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  • Writer's pictureLogica

Variable Variables

From Calm to Chaos

"Assumptions are the termites of relationships' ~ Henry Winkler I warmly recall my long-ago best friend Darren. In the late 90’s, he and I were an unstoppable riot act, laughing our way through hours upon hours of conversation, hanging out, dining out, biking through Central Park on weekends, and being all around adventure buddies. Then, around 2009, I met Casey, an amazing woman who I ended up marrying in 2010. I was head over heels for her from the very beginning, and didn’t want to do anything but see her, talk to her, and just all around be with her, as if her gravitational field had my name on it. But I couldn’t just write off my best buddy Darren. So, for awhile, I did what many of us have likely done in a similar situation, I tried to include both of them in gatherings as often as made sense. But it didn’t work out the way I had hoped it would.What I soon realized was that while I connected so well with each of them, and could talk for hours on end about all things under the sun to one or the other of them, the two of them barely shared this with each other. The harmony imploded when all three of us were together; the enthusiasm went into hibernation and the relentless laughter left the room in confusion. Our time -hanging out was still fun, with intermittent laughs and mediocre discussions, but something big was lacking. I thought deeply about this at the time, struggling with splitting myself between two people I cared very much about. It was fascinating to me, conceptually, how I could be so close to each of them, while the two of them barely connected. The relationship triangle didn’t add up to 180 degrees; I had straight lines of communication each way, but they had a warped line to each other. I soon came to understand that the incongruence was a result of some form of underlying competition between them that made fusion unattainable. Competition was the confounding variable that changed the “co-relation.” This odd facet of relationships, and specifically, the hidden variable that finds its way into the existing harmony,now comes full circle into my experience in portfolio management, and in particular, in seeking to balance portfolio risk exposures. The widespread attempt across our industry for “diversification” is one that I don’t necessarily agree with in a vacuum. As an easy example, adding more long positions to a portfolio does not reduce directional exposure, and to that end, I’d rather have 10 longs and 10 shorts, than 50 longs. While this is certainly a simplistic example, the general idea goes significantly further, and gets incredibly more complicated, as one layers on exposures to mitigate. As I touched upon in my last post, it was some newly infused exogenous influence which slammed head-on into the long term stable behavior of my otherwise market neutral portfolio. What Happened this Year? While exposures like directional risk (through neutrality), company specific risk (through number of positions), and volatility (through weighting/normalization) were all well handled, a new risk -- before unseen -- surfaced. This was particularly surprising to me because I had methodically gone through and assessed all the foreseeable exposures. But what I had clearly missed was “correlation risk,” or more specifically, the correlation of portfolio components to some exogenous lurking factor, such that when something in the broader environment did “x and y”, my purportedly risk controlled portfolio flipped out. I have realized since, that just like the law of conservation of energy, risk never really goes away, it just transfers. Diversifying idiosyncratic risk, by adding more positions, further concentrates systemic risk (ie market or factor risk). More importantly, the risk that is being infused, via transfer, may not reveal itself anytime soon. To an extent, the attempted reduction of volatility may, inevitably, always result in an increase in unrealized volatility. Can there really be no ideal solution to more permanently mitigating risk? With that question, I refer back to my relationship circle, and how, analogously, it reminds me of the 3 body problem. The 3 body problem is a long pondered issue at the heart of physics -- while it is very possible, and relatively easy, to solve for the future position of 2 moving bodies using the universal laws of gravity and motion, it becomes impossibly difficult to solve for the same given the introduction of just one more body. Technically, there is no closed form solution given all sets of initial conditions, and so approximations must be relied upon. But how can this be? Why is it that we can utilize the precise laws of the nature to calculate the exact location of the moon, relative to the earth, in 107,682 days from now, but only if there is no influence from the sun or any of the other planets? Introduce more bodies into the system -- or rather, just one more body -- and precision unfolds to chaos. This is just like my relationship triangle conundrum, where the 1 by 1 connections were fluid and easy, while the 3 of us together brought about a choppy and awkwardly complex interaction. The introduction of a new variable, even when existing correlations were well understood, did nothing to extrapolate the new multi-variable dynamics; linearity unraveled into non-linearity. It is a given that correlation is not stationary (what has correlated for awhile may not correlate tomorrow), so is inherently unreliable on a 1:1 basis. But this characteristic is generally dependent on establishing the organic causal relationship between the two components; the higher the causal relationship, the more reliable the correlation. The strange thing about the relationship circle was that there was high causality -- I cared a lot about my best friend, and more so, with the woman I was to marry -- but, the 3 way relationship crumbled. In part because of their dynamics, and in part because my discomfort in the presence of their friction caused me to act differently. Simpson's Paradox This construct leads me to introducing an even more extreme problem in correlation across numerous variables: Simpson’s Paradox, which is also aptly dubbed “reversal paradox” or “amalgamation paradox”. In this paradox, a strong correlation can appear between datasets, but will literally be reversed -- from a positive to negative, or vice versa -- by merely bifurcating them! It’s confounding bliss. A great example in the financial markets is when we observe a company consistently raise its price on a product and the demand concurrently increases, as if all the established rules of supply and demand are cooly dismissed. How can increasing price be positively correlated with increasing demand? Some, (i.e. those who sidestep Simpson’s Paradox) might suggest a new paradigm. But no, nothing new under the sun, there’s just a confounding variable that, when brought out of hiding, puts things back into their rightful place. In the price/demand correlation conundrum, the confounder is time. Once we bifurcate price and demand, and assess them each independently with respect to time, we can once again rejoice that no paradigms have collapsed, as the expected negative correlation reveals itself over various fixed timeframes. The reversal of correlation to positive of course comes back, if we ignore the influence of time and simply regress demand against price. With this enlightening example, and many others of the same nature, I have come to believe, very strongly, that idiosyncratic risk may actually be “safer” than correlation risk. Idiosyncratic risk screams at us, but correlation risk is a silent killer. Correlation is not only unstable to begin with, and so inherently unreliable, its instability, and even reversibility, can lead to the total demise of a portfolio. In sum, there is extreme danger in interconnectedness.With this knowledge, I lean toward being significantly more aware of the interplay between portfolio components, not just in regard to those we know of, and are actually trying to mitigate (such as beta neutralizing long/short exposure), but more so, with respect to those that might be creeping up as a result of the very mitigations we are performing (such as the beta neutralization introducing asymmetric volatility risk). At large, I start to think about risk management not as a list of items, but as a tree -- where the roots intertwine as the branches extend -- and accordingly, build a better toolset. If only I had that toolset ten years ago, I might have been able to maintain a better friendship with my buddy Darren. Wayne Himelsein Chief Investment Officer Logica Captial Advisers, LLC

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