Original paper
Abstract
We present a new profitable trading and risk management strategy with transaction cost for an adaptive equally weighted portfolio. Moreover, we implement a rule-based expert system for the daily financial decision making process by using the power of spectral analysis. We use several key components such as principal component analysis, partitioning, memory in stock markets, percentile for relative standing, the first four normalized central moments, learning algorithm, switching among several investments positions consisting of short stock market, long stock market and money market with real risk-free rates. We find that it is possible to beat the proxy for equity market without short selling for S&P 500-listed 168 stocks during the 1998-2008 period and Russell 2000-listed 213 stocks during the 1995-2007 period. Our Monte Carlo simulation over both the various set of stocks and the interval of time confirms our findings.
Keywords:Â portfolio risk management, algorithmic trading, out-of-sample prediction, long memory in stocks, adaptive learning algorithm, market timing, principal component analysis, simulation
Trading rules
- Apply Principal Component Analysis (PCA) daily on the recent 100-day price data of 168 prominent stocks from the S&P 500 index.
- Evaluate the highest eigenvalue from the correlation matrix derived from stock prices.
- Shift to a risk-free asset if this eigenvalue is not within a predefined percentage range, for instance, between A% and B% (such as 35% to 77%).
- For each of the 168 stocks, compute parameters over the last 100 days: average return, volatility, skewness, and kurtosis.
- Evaluate the mean of the computed parameters for the entire stock set.
- Identify percentile partition for each parameter based on historical values, representing different dimensions of the state vector.
- Record the average yield across N securities tied to the current market state.
- Explore historical market states matching the present state's parameters.
- Opt for risk-free assets the following day if there's a lack of historical data.
- If historical data exists, calculate the average historical return relative to its variance for that state.
- Investment decisions for the upcoming day should be:
- Enter a long position if the ratio of average return to variance exceeds 1.
- Enter a short position if this ratio is below -1.
- Maintain a cash position in other scenarios.
Python code
Backtrader
import numpy as np
import pandas as pd
from scipy.stats import skew, kurtosis
from sklearn.decomposition import PCA
import backtrader as bt
class PCA_MarketTiming(bt.Strategy):
def __init__(self):
self.data_close = self.datas[0].close
self.risk_free_rate = 0.02 # Annualized risk-free rate self.pct_range = (0.35, 0.77)
self.lookback_period = 100
self.stock_data = {} # To store stock data
self.pca = PCA(n_components=1)
def next(self):
if len(self.data_close) < self.lookback_period:
return
# PCA
stock_returns = []
for stock, data in self.stock_data.items():
stock_returns.append(np.diff(np.log(data.close.get(size=self.lookback_period))))
pca_returns = self.pca.fit_transform(stock_returns)
# Maximum eigenvalue function value
max_eigenvalue = np.amax(self.pca.explained_variance_ratio_)
# Calculate parameters
mean_returns = np.mean(pca_returns, axis=0)
std_returns = np.std(pca_returns, axis=0)
skew_returns = skew(pca_returns, axis=0)
kurt_returns = kurtosis(pca_returns, axis=0)
# Determine percentile partition
percentiles = [np.percentile(self.stock_data[stock].close.get(size=self.lookback_period), q) for q in [25, 50, 75]]
if not (self.pct_range[0] <= max_eigenvalue <= self.pct_range[1]):
# Invest in risk-free asset
self.order_target_percent(self.data_close, target=0)
else:
mean_value_per_variance = mean_returns / std_returns
if mean_value_per_variance > 1:
# Go long
self.order_target_percent(self.data_close, target=1)
elif mean_value_per_variance < -1:
# Go short
self.order_target_percent(self.data_close, target=-1)
else:
# Stay in cash
self.order_target_percent(self.data_close, target=0)
# Backtest setup
cerebro = bt.Cerebro()
cerebro.addstrategy(PCA_MarketTiming)
# Add S&P 500 large-cap stocks data
for stock in sp500_large_cap_stocks:
data = bt.feeds.PandasData(dataname=stock_data)
cerebro.adddata(data)
self.stock_data[stock] = data
# Set initial cash and run backtest
cerebro.broker.setcash(100000.0)
results = cerebro.run()This code provides a basic implementation of the described trading strategy using Backtrader. Note that you will need to replace sp500_large_cap_stocks with the actual list of 168 large-cap stocks from the S&P 500 index and stock_data with the corresponding historical price data.