A rolling stone gathers no moss, but an old risk model does
Investors have been talking about risk ever since the first time one of them got a forecast wrong. Given the impossibility of the investor in question being blamed for this outrageously unpredictable outcome, a third-party had to be named to take the fall and, thus, ‘risk’ was born. Like all negative things in life, we would rather not think about risk and instead refer to it in abstract terms, simply as the probability (real or imagined) of losing part or all of our investment. Over time we have come think of risk as an immutable fact of life, much like the laws of physics. For every action, there is a reaction, and the probability of the latter being rather ‘unpleasant’ is simply non-zero. Attempting to quantify it any further was seen as inviting darkness. Since then, however, humans have discovered that the earth is indeed round and have voyaged to the moon (and beyond). Given that those discoveries have yet to turn us into stone, building a risk model might be considered a safe endeavor. But what about building a second one? Surely, if the first attempt was considered “good enough” for general consumption, and a new one is meant to forecast the same exact thing as the first, then the effort comes dangerously close to the definition of insanity. The very same criticism could be made today of mobile phone manufacturers, if – and it’s a big if – phone usage had not changed since the days of Graham Bell.
And therein lies the rub.
Reality is, of course, entirely different. For one, risk isn’t static and although it represents something we can never accurately measure, it is driven by constantly changing sources which we can identify, measure, and track through time for changing levels of explanatory power. We need to acknowledge the fact that markets, no less than species, are shaped by a continuous process of evolution, and as such, they constantly change and adapt to new sources of risk. Just like mobile phone usage, today’s portfolio strategies are different from five, ten, twenty years ago, and the sources of risk driving their returns have likewise changed through time. For example, when treasuries yielded above 6% (1994) or above 4% (2004), no one was building an equity portfolio for ‘income’; but after a decade of QE programs, the search for yield has driven liquidity to the stock market and away from bonds.
If we think of a risk model as a deterministic framework designed to provide a cause and effect definition of the interrelationships between time-varying sources of return based on a series of assumptions about the data generating process in the market, we can easily imagine how revisions might become necessary over time. Old sources of risk fade in explanatory power (or are simply arbitraged out of the market), new ones are identified, and the interaction between them, data calibration issues, distribution assumptions, exposure approximations, and so on, will all need to be revisited. The misalignment between the sources of risk identified in an ‘old’ model and the ones driving a ‘new’ strategy can lead to large risk under-predictions and leave investors much more vulnerable to outsized losses then they think they are. Viewed under this light, a risk modeler has not merely a right to revise his previous work, but a positive duty.
Multi-factor models, the kinds Axioma builds, have two parts. A return model made up of a set of identifiable factors (in the case of our fundamental factor models) used to explain the observed return history as an aggregation of factor returns, and a risk model describing their interrelationships in the form of a mathematical construct of variance, covariance, and a residual piece. The former is often referred to as the ‘Art’ – or the ‘Religion’ depending on who you talk to - of risk modeling and the latter as the ‘Science’. Both are used by the model builder in dealing with the multiple compromises required in a commercial risk model, and any request for change to how these compromises are dealt with necessitates constant revisions to both underlying models.
Critics of quantitative risk models often point to the fact that they are built by someone looking in the rear-view mirror; the past is not prologue, they say. This, in effect, is akin to describing markets as the off-spring of a Virgin Birth, emerging ex nihilo, untainted by any trace of their risk DNA. Yet those same critics are reluctant to give any credibility to a vision of future returns that omits proper account of the past. Drivers of risk are no less contingent on systematic influences of the past than their return counterpart, and to trace the origins of a return signal, but not a risk one, is being in a state of profound quantitative denial.
An academic defense of risk modeling is well beyond the scope of this post, and, truth be told, of my own capabilities. Suffice it to say that the difference in modeling risk versus return has little to do with hubris or a general state of navel-gazing on the part of both participants, and more with the fact that the two disciples are searching for two radically different perspectives. For one, a risk factor is only useful if it is significant, affects a very large segment of the market, and is consistent through time. A return signal, on the other hand, can represent a small mispricing, be selective in its constituency, and available only at certain times. Properly designed and maintained, both can be a source of invaluable decision support. Left stale, however, they can only foster an agonized consciousness that history might be a nightmare from which we have not yet awaken.
Axioma has just released upgraded versions of its Japan and Australian suite of risk models with marked improvements in both the return model (three new Style factors) and the risk model (methodology improvements to increase stability and intuition). Built on the latest market environment, and ‘aware’ of newer popular strategies, I strongly recommend taking the time to analyze your portfolios with these newer models to discover if the sources of risk in your portfolio are still the ones you thought