wukan1986 / demo_strategy

Demonstrative examples for developing quantitative strategies

Demo Strategy

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author: Joseph Chen
date: Sep 14th, 2022

This demo will show how to build a practical strateqy (pairs trading) from scratch in the framework of QTrader.

Python environment

It is recommended to use conda to manage your environment. The following code creating a virtual environment named demo_strategy and installing the relevant packages:

> chmod +x ./preparations.sh 
> ./preparations.sh

Or you can manually input the following commands:

> conda create -n demo_strategy python=3.8
> conda activate demo_strategy
> pip install --force-reinstall git+https://github.com/josephchenhk/qtrader@master
> pip install dill finta termcolor pyyaml func_timeout scipy statsmodels hyperopt jupyter seaborn

EDA and Data Preparations

Refer to notebook EDA.ipynb for exploratory data analysis. After running the notebook, you should have prepared a data folder named clean_data in your current working directory. We will use this dataset to backtest our model.

Model Description

Cryptocurrencies are more inclined to co-move due to some common market sentiment than traditional assets. Therefore, they could be good candidates for a pairs trading strategy, which is based on exploiting the mean reversion in prices of securities.

There are two key things concerning a pairs trading strategy:

• Determine the candidate pairs

• Determine the entry and exit rules

The following paragraphs explain these in details:

Suppose S1 and S2 are the prices of two securities. In the training window, the linear regression of the logarithmic prices give:

$$\log(S_1) = \gamma\cdot\log(S_2) + \epsilon$$

where the slope $\gamma$ represents the hedge ratio. We can define the residual term $\epsilon$ as the spread $s = \log(S_1) - \gamma\cdot\log(S_2)$, which is expected to exhibit mean-reverting properties.

A Two-step method will be used to find out the candidate pairs. In step 1, for the given lookback window, the correlation of the logarithm prices will be calculated, and only those with a correlation higher than the threshold will be selected to enter step 2. In step 2, we will employ an Augmented Dicky Fuller (ADF) test on the shortlisted pairs from step 1, and only those with a p-value smaller than the predetermined threshold will be added to the final candidate pool. In the ADF test, linear regression is carried out and regression coefficients $\gamma$ and $\mu$ are obtained. These values are assumed to be constant throughout the testing period. Once the testing period completes, the training window will move forward to latest timestamp, and repeat this two-step calculation to determine candidate pairs in next testing period.

The main assumptions of this strategy could be summarized as:

1. The mean-reversion behaviors observed in the training period will continue to exist in the testing period, and the spread will mean-revert to its historical mean.

2. Once a candidate pair is determined by the two-step method, it is valid throughout the next testing period, and the hedge ratio will also remain unchanged.

Note that in reality, there is no guarantee for any of the assumptions above. Violation of the assumptions could lead to failures of the strategy.

Once we have determined the candidate pairs and their corresponding parameter $\gamma$, the model is ready to observe the signals by feeding price information. A pairs trading strategy can be implemented as follows: when the latest spread $s$ exceeds $\text{mean}(s) + \delta\cdot\text{std}(s)$, security 1 is over-valued, and security 2 is under-valued, therefore we open 1 unit of short position for security 1, and $\gamma$ unit of long position for security 2; when the latest $s$ is less than $\text{mean}(s) - \delta\cdot\text{std}(s)$, security 1 is under-valued, and security 2 is over-valued, as a result we open 1 unit of long position for security 1, and $\gamma$ unit of short position for security 2. The parameter $\delta$ here is a threshold number that should be measured with simulation data.

To control the risk, we also need to apply the stop loss rule to the strategy: if we are long security 1, and short security 2, when $s$ does not mean-revert to its historical mean $\text{mean}(s)$, but instead deviates further to be even smaller than $\text{mean}(s) - \Delta\cdot\text{std}(s)$, where $\Delta$ is a multiplier which is usually larger than entry threshold $\delta$, we will close the position and realize the loss. Similarly, when we are short security 1, long security 2, and $s$ does not mean-revert to its historical mean $\text{mean}(s)$, but moves further to be even larger than $\text{mean}(s) + \Delta\cdot\text{std}(s)$, the position will be closed and a loss will be realized. Similar to $\delta$, the exit threshold $\Delta$ is also a number that needs to be found out with training data.

Besides the z-score condition, there are also other entry conditions: when a pair is on, the hedge ratio $\gamma$ should be positive. This is to ensure that we always have a market-neutral position, i.e., long position in one security and short position in another. And we also close existing positions and avoid opening new position at the end of the testing period.

Simulation Results

As discussed in EDA，the trading universe is six cryptocurrency pairs:BTC.USD, EOS.USD, ETH.USD, LTC.USD, TRX.USD, andXRP.USD.

