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Co-Evolving Thousands of Portfolios for Robustness in Portfolio Selection
Optimizing market neutral robust portfolios that would generalize well to the future is still a big challenge.
This fact has proven itself by the reported fund performances during the most recent stock market crash.
Seven decades ago, Harry Markowitz famously said: “Diversification is the only free lunch in investing.”
Diversification prevents weight concentration to few assets and reduces the exposure to idiosyncratic shocks.
Yet, diversification seems to be not perfectly leveraged by many quantitative finance specialists for a long-time.
Warren Buffett defined diversification as a protection against ignorance that makes a very little sense for experts.
In portfolio optimization literature, one can find many methods ensuring the genotype diversity of portfolios.
Per-asset risk diversification metrics (Max. risk contribution, Diversification ratio, Concentration ratio) are flawed.
Although they are less exposed to idiosyncratic shocks, they are vulnerable to systemic shocks by ignoring correlations.
They do not ensure the robustness of a portfolio in any market condition by diversifying hierarchical sources of risks.
To ensure the out-of-sample robustness, a portfolio should consist of a large amount of uncorrelated sub-portfolios.
Hierarchical Risk Parity from Marcos Lopez de Prado known to result in a better out-of-sample performance.
This is because HRP aims to construct a portfolio that can be hierarchically decomposed into uncorrelated bets.
In other words, HRP tries to heuristically diversify the risk into several Uncorrelated Exposures (as referred by Meucci).
This helps HRP to be less vulnerable to not only idiosyncratic but also systemic shocks compared to other methods.
Monte Carlo Simulation is often used to verify the robustness under different scenarios sampled from the past.
Just like HRP targets, the aim of portfolio selection should be constructing a behaviorally diverse portfolio ensemble.
This is also what meant to happen intrinsically when one optimizes a portfolio using the minimum variance objective.
Ensembles empirically tend to yield better test results when there is diversity among their individual hypotheses.
Penalizing the correlation in-between high-quality sub-portfolios improves the generalization of their ensemble.
In this way, the ensemble portfolio can be robust against black swans, even if some of its constructs perform badly.
Thus, I constructed an ensemble from behaviorally diverse and high-quality portfolios co-evolved in parallel via GPU.
The members are co-evolved for maximizing their Probabilistic Sharpe Ratio while minimizing their highest correlations.
Although some of the high-quality portfolios of the training set have bad test performances, their ensemble stays robust.
The sub-portfolios are co-evolved using a novel population-based large-scale non-convex global optimization method.
Quadratic optimizers generally produce unreliable solutions as they fail to invert the positive-definite covariance matrix.
The proposed method can also enable co-evolving a population of “tactical investment algorithms” in the same manner.
Such population of optimal individuals for different market regimes can dynamically be ensembled by nowcasting.
In this way, those behaviorally diverse individuals can compete with each other for dynamically allocated resources.
More advanced ensembling methods that can be dynamically applied during live trading should further be investigated.
It is also straightforward to incorporate views (such as forecasted returns, etc) to this method, similar to Black-Litterman.
In this article, I have claimed that robustness in portfolio optimization can be done by co-evolving a diverse ensemble.
Population-based Quality-Diversity optimization (or Illumination) is also becoming popular in other science fields.
This research can hopefully point light to many other fields of optimization where ensuring the robustness is critical.
Ensemble models also shown to improve the accuracy, uncertainty and out-of-distribution robustness of Deep Learning.
Here, you can check the weights of the assets within the ensemble portfolio:
Here is a QuantConnect for a long-only portfolio evolved using this method:
DeMiguel, Victor, Lorenzo Garlappi, and Raman Uppal. “Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy?.” The review of Financial studies 22, no. 5 (2009): 1915–1953.
Meucci, Attilio. “Managing diversification.” Risk (2009): 74–79.
Lopez de Prado, Marcos. “Building diversified portfolios that outperform out of sample.” The Journal of Portfolio Management 42, no. 4 (2016)
Bailey, David H., and Marcos Lopez de Prado. “The Sharpe ratio efficient frontier.” Journal of Risk 15, no. 2 (2012): 13.
Lopez de Prado, Marcos. “Tactical investment algorithms.” Available at SSRN 3459866 (2019).
Lipton, Alex, and Marcos Lopez de Prado. “What Quants Can Learn from the COVID Crisis.” Risk Magazine, April (2020).
Fort, Stanislav, Huiyi Hu, and Balaji Lakshminarayanan. “Deep ensembles: A loss landscape perspective.” arXiv preprint arXiv:1912.02757 (2019).
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