9
Fundamental Algorithmic Trading Strategies
is chapter outlines several algorithms profitable on the given stock, given a time window and certain parameters, with the aim of helping you to formulate an idea of how to develop your own trading strategies.
In this chapter, we will discuss the following topics:
What is an algorithmic trading strategy?
Learning momentum-based/trend-following strategies Learning mean-reversion strategies
Learning mathematical model-based strategies
Learning time series prediction-based strategies
Technical requirements
e Python code used in this chapter is available in the Chapter09/signals_and_ strategies.ipynb notebook in the book’s code repository.
246 Fundamental Algorithmic Trading Strategies
What is an algorithmic trading strategy?
Any algorithmic trading strategy should entail the following:
It should be a model based on an underlying market theory since only then can you
find its predictive power. Fitting a model to data with great backtesting results is simple, but usually does not provide sound predictions.
It should be as simple as possible the more complex the strategy, the less likely it is
to perform well in the long term (overfitting).
It should restrict the strategy for a well-defined set of financial assets (trading
universe) based on the following:
1) eir returns profile.
1) eir returns not being correlated.
1) eir trading patterns you do not want to trade an illiquid asset; you restrict yourself just to significantly traded assets.
It should define the relevant financial data:
1) Frequency: Daily, monthly, intraday, and suchlike
1) Data source
It should define the model’s parameters.
It should define their timing, entry, exit rules, and position sizing strategy for
example, we cannot trade more than 10% of the average daily volume; usually, the decision to enter/exit is made by a composition of several indicators.
It should define the risk levels how much of a risk a single asset can bear. It should define the benchmark used to compare performance against.
It should define its rebalancing policy as the markets evolve, the position sizes
and risk levels will deviate from their target levels and then it is necessary to adjust the portfolios.
Usually, you have a large library of algorithmic trading strategies, and backtesting will suggest which of these strategies, on which assets, and at what point in time they may generate a profit. You should keep a backtesting journal to keep track of what strategies did or didn’t work, on what stock, and during what period.
What is an algorithmic trading strategy? 247
How do you go about finding a portfolio of stocks to consider for trading? e options are as follows:
Use ETF/index components for example, the members of the Dow Jones
Industrial Average.
Use all listed stocks and then restrict the list to the following:
1) ose stocks that are traded the most
1) Just non-correlated stocks
1) ose stocks that are underperforming or overperforming using a returns model, such as the Fama-French three-factor model
You should classify each stock into as many categories as possible:
1) Value/growth stocks
1) By industry
Each trading strategy depends on a number of parameters. How do you go about finding the best values for each of them? e possible approaches are as follow:
A parameter sweep by trying each possible value within the range of possible
values for each parameter, but this would require an enormous amount of computing resources.
Very o en, a parameter sweep that involves testing many random samples, instead
of all values, from the range of possible values provides a reasonable approximation.
To build a large library of algorithmic trading strategies, you should do the following:
Subscribe to financial trading blogs.
Read financial trading books.
e key algorithmic trading strategies can be classified as follows:
Momentum-based/trend-following strategies
Mean-reversion strategies
Mathematical model-based strategies
Arbitrage strategies
Market-making strategies
Index fund rebalancing strategies
Trading timing optimization strategies (VWAP, TWAP, POV, and so on)
248 Fundamental Algorithmic Trading Strategies
In addition, you yourself should classify all trading strategies depending on the environment where they work best some strategies work well in volatile markets with strong trends, while others do not.
e following algorithms use the freely accessible Quandl data bundle; thus, the last trading date is January 1, 2018.
You should accumulate many different trading algorithms, list the number of possible parameters, and backtest the stocks on a number of parameters on the universe of stocks (for example, those with an average trading volume of at least X) to see which may be profitable. Backtesting should happen in a time window such as the present and near future for example, the volatility regime.
e best way of reading the following strategies is as follows:
Identify the signal formula of the strategy and consider it for an entry/exit rule for
your own strategy or for a combination with other strategies some of the most profitable strategies are combinations of existing strategies.
Consider the frequency of trading daily trading may not be suitable for all
strategies due to the transaction costs.
Each strategy works for different types of stocks and their market some work only
for trending stocks, some work only for high-volatility stocks, and so on.
Learning momentum-based/trend-following strategies
Momentum-based/trend-following strategies are types of technical analysis strategies. ey assume that the near-time future prices will follow an upward or downward trend.
Rolling window mean strategy
is strategy is to own a financial asset if its latest stock price is above the average price over the last X days.
In the following example, it works well for Apple stock and a period of 90 days:
%matplotlib inline
from zipline import run_algorithm
from zipline.api import order_target_percent, symbol, set_ commission
Learning momentum-based/trend-following strategies 249
from zipline.finance.commission import PerTrade import
pandas as pd
import pyfolio as pf
import warnings warnings.filterwarnings('ignore')
def initialize(context):
context.stock = symbol('AAPL')
context.rolling_window = 90 set_commission(PerTrade(cost=5))
def handle_data(context, data):
price_hist = data.history(context.stock, "close",
context.rolling_window, "1d")
order_target_percent(context.stock, 1.0 if price_hist[-1] > 
)price_hist.mean() else 0.0)
def analyze(context, perf):
returns, positions, transactions = \ pf.utils.extract_rets_pos_txn_from_zipline(perf) pf.create_returns_tear_sheet(returns,
benchmark_rets = None)
start_date = pd.to_datetime('2000-1-1', utc=True) end_date = pd.to_datetime('2018-1-1', utc=True)
results = run_algorithm(start = start_date, end = end_date, initialize = initialize, 
analyze = analyze,
handle_data = handle_data,
capital_base = 10000,
data_frequency = 'daily',
bundle ='quandl')
250 Fundamental Algorithmic Trading Strategies
e outputs are as follows:
Figure 9.1 Rolling window mean strategy; summary return and risk statistics
When assessing a trading strategy, the preceding statistics are the first step. Each provides a different view on the strategy performance:
Sharpe ratio: is is a measure of excess return versus standard deviation of the
excess return. e higher the ratio, the better the algorithm performed on a risk- adjusted basis.
Calmar ratio: is is a measure of the average compounded annual rate of return
versus its maximum drawdown. e higher the ratio, the better the algorithm performed on a risk-adjusted basis.
Learning momentum-based/trend-following strategies 251
Stability: is is defined as the R-squared value of a linear fit to the cumulative log
returns. e higher the number, the higher the trend in the cumulative returns.
Omega ratio: is is defined as the probability weighted ratio of gains versus losses.
It is a generalization of the Sharpe ratio, taking into consideration all moments of the distribution. e higher the ratio, the better the algorithm performed on a risk- adjusted basis.
Sortino ratio: is is a variation of the Sharpe ratio it uses only the standard
deviation of the negative portfolio returns (downside risk). e higher the ratio, the better the algorithm performed on a risk-adjusted basis.
Tail ratio: is is defined as the ratio between the right 95% and the le tail 5%. For
example, a ratio of 1/3 means that the losses are three times worse than the profits. e higher the number, the better.
In this example, we see that the strategy has a very high stability (.92) over the trading window, which somewhat offsets the high maximum drawdown (-59.4%). e tail ratio is most favorable:
Figure 9.2 Rolling window mean strategy; worst five drawdown periods
252 Fundamental Algorithmic Trading Strategies
While the worst maximum drawdown of 59.37% is certainly not good, if we adjusted the entry/exit strategy rules, we would most likely avoid it. Notice the duration of the drawdown periods more than 3 years in the maximum drawdown period.
Figure 9.3 Rolling window mean strategy; cumulative returns over the investment horizon
As the stability measure confirms, we see a positive trend in the cumulative returns over the trading horizon.
Figure 9.4 Rolling window mean strategy; returns over the investment horizon
Learning momentum-based/trend-following strategies 253
e chart confirms that the returns oscillate widely around zero.
Figure 9.5 Rolling window mean strategy; 6-month rolling volatility over the investment horizon
is chart illustrates that the strategy’s return volatility is decreasing over the time horizon.
Figure 9.6 Rolling window mean strategy; 6-month rolling Sharpe ratio over the investment horizon
We see that the maximum Sharpe ratio of the strategy is above 4, with its minimum value below -2. If we reviewed the entry/exit rules, we should be able to improve the strategy’s performance.
