Deep neural networks, gradient-boosted trees, random forests: Statistical arbitrage on the S&P 500 — part2: results and analysis

Wenchen Li
Jul 25, 2017 · 4 min read

To continue from Deep neural networks, gradient-boosted trees, random forests: Statistical arbitrage on the S&P 500 — part1: data preparation and model

general results

the above figure shows Daily performance metrics for long-short portfolios of different sizes: Mean return, standard deviation, and directional accuracy from December 1992 until October 2015. Portfolios consisting of the top k stocks, with k ∈ {10, 50, 100, 150, 200}

For k = 10 ( with 10 long and 10 short positions). The results observe that the ensemble produces returns of 0.45 percent per day, followed by the random forest with 0.43 percent, the gradient-boosted trees with 0.37 percent, and the deep neural networks with 0.33 percent per day.

These results show increasing k, i.e., including stocks with higher uncertainty, leads to decreasing returns and directional accuracy.

Strategy performance

daily return

Daily return characteristics of k = 10 portfolio, prior to and after transaction costs for DNN,

GBT, RAF, ENS compared to general market (MKT) from December 1992 until October 2015. NW denotes Newey-West standard errors with with one-lag correction.

In this respect, RAFs exhibit the lowest risk and DNNs the highest. Compared to other strategies, such as classical pairs trading, the tail risk is substantial.

Distance-based pairs trading is an equilibrium strategy, prone to construct pairs exhibiting low volatility. However, lower risk comes at low return (classical pairs trading only achieves annualized excess returns of 11 percent), so lower returns go along with lower tail risk. This result applies similarly for the conditional value at risk (CVaR).

annualized risk-return

After transaction costs, annualized returns amount to 73 percent for the ensemble, compared to 67 percent for random forests, 46 percent for gradient-boosted trees, and 27 percent for deep neural networks. All strategies largely outperform the general market with average returns of 9 percent p.a.

Annualized returns and risk measures of k = 10 portfolio, prior to and after transaction costs for DNN, GBT, RAF, ENS compared to general market (MKT) from December 1992 until October 2015.

We see that downside deviation ranges between 0.20 (RAF) and 0.26 (DNN), with a value of 0.22 for the ensemble — around 1.7 times the level of the general market. Hence, downside deviations are less expressed for the machine learning strategies compared to those of the general market, leading to favorable Sortino ratios for machine learning model objectives or as at least include this ingrident.

exposure of returns to common sources of systematic risk

Ensemble strategy with k = 10: Exposure to systematic sources of risk after transaction costs for DNN, GBT, RAF, ENS from December 1992 until October 2015. Standard errors are depicted in parentheses.

They conclude that the ensemble strategy produces statistically and economically significant daily alphas between 0.14 and 0.24 percent — depending on the employed factor model.

sub period analysis

  1. 12/92 to 03/01 corresponds to a period of strong and consistent outperformance, prior to the invention and propagation of the machine learning algorithms employed in this paper.
  2. 04/01 to 08/08 and corresponds to a period of mod- eration
  3. 09/08 to 12/09 and corresponds to the global financial crisis.
  4. 01/01 to 10/15 and corresponds to a period of dete- rioration.

Sub-periods profile of k = 10 portfolio, after transaction costs for DNN, GBT, RAF, ENS compared to general market (MKT) and the VIX index from December 1992 until October 2015.

Variable importances

Annualized risk-return characteristics per sub-period for DNN, GBT, RAF, ENS.

model parameters

Panel A: Design of baseline configuration versus lower parametrization (alternative 1) and higher parametrization (alternative 2). DNN is also compared with a standard neural network with one hidden layer with 31 hidden neurons, no dropout regularization and tanh activation function (alternative 3).

Panel B: Mean return per day for the k = 10 portfolio from December 1992 until October 2015 before transaction costs.

reference:

  1. Krauss, Christopher, Xuan Anh Do, and Nicolas Huck. “Deep neural networks, gradient-boosted trees, random forests: Statistical arbitrage on the S&P 500.” European Journal of Operational Research 259.2 (2017): 689–702.

Wenchen Li

Written by

objective: happiness, dataset: life, model: brain, optimization algorithm: SGD, code at https://github.com/WenchenLi

Welcome to a place where words matter. On Medium, smart voices and original ideas take center stage - with no ads in sight. Watch
Follow all the topics you care about, and we’ll deliver the best stories for you to your homepage and inbox. Explore
Get unlimited access to the best stories on Medium — and support writers while you’re at it. Just $5/month. Upgrade