The OHLCV data of different intervals (5-min, 15-min, and 30-min) are used for simulations. The look-back window is fixed to be 960 bars (lookback_period=960). In the training period, we apply a two-step statistical method to the data in lookback window to determine the candidate pairs. Only those pairs with a correlation higher than the threshold (correlation_threshold=0.8) and an ADF p-value less than the threshold (cointegration_pvalue_entry_threshold=0.1) will be shortlisted. The trading window is next 480 bars (recalibration_interval=480) immediately following the previous training period. When the trading period completes, the dynamic rolling window will be automatically shifted 480 bars ahead for the next training and trading periods. In the trading period, the spread $s = \log(S_1) - \gamma\cdot\log(S_2)$ is updated by feeding the new price $S_1$ and $S_2$, and entry and exit are determined by z-score of the calculated spread.

The entry threshold is defined as anything between 1.5-sigma and 2-sigma (1.5 < entry_threshold < 2.0); and the exit threshold is defined as anything between 2.5-sigma and 3.5-sigma (2.5 < exit_threshold < 3.5). These parameters will change as per the backtesting results and individual security without risking overfitting data. We also assume for each trading opportunity, the maximum capital allocated to individual security is USD 1 million (capital_per_entry=1000000). And we only enter the trade once for repeating signals (max_number_of_entry=1).

A summary of the strategy parameters is shown below:

"lookback_period": 960,
"correlation_threshold": 0.8,
"recalibration_interval": 480,
"cointegration_pvalue_entry_threshold": 0.1,
"entry_threshold": [1.5, 2.0],
"exit_threshold": [2.5, 3.5],
"max_number_of_entry": 1,
"capital_per_entry": 1000000

Optimization Objective Function

The objective of the strategy is to maximize the Sharpe ratio and the total return. Therefore, the objective function is defined as minimizing $f$:

$$ f(entry\textunderscore threshold, exit\textunderscore threshold) = -\min(\max(\text{SR}, 0), 0.5) * \text{TOTR} $$

where $\text{SR}$ is the Sharpe ratio, and $\text{TOTR}$ is the total return.

5-min Interval

We firstly test the strategy in a 5-min interval. This means we have a training window (lookback window) of 80 hours ($5 * 960 / 60 = 80$), and a testing window (trading window) of 40 hours.

In the training dataset (in-sample), we trained the model and selected the cryptocurrency pairs with negative best loss as we are minimizing the objective function. There are 7 pairs that are selected. And the strategy will be tested on both in-sample and out-of-sample datasets.

{
    ('EOS.USD', 'ETH.USD'): {
        'entry_threshold': 1.5000392943615142, 
        'exit_threshold': 3.376602464111785, 
        'best_loss': -0.03475020027151503}, 
    ('TRX.USD', 'XRP.USD'): {
        'entry_threshold': 1.551051140512154, 
        'exit_threshold': 3.017624989640105, 
        'best_loss': -0.08643681591995156}, 
    ('BTC.USD', 'EOS.USD'): {
        'entry_threshold': 1.9633378226348694, 
        'exit_threshold': 3.329967191852652, 
        'best_loss': -0.017663755051963572}, 
    ('EOS.USD', 'LTC.USD'): {
        'entry_threshold': 1.7693316696798091,
        'exit_threshold': 2.5532912245203043, 
        'best_loss': -0.016165476679308892}, 
    ('BTC.USD', 'LTC.USD'): {
        'entry_threshold': 1.8775675045977969, 
        'exit_threshold': 2.670390189458025, 
        'best_loss': -0.007816275748584213}, 
    ('ETH.USD', 'LTC.USD'): {
        'entry_threshold': 1.762856210892485, 
        'exit_threshold': 2.707378771966564, 
        'best_loss': -0.014213080160328405}, 
    ('BTC.USD', 'ETH.USD'): {
        'entry_threshold': 1.9332887682355882, 
        'exit_threshold': 3.407991025881241, 
        'best_loss': -0.005658161919799375}
}

In-sample

Below is the Backtest result from 2021-01-01 to 2021-12-31:

____________Performance____________
Start Date: 2021-01-01
End Date: 2022-01-01
Number of Trading Days: 365
Number of Instruments: 7
Number of Trades: 168
Total Return: 6.38%
Annualized Return: 6.38%
Sharpe Ratio: 0.96
Rolling Maximum Drawdown: -5.39%

Out-of-sample

Below is the Backtest result from 2021-01-01 to 2022-01-01:

____________Performance____________
Start Date: 2022-01-01
End Date: 2022-08-01
Number of Trading Days: 212
Number of Instruments: 7
Number of Trades: 89
Total Return: 1.82%
Annualized Return: 3.14%
Sharpe Ratio: 0.82
Rolling Maximum Drawdown: -3.00%

15-min Interval

We then test the strategy in a 15-min interval. This means we have a training window (lookback window) of 10 days ($15 * 960 / (60 * 24) = 10$), and a testing window (trading window) of 5 days.

As discussed, there are 5 pairs that are selected. And the strategy will be tested on both in-sample and out-of-sample datasets.

