Effective Convergence Trading of Sparse, Mean Reverting Portfolios

Abstract This paper introduces an effective convergence trading algorithm for mean reverting portfolios using Long Short Term Memory ( LSTM ) neural networks. Utilizing known techniques for selection of sparse, mean reverting portfolios from asset dynamics following the VAR (1) model, we introduce a 2-step technique to effectively trade the optimal portfolio. Sequence-to-sequence ( Seq 2 Seq ) LSTM architecture is implemented to make longer term prediction of future portfolio values and establish a trading range. In addition, a simple LSTM network is applied to predict very precisely one time step ahead. Combining these two constructions, a sophisticated convergence trading algorithm is implemented which produced Sharpe ratios around 1.0 on optimal portfolios selected from historical $$ S[NONSPACE] \&amp; P500$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mo>[</mml:mo> <mml:mi>N</mml:mi> <mml:mi>O</mml:mi> <mml:mi>N</mml:mi> <mml:mi>S</mml:mi> <mml:mi>P</mml:mi> <mml:mi>A</mml:mi> <mml:mi>C</mml:mi> <mml:mi>E</mml:mi> <mml:mo>]</mml:mo> <mml:mo>&amp;</mml:mo> <mml:mi>P</mml:mi> <mml:mn>500</mml:mn> </mml:mrow> </mml:math> stocks during $$2015-2022$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2015</mml:mn> <mml:mo>-</mml:mo> <mml:mn>2022</mml:mn> </mml:mrow> </mml:math> . This represents a very significant improvement compared to the previous convergence trading algorithms on the same set of portfolios by around $$141\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>141</mml:mn> <mml:mo>%</mml:mo> </mml:mrow> </mml:math> on average.