Cluster shrinkage and the curse of dimensionality

At GestaltU we see ourselves as incrementalists. We aren’t so much prone to true quantum leaps in thinking, but we excel at finding novel ways to apply others’ brilliant concepts. In other words, we appreciate the fact that, for the most part, we ‘stand on the shoulders of giants’.

There are of course some true giants in the field of portfolio theory. Aside from timeless luminaries like Markowitz, Black, Sharpe, Thorpe and Litterman,  we perceive thinkers like Thierry Roncalli, Attilio Meucci, and Yves Choueifetay to be modern giants. We also admire the work of David Varadi for his contributions in the field of heuristic optimization, and his propensity to introduce concepts from fields outside of pure finance and mathematics. Also, Michael Kapler has created a truly emergent phenomenon in finance with his Systematic Investor Toolkit, which has served to open up the previously esoteric field of quantitative finance to a much wider set of practitioners. I (Adam) know I’ve missed many others, for which I deeply apologize and take full responsibility. I never was very good with names. 

In this article, we would like to integrate the cluster concepts we introduced in our article on Robust Risk Parity with some ideas proposed and explored by Varadi and Kapler in the last few months (see here andhere). Candidly, as so often happens with the creative process, we stumbled on these ideas in the process of designing a Monte-Carlo based robustness test for our production algorithms, which we intend to explore in greater detail in a future post.