Figure 9.7 Rolling window mean strategy; top five drawdown periods over the investment horizon
254 Fundamental Algorithmic Trading Strategies
A graphical representation of the maximum drawdown indicates that the periods of maximum drawdown are overly long.
Figure 9.8 Rolling window mean strategy; monthly returns, annual returns, and the distribution of monthly returns over the investment horizon
e Monthly returns chart shows that we have traded during most months. e
Annual returns bar chart shows that the returns are overwhelmingly positive, while the Distribution of monthly returns chart shows that the skew is positive to the right.
e rolling window mean strategy is one of the simplest strategies and is still very profitable for certain combinations of stocks and time frames. Notice that the maximum drawdown for this strategy is significant and may be improved if we added more advanced entry/exit rules.
Simple moving averages strategy
is strategy follows a simple rule: buy the stock if the short-term moving averages rise above the long-term moving averages:
%matplotlib inline
from zipline import run_algorithm
from zipline.api import order_target_percent, symbol, set_ commission
from zipline.finance.commission import PerTrade import pandas as pd
import pyfolio as pf
import warnings warnings.filterwarnings('ignore')
Learning momentum-based/trend-following strategies 255
def initialize(context): 
context.stock = symbol('AAPL')
context.rolling_window = 90 set_commission(PerTrade(cost=5))
def handle_data(context, data):
price_hist = data.history(context.stock, "close",
context.rolling_window, "1d")
price_hist.rolling(window=45, center=False).mean() rolling_mean_long_term = \
price_hist.rolling(window=90, center=False).mean()
if rolling_mean_short_term[-1] > rolling_mean_long_term[- 1]:
order_target_percent(context.stock, 1.0)
elif rolling_mean_short_term[-1] < rolling_mean_long_term[- 1]:
order_target_percent(context.stock, 0.0)
def analyze(context, perf):
returns, positions, transactions = \ pf.utils.extract_rets_pos_txn_from_zipline(perf) pf.create_returns_tear_sheet(returns,
benchmark_rets = None)
start_date = pd.to_datetime('2000-1-1', utc=True) end_date = pd.to_datetime('2018-1-1', utc=True)
results = run_algorithm(start = start_date, end = end_date, initialize = initialize, 
analyze = analyze,
handle_data = handle_data,
capital_base = 10000,
data_frequency = 'daily',
bundle ='quandl')
256 Fundamental Algorithmic Trading Strategies
e outputs are as follows:
Figure 9.9 Simple moving averages strategy; summary return and risk statistics
e statistics show that the strategy is overwhelmingly profitable in the long term (high stability and tail ratios), while the maximum drawdown can be substantial.
Figure 9.10 Simple moving averages strategy; worst five drawdown periods
Learning momentum-based/trend-following strategies 257
e worst drawdown periods are rather long more than 335 days, with some even taking more than 3 years in the worst case.
Figure 9.11 Simple moving averages strategy; cumulative returns over the investment horizon
is chart does, however, confirm that this long-term strategy is profitable we see the cumulative returns grow consistently a er the first drawdown.
Figure 9.12 Simple moving averages strategy; returns over the investment horizon
258 Fundamental Algorithmic Trading Strategies
e chart illustrates that there was a major negative return event at the very start of the trading window and then the returns oscillate around zero.
Figure 9.13 Simple moving averages strategy; 6-month rolling volatility over the investment horizon
e rolling volatility chart shows that the rolling volatility is decreasing with time.
Figure 9.14 Simple moving averages strategy; 6-month rolling Sharpe ratio over the investment horizon
While the maximum Sharpe ratio was over 4, with the minimum equivalent being below -4, the average Sharpe ratio was 0.68.
Figure 9.15 Simple moving averages strategy; top five drawdown periods over the investment horizon
Learning momentum-based/trend-following strategies 259
is chart confirms that the maximum drawdown periods were very long.
Figure 9.16 Simple moving averages strategy; monthly returns, annual returns, and the distribution of monthly returns over the investment horizon
e monthly returns table shows that there was no trade across many months. e annual returns were mostly positive. e Distribution of monthly returns chart confirms that the skew is negative.
e simple moving averages strategy is less profitable and has a greater maximum drawdown than the rolling window mean strategy. One reason may be that the rolling window for the moving averages is too large.
Exponentially weighted moving averages strategy
is strategy is similar to the previous one, with the exception of using different rolling windows and exponentially weighted moving averages. e results are slightly better than those achieved under the previous strategy.
Some other moving average algorithms use both simple moving averages and exponentially weighted moving averages in the decision rule; for example, if the simple moving average is greater than the exponentially weighted moving average, make a move:
%matplotlib inline
from zipline import run_algorithm
from zipline.api import order_target_percent, symbol, set_ commission
from zipline.finance.commission import PerTrade import pandas as pd
260 Fundamental Algorithmic Trading Strategies
import warnings warnings.filterwarnings('ignore')
def initialize(context):
context.stock = symbol('AAPL')
context.rolling_window = 90 set_commission(PerTrade(cost=5))
def handle_data(context, data):
price_hist = data.history(context.stock, "close",
context.rolling_window, "1d")
price_hist.ewm(span=5, adjust=True, ignore_na=True).mean() rolling_mean_long_term = \
price_hist.ewm(span=30, adjust=True, ignore_na=True).mean()
if rolling_mean_short_term[-1] > rolling_mean_long_term[- 1]:
order_target_percent(context.stock, 1.0)
elif rolling_mean_short_term[-1] < rolling_mean_long_term[- 1]:
order_target_percent(context.stock, 0.0)
def analyze(context, perf):
returns, positions, transactions = \ pf.utils.extract_rets_pos_txn_from_zipline(perf) pf.create_returns_tear_sheet(returns,
benchmark_rets = None)
start_date = pd.to_datetime('2000-1-1', utc=True) end_date = pd.to_datetime('2018-1-1', utc=True)
results = run_algorithm(start = start_date, end = end_date, initialize = initialize, 
Learning momentum-based/trend-following strategies 261
analyze = analyze, 
handle_data = handle_data, capital_base = 10000,
data_frequency = 'daily', bundle ='quandl')
e outputs are as follows:
Figure 9.17 Exponentially weighted moving averages strategy; summary return and risk statistics
262 Fundamental Algorithmic Trading Strategies
e results show that the level of maximum drawdown has dropped from the previous strategies, while still keeping very strong stability and tail ratios.
Figure 9.18 Exponentially weighted moving averages strategy; worst five drawdown periods
e magnitude of the worst drawdown, as well as its maximum duration in days, is far better than for the previous two strategies.
Figure 9.19 Exponentially weighted moving averages strategy; cumulative returns
over the investment horizon
Learning momentum-based/trend-following strategies 263
As the stability indicator shows, we see consistent positive cumulative returns.
Figure 9.20 Exponentially weighted moving averages strategy; returns over the investment horizon
e returns oscillate around zero, being more positive than negative.
Figure 9.21 Exponentially weighted moving averages strategy; 6-month rolling
volatility over the investment horizon
e rolling volatility is dropping over time.
Figure 9.22 Exponentially weighted moving averages strategy; 6-month rolling
Sharpe ratio over the investment horizon
264 Fundamental Algorithmic Trading Strategies
We see that the maximum Sharpe ratio reached almost 5, while the minimum was slightly below -2, which again is better than for the two previous algorithms.
Figure 9.23 Exponentially weighted moving averages strategy; top five drawdown
periods over the investment horizon
Notice that the periods of the worst drawdown are not identical for the last three algorithms.
Figure 9.24 Exponentially weighted moving averages strategy; monthly returns, annual returns,
and the distribution of monthly returns over the investment horizon
e Monthly returns table shows that we have traded in most months. e Annual returns chart confirms that most returns have been positive. e Distribution of monthly returns chart is positively skewed, which is a good sign.
e exponentially weighted moving averages strategy performs better for Apple’s stock over the given time frame. However, in general, the most suitable averages strategy depends on the stock and the time frame.
Learning momentum-based/trend-following strategies 265
RSI strategy
is strategy depends on the stockstats package. It is very instructive to read the source code at https://github.com/intrad/stockstats/blob/master/ stockstats.py.
