Supervised portfolios

Abstract

We propose an asset allocation strategy that engineers optimal weights before feeding them to a supervised learning algorithm. In contrast to the traditional approaches, the machine is able to learn risk measures, preferences, and constraints beyond simple expected returns, within a flexible, forward-looking, and non-linear framework. Our empirical analysis illustrates that predicting the optimal weights directly instead of the traditional two-step approach leads to more stable portfolios with statistically better risk-adjusted performance measures.

Keywords:

• Portfolio choice
• Supervised learning
• Boosted trees
• Asset allocation

Acknowledgements

The authors are grateful for the comments of two referees which have helped clarify and improve the empirical part of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 For the sake of completeness, we mention that López de Prado (2016) and Raffinot (2017) have introduced a new way to allocate capital based on unsupervised machine learning, namely hierarchical clustering algorithms.

2 Outside financial applications, Elmachtoub and Grigas (2022) provide theoretical results on various ‘predict, then optimize’ tasks.

3 Previous attributes are also mentioned in asset pricing, like past returns (Jegadeesh and Titman 1993, Asness et al. 2013) or realized volatility (Baker et al. 2011, Li et al. 2016)

4 In economics, the agent often maximize expected utility over terminal wealth. In finance, it is customary to work on returns instead, see Campbell and Viceira (2002)

5 We use the $L^2$ norm of weights to measure diversification, as in Goetzmann and Kumar (2008). The integration of diversification constraints in standard portfolio optimization is discussed in Coqueret (2015). In practice, the minimum feasible κ is 1/N, where N is the number of assets, and it is reached for the equally-weighted portfolio.

6 More generally, the utility could be written as $u({\mathit{w}}_s,{\mathcal{E}}_s)$, but we stick to simpler notations to ease readability.

7 Available at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.

8 It is available here.

9 In a similar vein, Han et al. (2013), Han et al. (2016) and Han et al. (2021) show that technical indicators, based on past prices are also relevant predictors and are priced in the cross-section of stocks.

10 See Welch and Goyal (2008) and Hull and Qiao (2017) for more information on the ability of macroeconomic predictors to forecast returns.

11 Given the values of r over the timeframe of our study, a risk-free interest rate of zero is assumed when calculating the $\mathcal{S}\mathcal{R}$.

12 In full transparency, this claim is disputed in Chen (2021) and Jensen et al. (2022).