November, 8, 2023 - read
“Are optimizers error maximizers?”
- Mark Kritzman
That quote is curiously the title of an article1, which spawned a rebuttal and countless other articles. The abstract is below.
Small input errors to mean-variance2 optimizers often lead to large portfolio misallocations when assets are close substitutes for one another. In fact, when the assets are close substitutes, the return distribution of the presumed optimal portfolio is actually similar to the distribution of the truly optimal portfolio. Contrary to conventional wisdom, therefore, mean-variance optimizers usually turn out to be robust to small input errors when sensitivity is measured properly.
This tautology amounts to the same as the statement that you are always right except when you are wrong. The truth is that optimizers are susceptible to a number of issues. Sensitivity to the inputs, as mentioned earlier, can be problematic; an optimization that runs with imprecise inputs that can throw off the answer far from what an investor would like.
What else could go wrong with optimizers? Optimizers are best used in an optimization space where changes in the solution space vary smoothly with changes in the parameter space. In other words the landscape of possible solutions should not look like a prairie with a flagpole; it should be more like rolling hills; there are technical descriptors for this, but a mental picture suffices. Of course, just as bad as a solitary flagpole is a field of densely packed flagpoles; this raises the possibility of no unique convergence of a solution. The problem then becomes which flagpole to pick, and, given a solution, is that globally the best solution. Again, these topics all touch on concerns of practitioners and require lots of math and lots of judgement, but it is what keeps financial engineers awake at night. It is without a doubt that sub-optimal results happen when someone takes any set of numbers, shoves them blindly into an optimizer, and trusts the output without reflection.
Without delving more deeply into the literature and inspiring a rebuttal to this piece, we can say that optimizers are useful. At Trinary Capital we are adamant that the tools (machines) are at our disposal and not vice versa. We would expect that there is a right tool for the right job and not a tool for every job. Optimizers are just that and we have a place for them within our framework. We overcome a common problem with optimization of our traditional investments by putting up the appropriate guardrails. The conventional mean variance optimization takes historical prices and converts them into the right kind of input that the optimizer expects, that is, mean3 and variance4 (please see www.investopedia.org for conventional definitions). Mean variance optimization amounts to a set of calculations. As such it takes input and converts it into output. This is a simplified notion of the process, but it suffices for our use.
We draw the reader to the “Asset Allocation” piece, which is highlighted. Making the asset allocation subject to the inherent problems in the optimization process may not be judicious. The sensitivity can throw off the results. Also, it may be that the user has not taught the optimizer about the non-numerical risks inherent in some of the asset classes. For instance, an expected return of 5% in mid cap growth is NOT the same as an expected return of 5% in emerging markets due, in part, to the probability of default but also to other matters. A volatility of 8% in large cap is not the same as a volatility in private real estate of the same number due to stale pricing, which is often called “smoothing”. Many times, optimizers give what is known as “corner solutions” if they do not have the appropriate constraints (corner solutions are marked by high concentration of portfolio allocation into only a few assets). We believe that conventional asset allocations are the true north of investing because there are ample data supporting them – while we have made modifications to asset allocations like the 60/40 portfolio, we know that they are the work horses in investment management; 60/40 is not dead!
Above is the workflow at Trinary Capital for mean variance optimization. We believe that asset allocation is an input, not an output, of the process. Once this decision is made, or once the guardrails are set, we know that our portfolio will not violate the constraints set by asset allocation and will focus on the best combination of managers that work well together. Working well together takes into account the risk versus reward question. Because the optimizer is constrained by the asset allocation, no corner solutions will result because the optimizer believes that only a few managers are worth investing in. We preserve our mandate of diversification, and this de facto approach is a risk-adjusted approach to the bets proposed by the optimizer. Left to its own devices, the optimizer will run amuck and offer up unwanted corner solutions. We believe in letting machines do what they are good at (sorting through a billion billion combinations of managers) but guided by the common sense of the human (the investor who chooses the asset allocation upfront via a risk tolerance questionnaire). We believe this is an essential step in using optimizers for the right reasons and in the right way. The machines are important, but they are never more important than the investor.
Trinary Capital believes in diversification and adhering to the asset allocation dictated by investors’ goals and risk tolerances. Trinary Capital employs certain techniques in an effort to accomplish this. While optimization is a crucial part of any portfolio implementation, Trinary Capital employs practices which we believe will help investors achieve their goals without exposing them to uncompensated and undo risk.
1 Are Optimizers Error Maximizers? | Portfolio Management Research (pm-research.com)
2 Mean-Variance Analysis Definition (investopedia.com)
3 Mean Return: Overview, Calculations, Benefits (investopedia.com)
4 How Is Covariance Used in Portfolio Theory? (investopedia.com)
Past performance is not indicative of future results. Remember, there can be no assurance that the future performance of any specific investment, investment strategy, or product (including the investment strategies discussed in this article) will be profitable, equal any corresponding indicated historical performance level(s), be suitable for your portfolio or individual situation, or prove successful. Please remember to always speak with your individual advisor before making any investment decisions.