The Risk Clock

Some things come in cycles; is a common saying I am sure we have all heard before. This seems to be even more so the case when we are presented with a complex disorder which is stubborn to stamp out. We will have moments when everything is going fine, only to be presented with a set of known preconditions over and over again that result in what we thought was under control, suddenly being less so.

Are risks more seasonal than we would like to first imagine?

Contagion Cycles

Perhaps one of the best places this can be evidenced is in the surveillance of diseases such as the "seasonal flu". If you were to take a look at data on positive cases of influenza infection across either the United States or Australia, it becomes apparent quite quickly that there seems to be a repetitive pattern of re-occurrence. That is, number of infections increase sharply, reach a peak in society, then decline as the community at large becomes healthy or immune. A few months go by and this cycle starts over again, making it just about impossible to eradicate the contagion entirely.

Seasonal Deaths from Influenza Virus

The statistical peaks and troughs of influenza circulation between the United States and Australia appear to be routinely "out of sync" and in a generalized manner. This would lead one to believe that seasonal weather patterns may play a substantial role in the infectious nature of the disease, either way the peaks and trough patterns seem to hold year on year.

Epidemic Threshold and Seasonal Baselines | CDC

The proportion of specimens testing positive for influenza during the 2010–11 season first exceeded 10%, indicating higher levels of virus circulation, during the week ending November 27, 2010. The proportion peaked at 36% during the week ending February 5, 2011, and declined to <10% during the week ending April 16, 2011.

In both United States and Australia disease data, a baseline of infection for an expected case load of influenza is present. This fluctuates in a sinusoidal manner and allows us to forecast the number of infections over each period but it also allows an analyst to detect when abnormalities are occurring in the viral community.

 

Oscillators & Hidden Markov Models

Most common approaches for modeling seasonal baseline data types use cyclical regression methods and one popular model that is popular, is the Serfling's approach. There is actually a good working example of this model on the Australian Department of Health Website and the link for it can be found here [ LINK ].

Serfling's method has gone through a lot of changes or enhancements overtime and the formula goes something like the following:

Serfling's Original Method | Hand written, sorry I don't like equation editor

The important point to note with Serfling's work is the use of the Sine and Cosine functions. These functions are actually the engine of model occurrence in periodic samples when seeing cyclical hazards from a Serfling perspective.  We can also extend this thinking into a Risk Clock which captures harmonic cycles of risk growing and decaying in uniform patterns. Such a Risk Clock has been shown below as an expansion on various notes from Wikipedia [ LINK ] and you can see how the risk clock works here by clicking on the image below.

The Risk Clock [Click to enlarge image]

The idea that there are natural harmonics of disorder that can be treated as an expected baseline is an interesting extension to the uncertainty conundrum and it assumes risk is a variable that is oscillating. It is also possible that there are hidden Markov properties in cyclical risk patterns and this idea has been written up by a team of analysts from Boston University. 

Their paper [ LINK ] is certainly deserving of a peruse.

Serfling seems to be everywhere

But let's take this Risk Clock concept further and ask ourselves where else can these natural risk harmonics be found?

Market Cycles

Certainly if we turn to financial markets, there are plenty of market indicators which are cyclical in nature. Take indicators such as Moving Average Convergence and Divergence just for example.  MACD is a trend like momentum indicator which is created to identify the significance between the two moving averages: The 26 day exponential moving average and the 12 day version of the equivalent.  The signal line is then plotted over the top of the MACD graph.

Example Technical Patterns in Markets

It doesn't stop with MACD line patterns and technical traders are swamped with plenty more oscillator signals that give them indication on when to take a position or to let it go.

Here are some other oscillators used by traders: Chaikin Oscillator, Percentage Price Oscillator, Double Exponential Moving Average, Chande Momentum Oscillator, Klinger Oscillator and many more.

Weather

One obvious place to expect oscillation modelling would be in weather and much work has been accomplished in this field. Earth has a natural climate pulse that can be quantified using a Primary Forcing Mechanism that assists analysts identify long-term displacements of regional high pressure systems from the expected baseline. Without any doubt, David Dilley's site is a piece of work too, incredible research actually and a link for his material can be found here [ LINK ].

Air crash investigations

Joan Lowy from the Associated Press takes note that the longest period without a catastrophic domestic airline accident is occurring since commercial aviation and while that may sound like fantastic news and an outcome of improved standards, it is also the largest factor that puts the Federal Aviation Administration in an uncomfortable place. Just because unwanted events haven't actualized, doesn't mean to say that all is well with aviation safety [ LINK ].

Cyclical Effects of Consumer Finance

Basel III has added many new risk elements to its regulatory toolkit and one such area of risk control is the management of procyclical effects in lending portfolios. However, while the creation of countercyclical buffers may be new for the Basel III banking accord, the concept of cyclical effects hidden within credit risk portfolios is not novel to banking.

Cyclical Effects in Credit Risk Models | BIS

It is almost axiomatic that defaults and credit problems would multiply in times of distressed macroeconomic conditions. Moreover, good economic times provide the rising tide that lifts even the shakiest of financial boats. Thus, ex post realizations of credit problems display clear procyclical patterns increasing during recessions and decreasing during expansions - Bank For International Settlements [ LINK ].

In fact, if we continue to review various areas of risk management, economics or science, the list is endless and it is quite easy to discover evidence of the procyclical impacts from the oscillation of casual risk factors.

All this aside, the practice of understanding the seasonality in exposure management is rarely given enough commercial focus in my opinion. There are several reasons why this tends to happen and I have taken to list three concerns below:
 

[1] Firstly during a waning cycle of risk events, management have a tendency to be lulled into a false sense of security and take great homage that their risk management strategies are totally sound. In a similar manner in which Joan Lowy describes, risk standards are met, compliance costs are high and complacency sets in, risk management standards then fall until a catastrophe occurs before the cycle starts over again.

[2] The next problem is algorithm based. That is, creating a model to manage cyclical impacts from causal factors to outcomes isn't so straight forward to achieve and it requires business managers to have a complete grasp across the numbers before the modelling even commences. Be that as it may, health organisations across the planet seem to have done very well with their methods for forecasting contagions and when it comes to weather, "cyclicality" modelling seems to be the heart of the science in meteorology.

[3] The final hurdle impeding the control of cycles in risk management comes from the behavioral corner.  It is always difficult to go against the crowd when markets are rising and profits are improving. Sadly, those risk managers who attempt to reign in risk taking attitudes through programs such a countercyclical buffering when everything looks blue-sky, tend to become unpopular very quickly.

In the end, perhaps the old idiom rings true, "make hey while the sun shines and always save for a rainy day."