To install it, use the following command:
pip install stockstats
e RSI indicator measures the velocity and magnitude of price movements and provides an indicator when a financial asset is oversold or overbought. It is a leading indicator.
It is measured from 0 to 100, with values over 70 indicating overbought, and values below 30 oversold:
%matplotlib inline
from zipline import run_algorithm
from zipline.api import order_target_percent, symbol, set_ commission
from zipline.finance.commission import PerTrade import pandas as pd
import pyfolio as pf
from stockstats import StockDataFrame as sdf
import warnings warnings.filterwarnings('ignore')
def initialize(context):
context.stock = symbol('AAPL')
context.rolling_window = 20 set_commission(PerTrade(cost=5))
def handle_data(context, data):
price_hist = data.history(context.stock,
["open", "high", "low","close"],
266 Fundamental Algorithmic Trading Strategies
stock=sdf.retype(price_hist) 
rsi = stock.get('rsi_12')
if rsi[-1] > 90:
order_target_percent(context.stock, 0.0) elif rsi[-1] < 10:
order_target_percent(context.stock, 1.0)
def analyze(context, perf):
returns, positions, transactions = \ pf.utils.extract_rets_pos_txn_from_zipline(perf) pf.create_returns_tear_sheet(returns,
benchmark_rets = None)
start_date = pd.to_datetime('2015-1-1', utc=True) end_date = pd.to_datetime('2018-1-1', utc=True)
results = run_algorithm(start = start_date, end = end_date, initialize = initialize, 
analyze = analyze,
handle_data = handle_data,
capital_base = 10000,
data_frequency = 'daily',
bundle ='quandl')
Learning momentum-based/trend-following strategies 267
e outputs are as follows:
Figure 9.25 RSI strategy; summary return and risk statistics
e first look at the strategy shows an excellent Sharpe ratio, with a very low maximum drawdown and a favorable tail ratio.
Figure 9.26 RSI strategy; worst five drawdown periods
268 Fundamental Algorithmic Trading Strategies
e worst drawdown periods were very short less than 2 months and not substantial a maximum drawdown of only -10.55%.
Figure 9.27 RSI strategy; cumulative returns over the investment horizon
e Cumulative returns chart shows that we have not traded across most of the trading horizon and when we did trade, there was a positive trend in the cumulative returns.
Figure 9.28 RSI strategy; returns over the investment horizon
Learning momentum-based/trend-following strategies 269
We can see that when we traded, the returns were more likely to be positive than negative.
Figure 9.29 RSI strategy; 6-month rolling volatility over the investment horizon
Notice that the maximum rolling volatility of 0.2 is far lower than for the previous strategies.
Figure 9.30 RSI strategy; 6-month rolling Sharpe ratio over the investment horizon
We can see that Sharpe’s ratio has consistently been over 1, with its maximum value over 3 and its minimum value below -1.
Figure 9.31 RSI strategy; top five drawdown periods over the investment horizon
270 Fundamental Algorithmic Trading Strategies
e chart illustrates short and insignificant drawdown periods.
Figure 9.32 RSI strategy; monthly returns, annual returns, and the distribution of monthly returns over the investment horizon
e Monthly returns table states that we have not traded in most months. However, according to the Annual returns chart, when we traded, we were hugely profitable. e Distribution of monthly returns chart confirms that the skew is hugely positive, with a large kurtosis.
e RSI strategy is highly performant in the case of Apple’s stock over the given time frame, with a Sharpe ratio of 1.11. Notice, however, that the success of the strategy depends largely on the very strict entry/exit rules, meaning we are not trading in certain months at all.
MACD crossover strategy
Moving Average Convergence Divergence (MACD) is a lagging, trend-following momentum indicator reflecting the relationship between two moving averages of stock prices.
Learning momentum-based/trend-following strategies 271
e strategy depends on two statistics, the MACD and the MACD signal line:
e MACD is defined as the difference between the 12-day exponential moving
average and the 26-day exponential moving average.
e MACD signal line is then defined as the 9-day exponential moving average of
the MACD.
e MACD crossover strategy is defined as follows:
A bullish crossover happens when the MACD line turns upward and crosses beyond
the MACD signal line.
A bearish crossover happens when the MACD line turns downward and crosses
under the MACD signal line.
Consequently, this strategy is best suited for volatile, highly traded markets:
%matplotlib inline
from zipline import run_algorithm
from zipline.api import order_target_percent, symbol, set_ commission
from zipline.finance.commission import PerTrade import pandas as pd
import pyfolio as pf
from stockstats import StockDataFrame as sdf
import warnings warnings.filterwarnings('ignore')
def initialize(context):
context.stock = symbol('AAPL')
context.rolling_window = 20 set_commission(PerTrade(cost=5))
def handle_data(context, data):
price_hist = data.history(context.stock, ["open","high", "low","close"],
272 Fundamental Algorithmic Trading Strategies
context.rolling_window, "1d") stock=sdf.retype(price_hist) 
signal = stock['macds'] macd = stock['macd']
if macd[-1] > signal[-1] and macd[-2] <= signal[-2]:
order_target_percent(context.stock, 1.0)
elif macd[-1] < signal[-1] and macd[-2] >= signal[-2]: order_target_percent(context.stock, 0.0) 
def analyze(context, perf):
returns, positions, transactions = \ pf.utils.extract_rets_pos_txn_from_zipline(perf) pf.create_returns_tear_sheet(returns,
benchmark_rets = None)
start_date = pd.to_datetime('2015-1-1', utc=True) end_date = pd.to_datetime('2018-1-1', utc=True)
results = run_algorithm(start = start_date, end = end_date, initialize = initialize, 
analyze = analyze,
handle_data = handle_data,
capital_base = 10000,
data_frequency = 'daily',
bundle ='quandl')
Learning momentum-based/trend-following strategies 273
e outputs are as follows:
Figure 9.33 MACD crossover strategy; summary return and risk statistics
e tail ratio illustrates that the top gains and losses are roughly of the same magnitude. e very low stability indicates that there is no strong trend in cumulative returns.
Figure 9.34 MACD crossover strategy; worst five drawdown periods
274 Fundamental Algorithmic Trading Strategies
Apart from the worst drawdown period, the other periods were shorter than 6 months, with a net drawdown lower than 10%.
Figure 9.35 MACD crossover strategy; cumulative returns over the investment horizon
e Cumulative returns chart confirms the low stability indicator value. e following is the Returns chart:
Figure 9.36 MACD crossover strategy; returns over the investment horizon
e Returns chart shows that returns oscillated widely around zero, with a few outliers.
Learning momentum-based/trend-following strategies 275
e following is the Rolling volatility chart:
Figure 9.37 MACD crossover strategy; 6-month rolling volatility over the investment horizon
e rolling volatility has been oscillating around 0.15. e following is the rolling Sharpe ratio chart:
Figure 9.38 MACD crossover strategy; 6-month rolling Sharpe ratio over the investment horizon
e maximum rolling Sharpe ratio of about 4, with a minimum ratio of -2, is largely favorable.
e following is the top five drawdown periods chart:
Figure 9.39 MACD crossover strategy; top five drawdown periods over the investment horizon
276 Fundamental Algorithmic Trading Strategies
We see that the worst two drawdown periods have been rather long.
Figure 9.40 MACD crossover strategy; monthly returns, annual returns, and the distribution of monthly returns over the investment horizon
e Monthly returns table confirms that we have traded across most months. e Annual returns chart indicates that the most profitable year was 2017. e Distribution of monthly returns chart shows a slight negative skew and large kurtosis.
e MACD crossover strategy is an effective strategy in trending markets and can be significantly improved by raising the entry/exit rules.
RSI and MACD strategies
In this strategy, we combine the RSI and MACD strategies and own the stock if both RSI and MACD criteria provide a signal to buy.
