INVESTED: In Markets, in the Future, and in Society.

Building a successful long-term financial portfolio is all about “weathering the storm”. It’s often easy to fly high when the market is booming, but a portfolio only shows its resiliency and robustness in how it responds to crises and changing market conditions. Such crises emerge when unforeseen circumstances impact the financial market and can manifest in a variety of ways. For instance, an unexpected change to supply or demand, like a shortage of wheat (as we are currently seeing), or an excess of oil (we saw in 2020), as well as less dramatic events, like an underwhelming earnings report for a specific company, or a hike in interest rates. While they may differ in their impact, all of these events work to change the investment environment. In any case, a change in market conditions can send waves rippling throughout the financial world, ultimately leading asset managers to adjust their portfolio holdings in some way. In essence, the way in which a portfolio manager adjusts their holdings is a “control strategy”, like the examples that I outlined in a previous invested article, this is analogous to the way you might respond in efforts to balance a long stick upright in your hand, or possibly, the way that a chess player responds to the moves of their opponent.

In quantitatively evaluating the success of a given financial response strategy, we can borrow some diagnostic tools from control theory. Specifically, the “sensitivity function” is a way that we can assign a particular number to a given response, with lower numbers being better (indicating that the response is robust) and higher numbers being worse (indicating that the response is fragile and prone to errors). For instance, we can investigate how a particular asset manager responds to changes in the relationship between stocks and bonds, and then assign them a score for their response to the changes; for example, over short timescales or long timescales. On a more technical level, the sensitivity function is measuring how sensitive a specific response is to noise in the input signal: all else being equal, how much impact can randomness in the input signal (such as a decrease in stock-bond correlation) ultimately influence our actions (the consequent changes to asset allocations in a financial portfolio)?

Now, while this type of sensitivity analysis can be useful in understanding the optimal way of tuning a strategy to respond best to a particular signal, the interesting and unintended consequence of a specifically robust strategy, is that, because of that robustness, its sensitivity to other unseen inputs becomes more fragile. For instance, in designing an optimal way of navigating stock and bond exposures during the COVID crash in March 2019, we would unknowingly make our response to more recent events more fragile. Much like a waterbed, pushing down our sensitivity—and making our response more robust—to a specific signal, increases our sensitivity to noise in other signals, making our responses more fragile. This is known as the waterbed theorem [i] [1]. Herein lies a central challenge in portfolio management: a fixation on the most recent behaviour of financial markets (a manifestation of the availability bias) and the tuning of responses to those most recent signals unwittingly exposes one to fragility in other scenarios (that inevitably occur in the future).

While there are, in principle, ways of navigating the waterbed theorem in feedback systems [2], and instead of playing whack-a-mole on the waterbed of economic signal sensitivities, a simpler solution is to avoid over-fixation on specific events and look more holistically at the behaviour of a portfolio in a multitude of economic environments. While it’s tempting to fine-tune a portfolio so that it would have performed best in response to recent events, you will inevitably be left chasing the ever-present creativity of markets to conjure up novel ways to surprise us all.
 

[1] For the expert reader, the waterbed theorem is a consequence of Bode’s gain-phase relationships, a close cousin to the more well-known Kramers-Kronig relations.

[2] Specifically, it’s possible to mitigate the impacts of the ‘fragile’ regions by using passive filtering in combination with active feedback, which is the general technique used at the LIGO gravitational wave observatory to achieve their jaw-dropping measurement accuracies.

[i] J. Bechhoefer “Control Theory for Physicists”, Cambridge University press, 2021