We want to maximize those characteristics while

minimizing overall portfolio volatility, which is all you do is part of a mean variance optimization. Very often when mean variance optimization comes up and really just optimization in general, there's this debate between the simple and the complex. And there's a whole lot of literature dedicated to trying to find the balance and the out-of-sample success of very simple and naive methodologies, like 1 over N and acknowledging that optimization techniques are very often unintentionally error maximizer, that they will take those statistics about which we are most uncertain and unintentionally overweight them. And I know this is an area you've waxed philosophical about quite a bit. Your firm makes heavy usage of optimization techniques. And so I was hoping you could just spend some time exploring this concept. How do you guys find the balance between the simple and the complex? And how do you address the fact that very often the statistics of which you are trying to use as sources of information within your portfolio construction

are often shrouded in this distribution of uncertainty? There's really two different concepts embedded in that statement, right? One is the question of when and how is optimization likely to deliver better results than naive methods? And two, how to best make use of ensemble methods? So probably we should unpack those different concepts separately, right? And we could start with optimization. But we started to get there with the discussion of the optimization machine. But I mean, really the question of whether naive or optimal diversification through numerical optimization, which one of those or along the continuum between those, what's most effective, is a function of what we believe to be true about our investment universe. So for example, if you look at one of the most popular papers that weighs in on this question, a paper called optimal versus naive diversification by Demigail, Garlappi and Upl in 2009, they examine the performance of portfolios formed using naive methods like equal weight, one of a REN relative to some very complex optimizations using based on shrinkage and all kinds of different complicated applications. But they apply it to a really equity centric universe. So for example, one of the universes that they run this naive versus optimization based process on is 10 industry groups from the Ken French library, which anyone can download. I would encourage you to download it and look into this yourself. So I just finished actually running some tests on that universe. And what Demigail and his crew found was that optimization is not as useful as just one over N methods and allocating to this industry group. And candidly, I started my investigation kind of skeptical of that claim because they use some really strange parameterizations. They're using five and 10 year monthly look backs. So I mean, the information decay on their volatility and correlation estimates based on that length of look back obviously raised questions about whether there's any information content at all. So I thought that we could use some, you know, use daily data, which is provided for free, use shorter look back horizons and come up with better results. So I ran it and the fact is I couldn't. The results from the optimization methods did not work as well. We ran minimum variance max diversification in verse fall in verse variance, ERC and a couple of heuristic methods like the hierarchical minimum variance. And we couldn't make head and tails of it. None of them many difference the equal way completely dominated.