Using multiple criteria provides a more complete view of the market (note that we generalize the RSI threshold values to 50):
%matplotlib inline
from zipline import run_algorithm
from zipline.api import order_target_percent, symbol, set_ commission
from zipline.finance.commission import PerTrade import pandas as pd
import pyfolio as pf
from stockstats import StockDataFrame as sdf
Learning momentum-based/trend-following strategies 277
warnings.filterwarnings('ignore')
def initialize(context):
context.stock = symbol('MSFT')
context.rolling_window = 20 set_commission(PerTrade(cost=5))
def handle_data(context, data):
price_hist = data.history(context.stock,
["open", "high", "low","close"],
context.rolling_window, "1d")
stock=sdf.retype(price_hist) 
rsi = stock.get('rsi_12')
signal = stock['macds'] macd = stock['macd']
if rsi[-1] < 50 and macd[-1] > signal[-1] and macd[-2] <= signal[-2]:
order_target_percent(context.stock, 1.0)
elif rsi[-1] > 50 and macd[-1] < signal[-1] and macd[-2] >= signal[-2]:
order_target_percent(context.stock, 0.0)
def analyze(context, perf):
returns, positions, transactions = \ pf.utils.extract_rets_pos_txn_from_zipline(perf) pf.create_returns_tear_sheet(returns,
benchmark_rets = None)
start_date = pd.to_datetime('2015-1-1', utc=True) end_date = pd.to_datetime('2018-1-1', utc=True)
278 Fundamental Algorithmic Trading Strategies
results = run_algorithm(start = start_date, end = end_date, initialize = initialize, 
analyze = analyze,
handle_data = handle_data,
capital_base = 10000,
data_frequency = 'daily',
bundle ='quandl')
e outputs are as follows:
Figure 9.41 RSI and MACD strategies; summary return and risk statistics
e high stability value, with a high tail ratio and excellent Sharpe ratio, as well as a low maximum drawdown, indicates that the strategy is excellent.
Learning momentum-based/trend-following strategies 279
e following is the worst five drawdown periods chart:
Figure 9.42 RSI and MACD strategies; worst five drawdown periods
We see that the worst drawdown periods were short less than 4 months with the worst net drawdown of -10.36%.
e following is the Cumulative returns chart:
Figure 9.43 RSI and MACD strategies; cumulative returns over the investment horizon
e high stability value is favorable. Notice the horizontal lines in the chart; these indicate that we have not traded.
280 Fundamental Algorithmic Trading Strategies
e following is the Returns chart:
Figure 9.44 RSI and MACD strategies; returns over the investment horizon
e Returns chart shows that when we traded, the positive returns outweighed the negative ones.
e following is the Rolling volatility chart:
Figure 9.45 RSI and MACD strategies; 6-month rolling volatility over the investment horizon
e rolling volatility has been decreasing over time and has been relatively low. e following is the Rolling Sharpe ratio chart:
Figure 9.46 RSI and MACD strategies; 6-month rolling Sharpe ratio over the investment horizon
Learning momentum-based/trend-following strategies 281
e maximum rolling Sharpe ratio was over 3, with a minimum of below -2 and an average above 1.0 indicative of a very good result.
e following is the Top 5 drawdown periods chart:
Figure 9.47 RSI and MACD strategies; top five drawdown periods over the investment horizon
We see that the drawdown periods were short and not significant.
e following are the Monthly returns, Annual returns, and Distribution of monthly returns charts:
Figure 9.48 RSI and MACD strategies; monthly returns, annual returns, and the distribution of monthly returns over the investment horizon
e Monthly returns table confirms we have not traded in most months. However, according to the Annual returns chart, when we did trade, it was hugely profitable. e Distribution of monthly returns chart is positive, with high kurtosis.
e RSI and MACD strategy, as a combination of two strategies, demonstrates excellent performance, with a Sharpe ratio of 1.27 and a maximum drawdown of -10.4%. Notice that it does not trigger any trading in some months.
282 Fundamental Algorithmic Trading Strategies
Triple exponential average strategy
e Triple Exponential Average (TRIX) indicator is an oscillator oscillating around the zero line. A positive value indicates an overbought market, whereas a negative value is
indicative of an oversold market:
%matplotlib inline
from zipline import run_algorithm
from zipline.api import order_target_percent, symbol, set_ commission
from zipline.finance.commission import PerTrade import pandas as pd
import pyfolio as pf
from stockstats import StockDataFrame as sdf
import warnings warnings.filterwarnings('ignore')
def initialize(context):
context.stock = symbol('MSFT')
context.rolling_window = 20 set_commission(PerTrade(cost=5))
def handle_data(context, data):
price_hist = data.history(context.stock, ["open","high", "low","close"],
context.rolling_window, "1d")
stock=sdf.retype(price_hist) 
trix = stock.get('trix')
if trix[-1] > 0 and trix[-2] < 0:
order_target_percent(context.stock, 0.0) elif trix[-1] < 0 and trix[-2] > 0:
order_target_percent(context.stock, 1.0)
Learning momentum-based/trend-following strategies 283
def analyze(context, perf):
returns, positions, transactions = \ pf.utils.extract_rets_pos_txn_from_zipline(perf) pf.create_returns_tear_sheet(returns,
benchmark_rets = None)
start_date = pd.to_datetime('2015-1-1', utc=True) end_date = pd.to_datetime('2018-1-1', utc=True)
results = run_algorithm(start = start_date, end = end_date, initialize = initialize, 
analyze = analyze,
handle_data = handle_data,
capital_base = 10000,
data_frequency = 'daily',
bundle ='quandl')
e outputs are as follows:
Figure 9.49 TRIX strategy; summary return and risk statistics
284 Fundamental Algorithmic Trading Strategies
e high tail ratio with an above average stability suggests, in general, a profitable strategy. e following is the worst five drawdown periods chart:
Figure 9.50 TRIX strategy; worst five drawdown periods
e second worst drawdown period was over a year. e worst net drawdown was -15.57%.
e following is the Cumulative returns chart:
Figure 9.51 TRIX strategy; cumulative returns over the investment horizon
Learning momentum-based/trend-following strategies 285
e Cumulative returns chart indicates that we have not traded in many months (the horizontal line) and that there is a long-term positive trend, as confirmed by the high stability value.
e following is the Returns chart:
Figure 9.52 TRIX strategy; returns over the investment horizon
is chart suggests that when we traded, we were more likely to reach a positive return. e following is the Rolling volatility chart:
Figure 9.53 TRIX strategy; 6-month rolling volatility over the investment horizon
e Rolling volatility chart shows that the rolling volatility has been decreasing with time, although the maximum volatility has been rather high.
e following is the Rolling Sharpe ratio chart:
Figure 9.54 TRIX strategy; 6-month rolling Sharpe ratio over the investment horizon
286 Fundamental Algorithmic Trading Strategies
e rolling Sharpe ratio has been more likely to be positive than negative, with its maximum value in the region of 3 and a minimum value slightly below -1.
e following is the top five drawdown periods chart:
Figure 9.55 TRIX strategy; top five drawdown periods over the investment horizon
e top five drawdown periods confirm that the worst drawdown periods have been long.
e following are the Monthly returns, Annual returns, and Distribution of monthly returns charts:
Figure 9.56 TRIX strategy; monthly returns, annual returns, and the distribution of monthly returns over the investment horizon
e Monthly returns table confirms that we have not traded in many months. e Annual returns chart shows that the maximum return was in the year 2015. e Distribution of monthly returns chart shows a very slightly positive skew with a somewhat large kurtosis.
Learning momentum-based/trend-following strategies 287
e TRIX strategy’s performance for some stocks, such as Apple, is very bad over the given time frame. For other stocks such as Microso , included in the preceding report, performance is excellent for certain years.
