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Coding for the entire group
Coding for my part I specialized: co-integration
Quantitive Methods Class:
Pair Trading for December 2025 (Group work of 4: Area of my specialty in Co-integration)
Fall semester "Paris Trading" in Quantitative Methods class:
Story behind 1:
For Quantitative methods class, we as a group selected "Pairs Trading" as a group topic project.
From this, we had "correlation method", "Distance Method", and "Co-integration" method. For my part, I focused in co-integration methods to make algorithmic trade.
Story behind 2:
For our strategy plans, we train the data for 1.5 to 2 years, and then test for about an year of backtest to see the results after the time period of formation period. We made trading spread tighter, such that we use flexible methods of z-score between 2 to 0.5 to optimize our backtesting PnL.
Story behind 3:
The backbone of the co-integration:
So what we mean by co-integration? The steps behind co-integration is, we at first test non-stationarity of the stocks since that is the optimal equity stocks. around 98 percent of our stocks we selected are non-statinoary, but we run it as a saftey measure to have the right stocks to design co-integrated pairs.
Next is the gist where we run the OLS model of spread relationship between two pairs of stocks, so we have hundreds to thousands of pairs that we run OLS to find. the stationarity of pairs. We learned from statistics class in the fall that stationarity in spread means means, and variance are constant. So such co-integrated pairs will have the best mean-reversion spread that can be profitable for trading.
Story behind 4: SP500 performs better than co-integrated pairs trading when market is good...?
So when we ran in the normal periods, we realized that SP 500 is actually more profitable then the co-integration methods. Then, my curiosity goes then how can co-integration actually make a profit if when market is good, SP 500 is a better investment method ?
Story behind 4:
Discovered that co-integration pairs are uniquely profitable when the market goes into a regime change and max drawdown for sp500 is high, while co-integration's max drawown is lower.
During this time, we received feedback about running a possible trading cost and frequency of the trade analysis. So we picked the timeframe for co-integration fixed window in Covid period from Feb of 2020 to August 2020#vs September 2020 to August 2021. As a result, we noticed Covid Period with around 125 trades, Post-Covid as around 290 trades. Also, Noticeably Sharp Ratio for covid was 0.8 while Post covid was 0.05. This indicates#that as volatiilty exploded, the sigma scale increased dramatically and z-score has denominator as the sigma scale. So due to the z-score value reduced, which suppressed the number of trades that exceeded the 1.5 to 2.0 sigma threshold#to exit and enter trades. On the other hand, the sharp ratio during covid was substantially high indcating stronger opportunities with stronger mean-reversion (spread quickly reached equilibrium) and provided profits. For post-covid,#there were many trades but weaker mean-reversion of spread as the sharp ratio was low as the post-covid period that had low volatility due to high liquidation in the market causing many signals and trades but weak profits.#Also, in terms of cost analysis, we see that P&L for each of the Covid Trade is extremely high with 0.03 average pnl per trade covid vs 0.0025 average pnl per trade for post covid as covid had few traedes with high returns and post covid had#high trades with low returns. The Net P&L/trade is near zero or negative and interestingly the trading cost analysis indicate that 20bps cost brings down the PnL to less than zero completely.
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