Time's Up - Time Is the Greater Evil
"Time is the longest distance between two places" ~ Tennessee Williams
When I was a little boy, I remember the excitement in the room the day my father brought home our first stereo. There was this silver box, with knobs and numbers on it, about 18 inches square, and about six inches tall, that sat alone on the dresser looking ever so interesting. When my father turned it on, a backlit glow woke it up, and we all looked around with wonder as the sweet sound of music permeated the room. I walked up to the machine and turned the knob, and something changed -- the music went from soft and melodic to upbeat with thumps. For some time, we all just listened; and every once in a while, I turned the knob. I don’t know about everyone else, but as a kid, I was blown away at how all that different music could be stored in a little box that fit on the dresser.
With my curiosity ever-present, later that evening, when my parents were out of that room, I proceeded to unplug the stereo box and take it into my bedroom. With my door closed, I grabbed the screwdriver I had gotten -- I had to know what was inside, and where all that music was stored. Within hours, I had a multitude of parts meticulously arranged across my bedroom floor, colors with colors, sizes with sizes, long things with long things, and fat things with fat things (i.e. capacitors and resistors, distinctly separated). But I did not have an answer. At some point later, there was a pronounced knock on my door “Waaayne” said the elevated voice of my father, “have you seen the stereo?” I was looking right at it, or at least, at all the pieces that aggregated to its existence. Without replaying the step-by-step, I’ll conclude the story by sharing that as much as my father was angry at what he saw when the door opened, he looked past it in favor of appreciating my drive to know how things worked.
I have since slowed down on physically taking things apart, but unable to curb my thirst to do so, I have since pursued rigorous cerebral dismantling of whatever it is I am trying to understand. To this end, and in follow up to my last post about the association of space and time in risk management in attempts to mitigate “area under water,” I continue to break down these two components of risk, separating pieces wherever I can like it was a home stereo. In my prior post, I concluded that, while deeply connected, time under water is perhaps the greater evil over drawdown depth. I now double down on this hypothesis with additional evidence.
Volatility, in and of itself, is not risk -- it is merely movement. It becomes risk, however, when it exhibits unexpected asymmetry, or said differently, when there is uncertainty with regards to the recovery being of equal measure to the drawdown. If something falls some scary percentage, and recovers quickly, and relatively symmetrically, it’s almost as if the event didn’t happen; the fear during the down, effectively, was just our projecting doubt as to the recovery potential. If we were highly certain of the pending equal magnitude recovery, volatility would be far more acceptable. More so, the longer the time spent in drawdown, the longer our minds have to wonder about the viability of recovery; imposing a compounding uncertainty as a function of the area of recovery. In fact, following the trough that establishes maximum depth, only time is left to leave us to build this uncertainty. The risk, therefore, is in the reliability of the symmetry of our process, which is weakened, with time.
Why Does Time Weaken Credibility?
Why does time weaken credibility? For this answer, and because we “experience” loss, I turn to behavioral finance, which interestingly, bifurcates risk aversion in a way that perfectly addresses this very issue. Standard “risk aversion” demonstrates the general human tendency to lower exposure to uncertainty, even when it’s not cost effective to do so (concave utility). An “uncertain” investor prefers a smaller payoff with higher odds over a larger payoff with lower odds in the face of a better expectancy for the larger payoff. They’ll put more money into an index fund with a lower but safer return vs. a single stock with twice the return potential but only 50% greater risk.
In contrast, there is a more discerning “ambiguity aversion,” which is the high level preference for known risks over unknown risks (aka known unknowns), once again, with a lower expectancy result – albeit, with a less informed expectancy for comparison (a potential concave utility, given that “unknown” has no discernable measure). An ambiguity-averse investor would rather choose an investment with a denser probability distribution with a discernable shape over one where the shape has not yet been revealed. We prefer a lower return of a longer track record over a higher return of a short one.
Bringing it all together, the distinction within risk aversion is crucial, yet subtle; uncertainty aversion selects between two knowns -- albeit with economically irrational preferences -- while ambiguity aversion selects for knowns over unknowns -- with potentially irrational preferences. Combined, we get a decision tree: in viewing risky vs. ambiguous alternatives, we first control for ambiguity, and then hone in on our utility to determine our risk premium for uncertainty. Uncertainty is the controllable one, ambiguity is not, and so ambiguity is the greater risk. Or said differently, ambiguity must be the deciding factor. For once ambiguity is accounted for, we can apply our known probabilities to optimize to our ideal risk/reward -- containing uncertainty within our comfort boundary.
With this in mind, we can now circle back around to the idea that drawdown symmetry (in equal depth and equal time) seems to provide us with a sense of comfort, as if we believe more in the underlying process. Why so? Because with passage of time comes ambiguity; the less the right side of the distribution behaves like the right side we expected, or have seen before, the greater unknown we have about the underlying process -- once established as “not” symmetric, the asymmetry can literally be any shape. Ambiguity explodes -- and the aversion kicks in.
Thus, in my further dismantling of risk, I re-confirm that time underwater is the greater concern. The problem with concluding this reality, however, is how in the world to then discern the risk component within a strategy that specifically contributes to time underwater. How can one solve for an unbounded unknown?
After pondering this question for a while (time to think being the ultimate benefit of time), the answer, I realized, was much like my father’s stereo: the music was not stored inside the box. In other words, my knowledge of the particular risks that lurked inside statistical arbitrage had come from years of listening to the music that the strategy played, but as it turned out, an unknown component of risk had found its way into the system -- and played a different song. This was the key; the contribution to time spent out of whack was the result of some exogenous variable. If some relative mispricing exists, and we assume significant confidence in the rationality of that mispricing, but with time, it does not resolve itself, and instead becomes even wider, than the contributing factor to its “misbehavior” is clearly something external. Simply, the larger misbehavior cannot be a result of the smaller misbehavior. Accordingly, we ask, “What is causing this misbehavior to continue?”
And with that question, the music changed to rock-n-roll, and my task assumed a laser focus: mitigate the influence of exogenous variables, which collectively, will reduce both time under water, and ambiguity, its evil cousin. I shall talk more about this effort in my next post…
Chief Investment Officer
Logica Captial Advisers, LLC