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The structural entropy indicator is normalised to range (0,1). A better technique using Random Matrix Theory to avoid this thresholding is currently out of scope for now. It uses a threshold of 0.6 correlation to decide if there exists an edge between two stocks and uses that to compute structural entropy. Here we compute the structural entropy on a rolling window basis every day using historical data.

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We then download SPY and IWM prices for 22 years and convert them into returns (not log returns because we use that to backtest). returns = data.pct_change().fillna(0).apply(np.log1p)

Since we work in return space, the prices are converted into log returns. data = pd.read_csv('spy_component_prices.zip', index_col=0, parse_dates=True, infer_datetime_format=True, header=0).sort_index()

#Wavelet denoise zip file#

To avoid downloading data for all of the S&P500 constituents we use a local zip file (created earlier) that contains the historical prices for all these stocks.

Ideally we should use changing components of SP500 but then when is financial data freely available? There is survivor bias in this experiment because we use latest SP500 components. Fetch Historical Prices import pandas as pd import numpy as np import yfinance as yf import matplotlib.pyplot as plt from tqdm import tqdm To evaluate, this article uses a buy and hold (or long position) in S&P500 (using SPY ETF), computes the structural entropy across S&P500 constituents, and uses this structural entropy measure to decide when to hedge the long position in SPY ETF with a short position in Russell 2000 (IWM ETF). The idea is that correlations between assets increase when markets are falling during stress events (like 2008 or COVID in 2020).Ī medium article that explains structural entropy and simplifies the implementation in Python is here.Ĭan we identify these downtrends or risky periods to effectively hedge long only portfolios? Can we forecast contagion in the markets? This allows them to identify moments of contagion in the financial markets (when risk is spreading across assets) and show different results where they employ this measure. The authors consider financial markets as a complex interconnected correlation network (graph with assets as nodes and correlation as edge) and define/describe a new measure called “Structural entropy”. I first read about structural entropy in this article. This article aims is to evaluate/demonstrate the effectiveness of hedging a long only portfolio of US equities with a short position in Russell 2000 (I used IWM ETF since I don’t have rolling future prices) using an extended version structural entropy indicator.