Williams R% strategy
is strategy was developed by Larry Williams, and the William R% oscillates from 0 to -100. e stockstats library has implemented the values from 0 to +100.
e values above -20 indicate that the security has been overbought, while values below -80 indicate that the security has been oversold.
is strategy is hugely successful for Microso ’s stock, while not so much for Apple’s stock:
%matplotlib inline
from zipline import run_algorithm
from zipline.api import order_target_percent, symbol, set_ commission
from zipline.finance.commission import PerTrade import pandas as pd
import pyfolio as pf
from stockstats import StockDataFrame as sdf
import warnings warnings.filterwarnings('ignore')
def initialize(context):
context.stock = symbol('MSFT')
context.rolling_window = 20 set_commission(PerTrade(cost=5))
def handle_data(context, data):
price_hist = data.history(context.stock,
["open", "high", "low","close"],
288 Fundamental Algorithmic Trading Strategies
stock=sdf.retype(price_hist) wr = stock.get('wr_6')
if wr[-1] < 10:
order_target_percent(context.stock, 0.0) elif wr[-1] > 90:
order_target_percent(context.stock, 1.0)
def analyze(context, perf):
returns, positions, transactions = \ pf.utils.extract_rets_pos_txn_from_zipline(perf) pf.create_returns_tear_sheet(returns,
benchmark_rets = None)
start_date = pd.to_datetime('2015-1-1', utc=True) end_date = pd.to_datetime('2018-1-1', utc=True)
results = run_algorithm(start = start_date, end = end_date, initialize = initialize,
analyze = analyze,
handle_data = handle_data,
capital_base = 10000,
data_frequency = 'daily',
bundle ='quandl')
Learning momentum-based/trend-following strategies 289
e outputs are as follows:
Figure 9.57 Williams R% strategy; summary return and risk statistics
e summary statistics show an excellent strategy high stability confirms consistency in the returns, with a large tail ratio, a very low maximum drawdown, and a solid Sharpe ratio.
e following is the worst five drawdown periods chart:
Figure 9.58 Williams R% strategy; worst five drawdown periods
290 Fundamental Algorithmic Trading Strategies
Apart from the worst drawdown period lasting about 3 months with a net drawdown of -10%, the other periods were insignificant in both duration and magnitude.
e following is the Cumulative returns chart:
Figure 9.59 Williams R% strategy; cumulative returns over the investment horizon
is chart confirms the high stability value of the strategy the cumulative returns are growing at a steady rate.
e following is the Returns chart:
Figure 9.60 Williams R% strategy; returns over the investment horizon
e Returns chart indicates that whenever we traded, it was more profitable than not.
Learning momentum-based/trend-following strategies 291
e following is the Rolling volatility chart:
Figure 9.61 Williams R% strategy; 6-month rolling volatility over the investment horizon
e Rolling volatility chart shows a decreasing value of rolling volatility over time. e following is the Rolling Sharpe ratio chart:
Figure 9.62 Williams R% strategy; 6-month rolling Sharpe ratio over the investment horizon
e Rolling Sharpe ratio chart confirms that the Sharpe ratio has been positive over the trading horizon, with a maximum value of 3.0.
e following is the top five drawdown periods chart:
Figure 9.63 Williams R% strategy; top five drawdown periods over the investment horizon
292 Fundamental Algorithmic Trading Strategies
e Top 5 drawdown periods chart shows that apart from one period, the other worst drawdown periods were not significant.
e following are the Monthly returns, Annual returns, and Distribution of monthly returns charts:
Figure 9.64 Williams R% strategy; monthly returns, annual returns, and the distribution of monthly returns over the investment horizon
e Monthly returns table suggests that while we have not traded in every month, whenever we did trade, it was largely profitable. e Annual returns chart confirms this. e Distribution of monthly returns chart confirms a positive skew with a large kurtosis.
e Williams R% strategy is a highly performant strategy for the Microso stock with a Sharpe ratio of 1.53 and a maximum drawdown of only -10% over the given time frame.
Learning mean-reversion strategies
Mean-reversion strategies are based on the assumption that some statistics will revert to their long-term mean values.
Bollinger band strategy
e Bollinger band strategy is based on identifying periods of short-term volatility.
Learning mean-reversion strategies 293
It depends on three lines:
e middle band line is the simple moving average, usually 20-50 days. e upper band is the 2 standard deviations above the middle base line. e lower band is the 2 standard deviations below the middle base line.
One way of creating trading signals from Bollinger bands is to define the overbought and oversold market state:
e market is overbought when the price of the financial asset rises above the upper
band and so is due for a pullback.
e market is oversold when the price of the financial asset drops below the lower
band and so is due to bounce back.
is is a mean-reversion strategy, meaning that long term, the price should remain within the lower and upper bands. It works best for low-volatility stocks:
%matplotlib inline
from zipline import run_algorithm
from zipline.api import order_target_percent, symbol, set_ commission
from zipline.finance.commission import PerTrade import pandas as pd
import pyfolio as pf
import warnings warnings.filterwarnings('ignore')
def initialize(context):
context.stock = symbol('DG')
context.rolling_window = 20 set_commission(PerTrade(cost=5))
def handle_data(context, data):
price_hist = data.history(context.stock, "close",
context.rolling_window, "1d")
294 Fundamental Algorithmic Trading Strategies
middle_base_line = price_hist.mean()
std_line = price_hist.std()
lower_band = middle_base_line - 2 * std_line upper_band = middle_base_line + 2 * std_line
if price_hist[-1] < lower_band:
order_target_percent(context.stock, 1.0) elif price_hist[-1] > upper_band:
order_target_percent(context.stock, 0.0)
def analyze(context, perf):
returns, positions, transactions = \ pf.utils.extract_rets_pos_txn_from_zipline(perf) pf.create_returns_tear_sheet(returns,
benchmark_rets = None)
start_date = pd.to_datetime('2000-1-1', utc=True) end_date = pd.to_datetime('2018-1-1', utc=True)
results = run_algorithm(start = start_date, end = end_date, initialize = initialize, 
analyze = analyze,
handle_data = handle_data,
capital_base = 10000,
data_frequency = 'daily',
bundle ='quandl')
Learning mean-reversion strategies 295
e outputs are as follows:
Figure 9.65 Bollinger band strategy; summary return and risk statistics
e summary statistics do show that the stability is solid, with the tail ratio favorable. However, the max drawdown is a substantial -27.3%.
e following is the worst five drawdown periods chart:
Figure 9.66 Bollinger band strategy; worst five drawdown periods
296 Fundamental Algorithmic Trading Strategies
e duration of the worst drawdown periods is substantial. Maybe we should tweak the entry/exit rules to avoid entering the trades in these periods.
e following is the Cumulative returns chart:
Figure 9.67 Bollinger band strategy; cumulative returns over the investment horizon
e Cumulative returns chart show we have not traded for 10 years and then we have experienced a consistent positive trend in cumulative returns.
e following is the Returns chart:
Figure 9.68 Bollinger band strategy; returns over the investment horizon
e Returns chart shows that the positive returns have outweighed the negative ones.
Learning mean-reversion strategies 297
e following is the Rolling volatility chart:
Figure 9.69 Bollinger band strategy; 6-month rolling volatility over the investment horizon
e Rolling volatility chart suggests that the strategy has substantial volatility. e following is the Rolling Sharpe ratio chart:
Figure 9.70 Bollinger band strategy; 6-month rolling Sharpe ratio over the investment horizon
e Rolling Sharpe ratio chart shows that the rolling Sharpe ratio fluctuates widely with a max value of close to 4 and a minimum below -2, but on average it is positive.
e following is the Top 5 drawdown periods chart:
Figure 9.71 Bollinger band strategy; top five drawdown periods over the investment horizon
298 Fundamental Algorithmic Trading Strategies
e Top 5 drawdown periods chart confirms the drawdown periods duration has been substantial.
e following are the Monthly returns, Annual returns, and Distribution of monthly returns charts:
Figure 9.72 Bollinger band strategy; monthly returns, annual returns, and the distribution of monthly returns over the investment horizon
e Monthly returns table shows that there has been no trade from 2000 to 2010 due to our entry/exit rules. e Annual returns chart, however, shows that whenever a trade did happen, it was profitable. e Distribution of monthly returns chart shows slight negative skew with enormous kurtosis.
e Bollinger band strategy is a suitable strategy for oscillating stocks. Here, we applied it to the stock of Dollar General (DG) Corp.
Pairs trading strategy
is strategy became very popular some time ago and ever since, has been overused, so is barely profitable nowadays.
is strategy involves finding pairs of stocks that are moving closely together, or are highly co-integrated. en, at the same time, we place a BUY order for one stock and a SELL
order for the other stock, assuming their relationship will revert back. ere are a wide range of varieties of tweaks in terms of how this algorithm is implemented are the prices log prices? Do we trade only if the relationships are very strong?
