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AI for portfolio management: from Markowitz to Reinforcement Learning

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AI for portfolio management: from Markowitz to Reinforcement Learning - 1

AI for portfolio management: from Markowitz to Reinforcement Learning

The evolution of quantitative asset management techniques with empirical evaluation and Python source code

AI for portfolio management: from Markowitz to Reinforcement Learning - 2This is how we’d like them to grow https://investresolve.com/blog/category/diversification/

AI for portfolio management: from Markowitz to Reinforcement Learning - 3

Classical optimization

Markowitz efficient frontier

AI for portfolio management: from Markowitz to Reinforcement Learning - 4

Custom objectives

AI for portfolio management: from Markowitz to Reinforcement Learning - 5

Minimal variance portfolio optimization function

AI for portfolio management: from Markowitz to Reinforcement Learning - 6

The maximum diversification portfolio optimization function

AI for portfolio management: from Markowitz to Reinforcement Learning - 7

Equal risk contribution portfolio optimization function

Unsupervised learning

Eigenportfolios

AI for portfolio management: from Markowitz to Reinforcement Learning - 8

An illustration of different principal components of a portfolio: https://systematicedge.wordpress.com/2013/06/02/principal-component-analysis-in-portfolio-management/

Autoencoder risk

AI for portfolio management: from Markowitz to Reinforcement Learning - 9

A visualization of the general idea behind autoencoder neural networks: https://sefiks.com/2018/03/21/autoencoder-neural-networks-for-unsupervised-learning/

Hierarchical risk parity

AI for portfolio management: from Markowitz to Reinforcement Learning - 10

Geometrically, a covariance matrix of the assets in the portfolio is a complete graph (on the left), can we figure out a tree-based model that will be more optimal?

AI for portfolio management: from Markowitz to Reinforcement Learning - 11

Supervised learning

Forecasting weights

AI for portfolio management: from Markowitz to Reinforcement Learning - 12

https://www.sciencedirect.com/science/article/pii/S0378437107001938

Reinforcement learning

Deep Q-learning

AI for portfolio management: from Markowitz to Reinforcement Learning - 13

An illustration of a reinforcement learning agent to decide when to enter or leave the position https://hackernoon.com/the-self-learning-quant-d3329fcc9915

Evaluation in the wild

ETF dataset

AI for portfolio management: from Markowitz to Reinforcement Learning - 14 AI for portfolio management: from Markowitz to Reinforcement Learning - 15 AI for portfolio management: from Markowitz to Reinforcement Learning - 16Minimal Variance, Maximal Returns and Maximal Sharpe portfolios (click on image to zoom)

AI for portfolio management: from Markowitz to Reinforcement Learning - 17
AI for portfolio management: from Markowitz to Reinforcement Learning - 18
AI for portfolio management: from Markowitz to Reinforcement Learning - 19
Maximal Decorrelation, PCA and HRP portfolios (click on image to zoom)
AI for portfolio management: from Markowitz to Reinforcement Learning - 20
AI for portfolio management: from Markowitz to Reinforcement Learning - 21
AI for portfolio management: from Markowitz to Reinforcement Learning - 22
Smoothing forecasting, Autoencoder, and RL agent portfolios (click on image to zoom)

Cryptocurrencies dataset

AI for portfolio management: from Markowitz to Reinforcement Learning - 23
AI for portfolio management: from Markowitz to Reinforcement Learning - 24
AI for portfolio management: from Markowitz to Reinforcement Learning - 25
Minimal Variance, Maximal Returns and Maximal Sharpe portfolios (click on image to zoom)
AI for portfolio management: from Markowitz to Reinforcement Learning - 26
AI for portfolio management: from Markowitz to Reinforcement Learning - 27
AI for portfolio management: from Markowitz to Reinforcement Learning - 28
Maximal Decorrelation, PCA and HRP portfolios (click on image to zoom)
AI for portfolio management: from Markowitz to Reinforcement Learning - 29
AI for portfolio management: from Markowitz to Reinforcement Learning - 30
AI for portfolio management: from Markowitz to Reinforcement Learning - 31
Smoothing forecasting, Autoencoder, and RL agent portfolios (click on image to zoom)

Results discussion

AI for portfolio management: from Markowitz to Reinforcement Learning - 32Statistics of the portfolios on the ETFs dataset

AI for portfolio management: from Markowitz to Reinforcement Learning - 33
Statistics of the portfolios on the cryptocurrencies dataset

A not on HRP

AI for portfolio management: from Markowitz to Reinforcement Learning - 34
AI for portfolio management: from Markowitz to Reinforcement Learning - 35
HRP performance on the more diversified portfolio. As we can see, in this case, it allocates weights over all the assets

A note on Reinforcement Learning

Other approaches

Conclusions