Feed to Cerebro cerebro.adddata(data) # Set our desired cash start cerebro.broker.setcash(1000.0) # Add a FixedSize sizer according to the stake cerebro.addsizer(bt.sizers.FixedSize, stake=10) # Set the commission cerebro.broker.setcommission(commission=0.0) # Run over everything cerebro.run(maxcpus=1) Instead of calling addstrategy to add a stratey class to Cerebro, the call is made to optstrategy. And instead of passing a value a range of values is passed. One of the “Strategy” hooks is added, the stop method, which will be called when the data has been exhausted and backtesting is over. It’s used to print the final net value of the portfolio in the broker (it was done in Cerebro previously) The system will execute the strategy for each value of the range. The following will be output: 2000-12-29, (MA Period 10) Ending Value 880.30 2000-12-29, (MA Period 11) Ending Value 880.00 2000-12-29, (MA Period 12) Ending Value 830.30 2000-12-29, (MA Period 13) Ending Value 893.90 2000-12-29, (MA Period 14) Ending Value 896.90 2000-12-29, (MA Period 15) Ending Value 973.90 2000-12-29, (MA Period 16) Ending Value 959.40 2000-12-29, (MA Period 17) Ending Value 949.80 2000-12-29, (MA Period 18) Ending Value 1011.90 2000-12-29, (MA Period 19) Ending Value 1041.90 2000-12-29, (MA Period 20) Ending Value 1078.00 2000-12-29, (MA Period 21) Ending Value 1058.80 2000-12-29, (MA Period 22) Ending Value 1061.50 2000-12-29, (MA Period 23) Ending Value 1023.00 2000-12-29, (MA Period 24) Ending Value 1020.10 2000-12-29, (MA Period 25) Ending Value 1013.30 2000-12-29, (MA Period 26) Ending Value 998.30 2000-12-29, (MA Period 27) Ending Value 982.20 2000-12-29, (MA Period 28) Ending Value 975.70 2000-12-29, (MA Period 29) Ending Value 983.30 2000-12-29, (MA Period 30) Ending Value 979.80 Results: For periods below 18 the strategy (commissionless) loses money. For periods between 18 and 26 (both included) the strategy makes money. Above 26 money is lost again. And the winning period for this strategy and the given data set is: 20 bars, which wins 78.00 units over 1000 $/€ (a 7.8%) Note The extra indicators from the plotting example have been removed and the start of operations is only influenced by the Simple Moving Average which is being optimized. Hence the slightly different results for period 15 Conclusion The incremental samples have shown how to go from a barebones script to a fully working trading system which even plots the results and can be optimized. A lot more can be done to try to improve the chances of winning: Self defined Indicators Creating an indicator is easy (and even plotting them is easy) Sizers Money Management is for many the key to success Order Types (limit, stop, stoplimit) Some others To ensure all the above items can be fully utilized the documentation provides an insight into them (and other topics) Look in the table of contents and keep on reading … and developing. Best of luck
07-08
数据集基本信息: <class 'pandas.core.frame.DataFrame'> RangeIndex: 3599999 entries, 0 to 3599998 Data columns (total 3 columns): # Column Dtype --- ------ ----- 0 2 int64 1 Stuning even for the non-gamer object 2 This sound track was beautiful! It paints the senery in your mind so well I would recomend it even to people who hate vid. game music! I have played the game Chrono Cross but out of all of the games I have ever played it has the best music! It backs away from crude keyboarding and takes a fresher step with grate guitars and soulful orchestras. It would impress anyone who cares to listen! ^_^ object dtypes: int64(1), object(2) memory usage: 82.4+ MB 数据前几行内容信息: 2 Stuning even for the non-gamer This sound track was beautiful! It paints the senery in your mind so well I would recomend it even to people who hate vid. game music! I have played the game Chrono Cross but out of all of the games I have ever played it has the best music! It backs away from crude keyboarding and takes a fresher step with grate guitars and soulful orchestras. It would impress anyone who cares to listen! ^_^ 0 2 The best soundtrack ever to anything. I'm reading a lot of reviews saying that this is the best 'game soundtrack' and I figured that I'd write a review to disagree a bit. This in my opinino is Yasunori Mitsuda's ultimate masterpiece. The music is timeless and I'm been listening to it for years now and its beauty simply refuses to fade.The price tag on this is pretty staggering I must say, but if you are going to buy any cd for this much money, this is the only one that I feel would be worth every penny. 1 2 Amazing! "This soundtrack is my favorite music of all time, hands down. The intense sadness of ""Prisoners of Fate"" (which means all the more if you've played the game) and the hope in ""A Distant Promise"" and ""Girl who Stole the Star"" have been an important inspiration to me personally throughout my teen years. The higher energy tracks like ""Chrono Cross ~ Time's Scar~"", ""Time of the Dreamwatch"", and ""Chronomantique"" (indefinably remeniscent of Chrono Trigger) are all absolutely superb as well.This soundtrack is amazing music, probably the best of this composer's work (I haven't heard the Xenogears soundtrack, so I can't say for sure), and even if you've never played the game, it would be worth twice the price to buy it.I wish I could give it 6 stars." 2 2 Excellent Soundtrack I truly like this soundtrack and I enjoy video game music. I have played this game and most of the music on here I enjoy and it's truly relaxing and peaceful.On disk one. my favorites are Scars Of Time, Between Life and Death, Forest Of Illusion, Fortress of Ancient Dragons, Lost Fragment, and Drowned Valley.Disk Two: The Draggons, Galdorb - Home, Chronomantique, Prisoners of Fate, Gale, and my girlfriend likes ZelbessDisk Three: The best of the three. Garden Of God, Chronopolis, Fates, Jellyfish sea, Burning Orphange, Dragon's Prayer, Tower Of Stars, Dragon God, and Radical Dreamers - Unstealable Jewel.Overall, this is a excellent soundtrack and should be brought by those that like video game music.Xander Cross 3 2 Remember, Pull Your Jaw Off The Floor After Hearing it If you've played the game, you know how divine the music is! Every single song tells a story of the game, it's that good! The greatest songs are without a doubt, Chrono Cross: Time's Scar, Magical Dreamers: The Wind, The Stars, and the Sea and Radical Dreamers: Unstolen Jewel. (Translation varies) This music is perfect if you ask me, the best it can be. Yasunori Mitsuda just poured his heart on and wrote it down on paper. 4 2 an absolute masterpiece I am quite sure any of you actually taking the time to read this have played the game at least once, and heard at least a few of the tracks here. And whether you were aware of it or not, Mitsuda's music contributed greatly to the mood of every single minute of the whole game.Composed of 3 CDs and quite a few songs (I haven't an exact count), all of which are heart-rendering and impressively remarkable, this soundtrack is one I assure you you will not forget. It has everything for every listener -- from fast-paced and energetic (Dancing the Tokage or Termina Home), to slower and more haunting (Dragon God), to purely beautifully composed (Time's Scar), to even some fantastic vocals (Radical Dreamers).This is one of the best videogame soundtracks out there, and surely Mitsuda's best ever. ^_^
最新发布
11-19
评论
添加红包

请填写红包祝福语或标题

红包个数最小为10个

红包金额最低5元

当前余额3.43前往充值 >
需支付:10.00
成就一亿技术人!
领取后你会自动成为博主和红包主的粉丝 规则
hope_wisdom
发出的红包
实付
使用余额支付
点击重新获取
扫码支付
钱包余额 0

抵扣说明:

1.余额是钱包充值的虚拟货币,按照1:1的比例进行支付金额的抵扣。
2.余额无法直接购买下载,可以购买VIP、付费专栏及课程。

余额充值