Learning mean-reversion strategies 299
For simplicity, we have chosen the Pepsi Cola (PEP) and Coca-Cola (KO) stocks. Another choice could be Citibank (C) and Goldman Sachs (GS). We have two conditions: first, the p-value of cointegration has to be very strong, and then the z-score
has to be very strong: %matplotlib inline
from zipline import run_algorithm
from zipline.api import order_target_percent, symbol, set_ commission
from zipline.finance.commission import PerTrade import pandas as pd
import pyfolio as pf
import numpy as np
import statsmodels.api as sm
from statsmodels.tsa.stattools import coint
import warnings warnings.filterwarnings('ignore')
def initialize(context):
context.stock_x = symbol('PEP')
context.stock_y = symbol('KO')
context.rolling_window = 500 set_commission(PerTrade(cost=5)) context.i = 0
def handle_data(context, data):
context.i += 1
if context.i < context.rolling_window: return
try:
x_price = data.history(context.stock_x, "close", context.rolling_window,"1d") x = np.log(x_price)
300 Fundamental Algorithmic Trading Strategies
y_price = data.history(context.stock_y, "close", 
context.rolling_window,"1d") y = np.log(y_price)
_, p_value, _ = coint(x, y) if p_value < .9: return
slope, intercept = sm.OLS(y, sm.add_constant(x, prepend=True)).fit().params
spread = y - (slope * x + intercept)
zscore = (\
spread[-1] - spread.mean()) / spread.std()
if -1 < zscore < 1: return
side = np.copysign(0.5, zscore) order_target_percent(context.stock_y,
-side * 100 / y_price[-1]) order_target_percent(context.stock_x,
side * slope*100/x_price[-1]) except:
pass
def analyze(context, perf):
returns, positions, transactions = \ pf.utils.extract_rets_pos_txn_from_zipline(perf) pf.create_returns_tear_sheet(returns,
benchmark_rets = None)
start_date = pd.to_datetime('2015-1-1', utc=True) end_date = pd.to_datetime('2018-01-01', utc=True)
Learning mean-reversion strategies 301
results = run_algorithm(start = start_date, end = end_date, initialize = initialize,
analyze = analyze,
handle_data = handle_data,
capital_base = 10000,
data_frequency = 'daily',
bundle ='quandl')
e outputs are as follows:
Figure 9.73 Pairs trading strategy; summary return and risk statistics
While the Sharpe ratio is very low, the max drawdown is also very low. e stability is average.
302 Fundamental Algorithmic Trading Strategies
e following is the worst five drawdown periods chart:
Figure 9.74 Pairs trading strategy; worst five drawdown periods
e worst five drawdown periods table shows that the max drawdown was negligible and very short.
e following is the Cumulative returns chart:
Figure 9.75 Pairs trading strategy; cumulative returns over the investment horizon
e Cumulative returns chart indicates that we have not traded for 2 years and then were hugely profitable until the last period.
Learning mean-reversion strategies 303
e following is the Returns chart:
Figure 9.76 Pairs trading strategy; returns over the investment horizon
e Returns chart shows that the returns have been more positive than negative for the trading period except for the last period.
e following is the Rolling volatility chart:
Figure 9.77 Pairs trading strategy; 6-month rolling volatility over the investment horizon
e Rolling volatility chart shows an ever-increasing volatility though the volatility magnitude is not significant.
e following is the Rolling Sharpe ratio chart:
Figure 9.78 Pairs trading strategy; 6-month rolling Sharpe ratio over the investment horizon
304 Fundamental Algorithmic Trading Strategies
e Rolling Sharpe ratio chart shows that if we improved our exit rule and exited earlier, our Sharpe ratio would higher than 1.
e following is the Top 5 drawdown periods chart:
Figure 9.79 Pairs trading strategy; top five drawdown periods over the investment horizon
e Top 5 drawdown periods chart tells us the same story the last period was the cause of why this backtesting result is not as successful as it could have been.
e following are the Monthly returns, Annual returns, and Distribution of monthly returns charts:
Figure 9.80 Pairs trading strategy; monthly returns, annual returns, and the distribution of monthly returns over the investment horizon
e Monthly returns table confirms we have not traded until the year of 2017. e
Annual returns chart shows that the trading in 2017 was successful and the Distribution of monthly returns chart shows a slightly negatively skewed chart with small kurtosis.
e pairs trading strategy has been overused over the last decade, and so is less profitable. One simple way of identifying the pair is to look for competitors in this example, PepsiCo and the Coca-Cola Corporation.
Learning mathematical model-based strategies 305
Learning mathematical model-based strategies
We will now look at the various mathematical model-based strategies in the following sections.
Minimization of the portfolio volatility strategy with monthly trading
e objective of this strategy is to minimize portfolio volatility. It has been inspired by https://github.com/letianzj/QuantResearch/tree/master/backtest.
In the following example, the portfolio consists of all stocks in the Dow Jones Industrial Average index.
e key success factors of the strategy are the following:
e stock universe perhaps a portfolio of global index ETFs would fare better. e rolling window we go back 200 days.
e frequency of trades the following algorithm uses monthly trading notice
the construct.
e code is as follows:
%matplotlib inline
from zipline import run_algorithm
from zipline.api import order_target_percent, symbol, set_ commission, schedule_function, date_rules, time_rules
from zipline.finance.commission import PerTrade import pandas as pd
import pyfolio as pf
from scipy.optimize import minimize
import numpy as np
import warnings warnings.filterwarnings('ignore')
306 Fundamental Algorithmic Trading Strategies
context.stocks = [symbol('DIS'), symbol('WMT'), 
symbol('DOW'), symbol('CRM'),
symbol('NKE'), symbol('HD'),
symbol('V'), symbol('MSFT'),
symbol('MMM'), symbol('CSCO'),
symbol('KO'), symbol('AAPL'),
symbol('HON'), symbol('JNJ'),
symbol('TRV'), symbol('PG'),
symbol('CVX'), symbol('VZ'),
symbol('CAT'), symbol('BA'),
symbol('AMGN'), symbol('IBM'),
symbol('AXP'), symbol('JPM'),
symbol('WBA'), symbol('MCD'),
symbol('MRK'), symbol('GS'),
symbol('UNH'), symbol('INTC')]
context.rolling_window = 200 set_commission(PerTrade(cost=5)) schedule_function(handle_data, date_rules.month_end(), time_rules.market_open(hours=1))
def minimum_vol_obj(wo, cov):
w = wo.reshape(-1, 1)
sig_p = np.sqrt(np.matmul(w.T,
np.matmul(cov, w)))[0, 0] return sig_p
def handle_data(context, data):
n_stocks = len(context.stocks) prices = None
for i in range(n_stocks):
price_history = \
data.history(context.stocks[i], "close", context.rolling_window, "1d")
Learning mathematical model-based strategies 307
price = np.array(price_history)
if prices is None:
prices = price
else:
prices = np.c_[prices, price]
rets = prices[1:,:]/prices[0:-1, :]-1.0 mu = np.mean(rets, axis=0)
cov = np.cov(rets.T)
w0 = np.ones(n_stocks) / n_stocks
cons = ({'type': 'eq',
'fun': lambda w: np.sum(w) - 1.0},
{'type': 'ineq', 'fun': lambda w: w})
TOL = 1e-12
res = minimize(minimum_vol_obj, w0, args=cov,
method='SLSQP', constraints=cons, tol=TOL, options={'disp': False})
if not res.success: return;
w = res.x
for i in range(n_stocks):
order_target_percent(context.stocks[i], w[i])
def analyze(context, perf):
returns, positions, transactions = \ pf.utils.extract_rets_pos_txn_from_zipline(perf) pf.create_returns_tear_sheet(returns,
benchmark_rets = None)
start_date = pd.to_datetime('2010-1-1', utc=True) end_date = pd.to_datetime('2018-1-1', utc=True)
308 Fundamental Algorithmic Trading Strategies
results = run_algorithm(start = start_date, end = end_date, initialize = initialize, 
analyze = analyze,
capital_base = 10000,
data_frequency = 'daily'
bundle ='quandl')
e outputs are as follows:
Figure 9.81 Minimization of the portfolio volatility strategy; summary return and risk statistics
e results are positive see the strong stability of 0.91 while the tail ratio is just over 1.
Notice the results are including the transaction costs and they would be much worse if we traded daily. Always experiment with the optimal trading frequency.
