Advanced Pairs Trading: The Principal Component Analysis (PCA) Approach

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In this video, Illya Barziy, Quant Research Team Lead at Hudson and Thames, goes over the approach proposed in the paper "Statistical arbitrage in the US equities market"(2010) by Avellaneda, M. and Lee, J.-H. This strategy produced an annualized Sharpe ratio of 1.44 over the period from 1997 to 2007.
The idea is to decompose stocks returns into a systematic component and an idiosyncratic component (residual). In order to get the systematic component, the eigen portfolios from the PCA Approach are used.
The portfolio representing the idiosyncratic component can then be traded based on its deviation from equilibrium values.
We will briefly cover the theory behind the trading strategy, show its use examples with the ArbitrageLab package, discuss upsides, downsides, and variations of the strategy.
Links to slides: docs.google.com/presentation/...
Learn more with the Definitive Guide to Pairs Trading: hudsonthames.org/definitive-g...

[@lionelshaneyfelt5607]

This channel is awesome.

[@blacksiddis]

At 10:36, for the standardization: Do you not introduce look-ahead bias into the return matrix when you standardize the return at time t using a sample standard deviation that is calculated from a sample with observations that manifested after time t?

[@illyabarziy5481]

Hey Nikolas, thank you for the question! We're standardizing only the returns from the past M+1 days prior to current time t (slide 13). So no future information is given to the algorithm in this step.

[@blacksiddis]

@@illyabarziy5481 Awesome, thanks for the reply and clarification! I hope to try to implement this paper myself some time soon!

[@anubhav0by0]

How did you obtain the beta values?

[@user-lx7ts7uv3i]

correlation matrix from standardised data will be equal to corr matrix from original returns data. Why do standardisation?

[@silverquant-info]

Firstly, thanks for the great video. I noticed this double-standardization too. And then also the eigenvector components get divided by the standard deviation once again during eigenportfolio creation. It's not clear to me why standardization is necessary at all, either during data preparation or in portfolio creation. Real portfolios "experience" covariance, not correlation. Consider an extreme example of a near zero covariance stock (with respect to a PCA component) but with near perfect (1) correlation. Standardization would result in a full weighting allocated to that stock although it never moves in practice. Finally, according to my understanding, the PCA eigenvectors have L2 norm equal to 1, but do not sum to 1 as required by portfolios weights. Should the eigenvectors by normalized by sum(vector)? It's not clear to me why that should be preferred to, say, a softmax operation. # An R example of near-zero covariance variables with unit correlation v1

[@m.willing7734]

@@silverquant-info you need to use the correlation matrix or the covariance matrix of the standardized returns too ensure that their is no overweight of a variable/stock in the computing of the pca components (in other fields this can happen for example if one variable is in cm and the other in m)

[@navketan1965]

Sir, In pair trading correlated currency pairs(say AUD/USD & NZD/USD) do you compare RSI value & sell overpriced pair & buy the weaker? OR do you compare CCI of each pair? Do you suggest using correlated cross currencies as pair trades(eg EUR/JPY & GBP/JPY)? On 4H chart sum up RSI 3, RSI 7,RSI 14, & compare added value on each pair & go. Thank you.

[@ricktrader3946]

Are you in "In Sample data" mode with this library ? If so it's biased ...

[@wobby7055]

Your mic is so bad