{
    ('EOS.USD', 'LTC.USD'): {
        'entry_threshold': 1.85083364536054, 
        'exit_threshold': 3.224360323840364, 
        'best_loss': -0.047703687981827114}, 
    ('EOS.USD', 'XRP.USD'): {
        'entry_threshold': 1.8869138038036657, 
        'exit_threshold': 2.9094095009860723, 
        'best_loss': -0.046187517027634906}, 
    ('BTC.USD', 'EOS.USD'): {
        'entry_threshold': 1.8767472177155844, 
        'exit_threshold': 2.6226223785191993, 
        'best_loss': -6.446680549378299e-05}, 
    ('EOS.USD', 'ETH.USD'): {
        'entry_threshold': 1.603040067942517, 
        'exit_threshold': 3.4874437489605867, 
        'best_loss': -0.10111409247066716}, 
    ('TRX.USD', 'XRP.USD'): {
        'entry_threshold': 1.5092092690764671,
        'exit_threshold': 2.912104597010566, 
        'best_loss': -0.0025735030462288046}
}

In-sample

Below is the Backtest result from 2021-01-01 to 2021-12-31:

____________Performance____________
Start Date: 2021-01-01
End Date: 2022-01-01
Number of Trading Days: 365
Number of Instruments: 5
Number of Trades: 33
Total Return: 8.14%
Annualized Return: 8.14%
Sharpe Ratio: 1.20
Rolling Maximum Drawdown: -4.92%

Out-of_sample

Below is the Backtest result from 2021-01-01 to 2022-01-01:

____________Performance____________
Start Date: 2022-01-01
End Date: 2022-08-01
Number of Trading Days: 212
Number of Instruments: 5
Number of Trades: 13
Total Return: -8.47%
Annualized Return: -14.59%
Sharpe Ratio: -1.38
Rolling Maximum Drawdown: -11.29%

60-min Interval

We then test the strategy in a 60-min interval. This means we have a training window (lookback window) of 40 days ($60 * 960 / (60 * 24) = 40$), and a testing window (trading window) of 10 days.

As discussed, there is one pair that are selected. And the strategy will be tested on both in-sample and out-of-sample datasets.

{
    ('BTC.USD', 'LTC.USD'): {
        'entry_threshold': 1.8959144645762966, 
        'exit_threshold': 2.9436715640836755, 
        'best_loss': -0.08387009026604986}
}

In-sample

Below is the Backtest result from 2021-01-01 to 2021-12-31:

____________Performance____________
Start Date: 2021-01-01
End Date: 2022-01-01
Number of Trading Days: 365
Number of Instruments: 1
Number of Trades: 1
Total Return: 16.77%
Annualized Return: 16.77%
Sharpe Ratio: 1.30
Rolling Maximum Drawdown: -4.40%

Out-of-sample

Below is the Backtest result from 2021-01-01 to 2022-01-01:

____________Performance____________
Start Date: 2022-01-01
End Date: 2022-08-01
Number of Trading Days: 212
Number of Instruments: 1
Number of Trades: 1
Total Return: 7.72%
Annualized Return: 13.28%
Sharpe Ratio: 1.15
Rolling Maximum Drawdown: -4.58%

Summary & Future Work

As can be seen, both the 5-min and 60-min intervals deliver positive returns in both in-sample and out-of-sample datasets. However, as the interval increases, the trading opportunities decrease.

Interval	Annualized Return		Sharpe Ratio		Maximum Drawdown		Number of Trades
	In-sample	Out-of-sample	In-sample	Out-of-sample	In-sample	Out-of-sample	In-sample	Out-of-sample
5-min	6.38%	3.14%	0.96	0.82	-5.39%	-3.00%	168	89
15-min	8.14%	-14.59%	1.20	-1.38	-4.92%	-11.29%	33	13
60-min	16.77%	13.28%	1.30	1.15	-4.4%	-4.58%	1	1

There is a lot of work to be done to improve the strategy, which is included but not limited to:

• (1). In practice, the model should be trained in a dynamic rolling window, i.e., recalibrating the parameters entry_threshold and exit_threshold regularly. The code for optimization is in optimization_pair.py.

• (2). Consider a vectorization (dataframe/numpy) implementation of the backtest, to increase the optimization speed. It is relatively difficult to fully replicate the strategy in dataframe operations. An illustrative example is given in pandas_pairs.py, which covers most of the features in the model, and with much less execution time.

• (3). Add an absolute stop loss to each traded pair to mitigate drawdowns.

• (4). Consider the actual volume to have a better estimation of executed shares.

• (5). Consider using total least squares intead of OLS to obtain the regression coefficients (hedge ratios).

• (6). Consider transaction costs in the simulation.

• (7). Consider different lookback window and trading window for different time intervals.

• (8). Utilize a one-period execution lag for all trade orders to approximate the bid-ask spread since contrarian trading strategies might be unknowingly buying for bid prices and vice versa.