Learning mathematical model-based strategies 309
e following is the worst five drawdown periods chart:
Figure 9.82 Minimization of the portfolio volatility strategy; worst five drawdown periods
e worst drawdown period was over a year with the net drawdown of -18.22%. e magnitude of the net drawdown for the other worst periods is below -10%.
e following is the Cumulative returns chart:
Figure 9.83 Minimization of the portfolio volatility strategy; cumulative returns over the investment horizon
We see that the cumulative returns are consistently growing, which is expected given the stability of 0.91.
310 Fundamental Algorithmic Trading Strategies
e following is the Returns chart:
Figure 9.84 Minimization of the portfolio volatility strategy; returns over the investment horizon
e Returns chart shows the returns’ oscillation around zero within the interval -0.3 to 0.04.
e following is the Rolling volatility chart:
Figure 9.85 Minimization of the portfolio volatility strategy; 6-month rolling volatility over the
investment horizon
e Rolling volatility chart illustrates that the max rolling volatility was 0.18 and that the rolling volatility was cycling around 0.1.
e following is the Rolling Sharpe ratio chart:
Figure 9.86 Minimization of the portfolio volatility strategy; 6-month rolling Sharpe ratio over the investment horizon
Learning mathematical model-based strategies 311
e Rolling Sharpe ratio chart shows the maximum rolling Sharpe ratio of 5.0 with the minimum slightly above -3.0.
e following is the Top 5 drawdown periods chart:
Figure 9.87 Minimization of the portfolio volatility strategy; top five drawdown periods over the
investment horizon
e Top 5 drawdown periods chart confirms that if we avoided the worst drawdown period by smarter choice of entry/exit rules, we would have dramatically improved the strategy’s performance.
e following are the Monthly returns, Annual returns, and Distribution of monthly returns charts:
Figure 9.88 Minimization of the portfolio volatility strategy; monthly returns, annual returns, and the distribution of monthly returns over the investment horizon
e Monthly returns table illustrates that we have not traded for the first few months of 2010. e Annual returns chart shows that the strategy has been profitable every year, but 2015. e Distribution of monthly returns chart draws a slightly negatively skewed strategy with small kurtosis.
312 Fundamental Algorithmic Trading Strategies
Minimization of the portfolio volatility strategy is usually only profitable for non-daily trading. In this example, we used monthly trading and achieved a Sharpe ratio of 0.93, with a maximum drawdown of -18.2%.
Maximum Sharpe ratio strategy with monthly trading
is strategy is based on ideas contained in Harry Markowitz’s 1952 paper Portfolio Selection. In brief, the best portfolios lie on the efficient frontier a set of portfolios with the highest expected portfolio return for each level of risk.
In this strategy, for the given stocks, we choose their weights so that they maximize the portfolio’s expected Sharpe ratio such a portfolio lies on the efficient frontier.
We use the PyPortfolioOpt Python library. To install it, either use the book’s conda environment or the following command:
pip install PyPortfolioOpt
%matplotlib inline
from zipline import run_algorithm
from zipline.api import order_target_percent, symbols, set_ commission, schedule_function, date_rules, time_rules
from zipline.finance.commission import PerTrade
import pandas as pd
import pyfolio as pf
import numpy as np
from pypfopt.efficient_frontier import EfficientFrontier from pypfopt import risk_models
from pypfopt import expected_returns
import warnings warnings.filterwarnings('ignore')
def initialize(context):
context.stocks = \ symbols('DIS','WMT','DOW','CRM','NKE','HD','V','MSFT', 'MMM','CSCO','KO','AAPL','HON','JNJ','TRV',
Learning mathematical model-based strategies 313
'PG','CVX','VZ','CAT','BA','AMGN','IBM','AXP', 'JPM','WBA','MCD','MRK','GS','UNH','INTC')
context.rolling_window = 252 set_commission(PerTrade(cost=5))
schedule_function(handle_data, date_rules.month_end(), time_rules.market_open(hours=1))
def handle_data(context, data):
prices_history = data.history(context.stocks, "close", context.rolling_window, "1d")
avg_returns = \ expected_returns.mean_historical_return(prices_history) cov_mat = risk_models.sample_cov(prices_history)
efficient_frontier = EfficientFrontier(avg_returns, cov_mat)
weights = efficient_frontier.max_sharpe()
cleaned_weights = efficient_frontier.clean_weights()
for stock in context.stocks:
order_target_percent(stock, cleaned_weights[stock])
def analyze(context, perf): 
returns, positions, transactions = \ pf.utils.extract_rets_pos_txn_from_zipline(perf) pf.create_returns_tear_sheet(returns,
benchmark_rets = None)
start_date = pd.to_datetime('2010-1-1', utc=True) end_date = pd.to_datetime('2018-1-1', utc=True)
results = run_algorithm(start = start_date, end = end_date, initialize = initialize, 
analyze = analyze,
capital_base = 10000,
314 Fundamental Algorithmic Trading Strategies
data_frequency = 'daily', bundle ='quandl')
e outputs are as follows:
Figure 9.89 Maximum Sharpe ratio strategy; summary return and risk statistics
e strategy shows solid stability of 0.76 with the tail ratio close to 1 (1.01). However, the annual volatility of this strategy is very high (17.0%).
e following is the worst five drawdown periods chart:
Figure 9.90 Maximum Sharpe ratio strategy; worst five drawdown periods
Learning mathematical model-based strategies 315
e worst drawdown period lasted over 2 years and had a magnitude of net drawdown
of -21.14%. If we tweaked the entry/exit rules to avoid this drawdown period, the results would have been dramatically better.
e following is the Cumulative returns chart:
Figure 9.91 Maximum Sharpe ratio strategy; cumulative returns over the investment horizon
e Cumulative returns chart shows positive stability. e following is the Returns chart:
Figure 9.92 Maximum Sharpe ratio strategy; returns over the investment horizon
316 Fundamental Algorithmic Trading Strategies
e Returns chart show that the strategy was highly successful at the very beginning of the investment horizon.
e following is the Rolling volatility chart:
Figure 9.93 Maximum Sharpe ratio strategy; 6-month rolling volatility over the investment horizon
e Rolling volatility chart shows that the rolling volatility has subsidized with time. e following is the Rolling Sharpe ratio chart:
Figure 9.94 Maximum Sharpe ratio strategy; 6-month rolling Sharpe ratio over the investment horizon
e Rolling Sharpe ratio chart illustrates that the rolling Sharpe ratio increased with time to the max value of 5.0 while its minimum value was above -3.0.
e following is the Top 5 drawdown periods chart:
Figure 9.95 Maximum Sharpe ratio strategy; top five drawdown periods over the investment horizon
Learning time series prediction-based strategies 317
e Top 5 drawdown periods chart shows that the maximum drawdown periods have been long.
e following are the Monthly returns, Annual returns, and Distribution of monthly returns charts:
Figure 9.96 Maximum Sharpe ratio strategy; monthly returns, annual returns, and the distribution of monthly returns over the investment horizon
e Monthly returns table proves that we have traded virtually in every month. e
Annual returns chart shows that the annual returns have been positive for every year but 2016. e Distribution of monthly returns chart is positively skewed with minor kurtosis.
e maximum Sharpe ratio strategy is again usually only profitable for non-daily trading.
Learning time series prediction-based strategies
Time series prediction-based strategies depend on having a precise estimate of stock prices at some time in the future, along with their corresponding confidence intervals. A calculation of the estimates is usually very time-consuming.
e simple trading rule then incorporates the relationship between the last known price and the future price, or its lower/upper confidence interval value.
More complex trading rules incorporate decisions based on the trend component and seasonality components.
318 Fundamental Algorithmic Trading Strategies
SARIMAX strategy
is strategy is based on the most elementary rule: own the stock if the current price is
lower than the predicted price in 7 days:
%matplotlib inline
from zipline import run_algorithm
from zipline.api import order_target_percent, symbol, set_ commission
from zipline.finance.commission import PerTrade import pandas as pd
import pyfolio as pf
import pmdarima as pm
import warnings warnings.filterwarnings('ignore')
def initialize(context):
context.stock = symbol('AAPL')
context.rolling_window = 90 set_commission(PerTrade(cost=5))
def handle_data(context, data):
price_hist = data.history(context.stock, "close",
context.rolling_window, "1d") try:
model = pm.auto_arima(price_hist, seasonal=True)
forecasts = model.predict(7)
order_target_percent(context.stock, 1.0 if price_hist[- 1] < forecasts[-1] else 0.0)
except: pass
def analyze(context, perf):
returns, positions, transactions = \ pf.utils.extract_rets_pos_txn_from_zipline(perf)
Learning time series prediction-based strategies 319
pf.create_returns_tear_sheet(returns, 
benchmark_rets = None)
start_date = pd.to_datetime('2017-1-1', utc=True) end_date = pd.to_datetime('2018-1-1', utc=True)
results = run_algorithm(start = start_date, end = end_date, initialize = initialize, 
analyze = analyze,
handle_data = handle_data,
capital_base = 10000,
data_frequency = 'daily',
bundle ='quandl')
e outputs are as follows:
Figure 9.97 SARIMAX strategy; summary return and risk statistics
320 Fundamental Algorithmic Trading Strategies
Over the trading horizon, the strategy exhibited a high tail ratio of 1.95 with a very low stability of 0.25. e max drawdown of -7.7% is excellent.
e following is the worst five drawdown periods chart:
Figure 9.98 SARIMAX strategy; worst five drawdown periods
e worst drawdown periods have displayed the magnitude of net drawdown below -10%. e following is the Cumulative returns chart:
Figure 9.99 SARIMAX strategy; cumulative returns over the investment horizon
e Cumulative returns chart proves that we have traded only in the first half of the trading horizon.
Learning time series prediction-based strategies 321
e following is the Returns chart:
Figure 9.100 SARIMAX strategy; returns over the investment horizon
e Returns chart shows that the magnitude of returns swing has been larger than with other strategies.
e following is the Rolling volatility chart:
Figure 9.101 SARIMAX strategy; 6-month rolling volatility over the investment horizon
e Rolling volatility chart shows that the rolling volatility has decreased with time. e following is the Rolling Sharpe ratio chart:
Figure 9.102 SARIMAX strategy; 6-month rolling Sharpe ratio over the investment horizon
322 Fundamental Algorithmic Trading Strategies
e Rolling Sharpe ratio chart shows that the Sharpe ratio in the first half of the trading horizon was excellent and then started to decrease.
e following is the Top 5 drawdown periods chart:
Figure 9.103 SARIMAX strategy; top five drawdown periods over the investment horizon
e Top 5 drawdown periods chart demonstrates that the worst drawdown period was the entire second half of the trading window.
e following are the Monthly returns, Annual returns, and Distribution of monthly returns charts:
Figure 9.104 Monthly returns, annual returns, and the distribution of monthly returns over the investment horizon
e Monthly returns table confirms we have not traded in the second half of 2017. e Annual returns chart shows a positive return for 2017 and the Distribution of monthly returns chart is negatively skewed with large kurtosis.
e SARIMAX strategy entry rule has not been triggered over the tested time horizon on a frequent basis. Still, it produced a Sharpe ratio of 1.01, with a maximum drawdown of -7.7%.
Learning time series prediction-based strategies 323
Prophet strategy
is strategy is based on the prediction confidence intervals, and so is more robust than the previous one. In addition, Prophet predictions are more robust to frequent changes than SARIMAX. e backtesting results are all identical, but the prediction algorithms are significantly better.
We only buy the stock if the last price is below the lower value of the confidence interval (we anticipate that the stock price will go up) and sell the stock if the last price is above the upper value of the predicted confidence interval (we anticipate that the stock price
will go down):
%matplotlib inline
from zipline import run_algorithm
from zipline.api import order_target_percent, symbol, set_ commission
from zipline.finance.commission import PerTrade import pandas as pd
import pyfolio as pf
from fbprophet import Prophet
import logging
logging.getLogger('fbprophet').setLevel(logging.WARNING)
import warnings warnings.filterwarnings('ignore')
def initialize(context):
context.stock = symbol('AAPL')
context.rolling_window = 90 set_commission(PerTrade(cost=5))
def handle_data(context, data):
price_hist = data.history(context.stock, "close",
context.rolling_window, "1d")
price_df = pd.DataFrame({'y' : price_hist}).rename_
324 Fundamental Algorithmic Trading Strategies
axis('ds').reset_index()
price_df['ds'] = price_df['ds'].dt.tz_convert(None)
model = Prophet()
model.fit(price_df)
df_forecast = model.make_future_dataframe(periods=7, freq='D')
df_forecast = model.predict(df_forecast)
last_price=price_hist[-1] forecast_lower=df_forecast['yhat_lower'].iloc[-1] forecast_upper=df_forecast['yhat_upper'].iloc[-1]
if last_price < forecast_lower:
order_target_percent(context.stock, 1.0) elif last_price > forecast_upper:
order_target_percent(context.stock, 0.0)
def analyze(context, perf):
returns, positions, transactions = \ pf.utils.extract_rets_pos_txn_from_zipline(perf) pf.create_returns_tear_sheet(returns,
benchmark_rets = None)
start_date = pd.to_datetime('2017-1-1', utc=True) end_date = pd.to_datetime('2018-1-1', utc=True)
results = run_algorithm(start = start_date, end = end_date, initialize = initialize,
analyze = analyze,
handle_data = handle_data,
capital_base = 10000,
data_frequency = 'daily',
bundle ='quandl')
Learning time series prediction-based strategies 325
e outputs are as follows:
Figure 9.105 Prophet strategy; summary return and risk statistics
In comparison with the SARIMAX strategy, the Prophet strategy shows far better results tail ratio of 1.37, Sharpe ratio of 1.22, and max drawdown of -8.7%.
e following is the worst five drawdown periods chart:
Figure 9.106 Prophet strategy; worst five drawdown periods
326 Fundamental Algorithmic Trading Strategies
e worst five drawdown periods confirms that the magnitude of the worst net drawdown was below 10%.
e following is the Cumulative returns chart:
Figure 9.107 Prophet strategy; cumulative returns over the investment horizon
e Cumulative returns chart shows that while we have not traded in certain periods of time, the entry/exit rules have been more robust than in the SARIMAX strategy compare both the Cumulative returns charts.
e following is the Returns chart:
Figure 9.108 Prophet strategy; returns over the investment horizon
e Returns chart suggests that the positive returns outweighed the negative returns.
Learning time series prediction-based strategies 327
e following is the Rolling volatility chart:
Figure 9.109 Prophet strategy; 6-month rolling volatility over the investment horizon
e Rolling volatility chart shows virtually constant rolling volatility this is the hallmark of the Prophet strategy.
e following is the Rolling Sharpe ratio chart:
Figure 9.110 Prophet strategy; 6-month rolling Sharpe ratio over the investment horizon
e Rolling Sharpe ratio chart shows that the max rolling Sharpe ratio was between -.50 and 1.5.
e following is the Top 5 drawdown periods chart:
Figure 9.111 Prophet strategy; top five drawdown periods over the investment horizon
328 Fundamental Algorithmic Trading Strategies
e Top 5 drawdown periods chart shows that even though the drawdown periods were substantial, the algorithm was able to deal with them well.
e following are the Monthly returns, Annual returns, and Distribution of monthly returns charts:
Figure 9.112 Prophet strategy; monthly returns, annual returns, and the distribution of monthly returns over the investment horizon
e Monthly returns table confirms we have traded in every single month, with an excellent annual return as confirmed by the Annual returns chart. e Distribution of monthly returns chart is positively skewed with minor kurtosis.
e Prophet strategy is one of the most robust strategies, quickly adapting to market changes. Over the given time period, it produced a Sharpe ratio of 1.22, with a maximum drawdown of -8.7.
Summary
In this chapter, we have learned that an algorithmic trading strategy is defined by a model, entry/leave rules, position limits, and further key properties. We have demonstrated how easy it is in Zipline and PyFolio to set up a complete backtesting and risk analysis/position analysis system, so that you can focus on the development of your strategies, rather than wasting your time on the infrastructure.
Even though the preceding strategies are well published, you can construct highly profitable strategies by means of combining them wisely, along with a smart selection of the entry and exit rules.
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