Non-Linearities and Capacity

I bought my current house 11 years ago.  The area where it is located was then in the middle of a long drought.  There was never any rain during the summer.  Spring rains were slight and winter snow in the mountains that fed the local rivers was well below normal for a number of years in a row.  The newspapers started to print stories about the levels of the reservoirs – showing that the water was slightly lower at the end of each succeeding summer.  One year they even outlawed watering the lawns and everyone’s grass turned brown.

Then, for no reason that was ever explained, the drought ended.  Rainy days in the spring became common and one week it rained for six days straight.

Every system has a capacity.  When the capacity of a system is exceeded, there will be a breakdown of the system of some type.  The breakdown will be a non-linearity of performance of the system.

For example, the ground around my house has a capacity for absorbing and running off water.  When it rained for six days straight,  that capacity was exceeded, some of the water showed up in my basement.   The first time that happened, I was shocked and surprised.  I had lived in the house for 5 years and there had never been a hint of water in the basement. I cleaned up the effects of the water and promptly forgot about it. I put it down to a 1 in 100 year rainstorm.  In other parts of town, streets had been flooded.  It really was an unusual situation.

When it happened again the very next spring, this time after just 3 days of very, very heavy rain.  The flooding in the local area was extreme.  People were driven from their homes and they turned the high school gymnasium into a shelter for a week or two.

It appeared that we all had to recalibrate our models of rainfall possibilities.  We had to realize that the system we had for dealing with rainfall was being exceeded regularly and that these wetter springs were going to continue to exceed the system.  During the years of drought, we had built more and more in low lying areas and in ways that we might not have understood at the time, we altered to overall capacity of the system by paving over ground that would have absorbed the water.

For me, I added a drainage system to my basement.  The following spring, I went into my basement during the heaviest rains and listened to the pump taking the water away.

I had increased the capacity of that system.  Hopefully the capacity is now higher than the amount of rain that we will experience in the next 20 years while I live here.

Financial firms have capacities.  Management generally tries to make sure that the capacity of the firm to absorb losses is not exceeded by losses during their tenure.  But just like I underestimated the amount of rain that might fall in my home town, it seems to be common that managers underestimate the severity of the losses that they might experience.

Writers of liability insurance in the US underestimated the degree to which the courts would assign blame for use of a substance that was thought to be largely benign at one time that turned out to be highly dangerous.

In other cases, though it was the system capacity that was misunderstood.  Investors miss-estimated the capacity of internet firms to productively absorb new cash from the investors.  Just a few years earlier, the capacity of Asian economies to absorb investors cash was over-estimated as well.

Understanding the capacity of large sectors or entire financial systems to absorb additional money and put it to work productively is particularly difficult.  There are no rules of thumb to tell what the capacity of a system is in the first place.  Then to make it even more difficult, the addition of cash to a system changes the capacity.

Think of it this way, there is a neighborhood in a city where there are very few stores.  Given the income and spending of the people living there, an urban planner estimates that there is capacity for 20 stores in that area.  So with encouragement of the city government and private investors, a 20 store shopping center is built in an underused property in that neighborhood.  What happens next is that those 20 stores employ 150 people and for most of those people, the new job is a substantial increase in income.  In addition, everyone in the neighborhood is saving money by not having to travel to do all of their shopping.  Some just save money and all save time.  A few use that extra time to work longer hours, increasing their income.  A new survey by the urban planner a year after the stores open shows that the capacity for stores in the neighborhood is now 22.  However, entrepreneurs see the success of the 20 stores and they convert other properties into 10 more stores.  The capacity temporarily grows to 25, but eventually, half of the now 30 stores in the neighborhood go out of business.

This sort of simple micro economic story is told every year in university classes.

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It clearly applies to macroeconomics as well – to large systems as well as small.  Another word for these situations where system capacity is exceeded is systemic risk.  The term is misleading.  Systemic risk is not a particular type of risk, like market or credit risk.  Systemic risk is the risk that the system will become overloaded and start to behave in severely non-linear manner.  One severe non-linear behavior is shutting down.  That is what the interbank lending did in 2008.

In 2008, many knew that the capacity of the banking system had been exceeded.  They knew that because they knew that their own bank’s capacity had been exceeded.  And they knew that the other banks had been involved in the same sort of business as them.  There is a name for the risks that hit everyone who is in a market – systematic risks.  Systemic risks are usually Systematic risks that grow so large that they exceed the capacity of the system.  The third broad category of risk, specific risks, are not an issue, unless a firm with a large amount of specific risk that exceeds their capacity is “too big to fail”.  Then suddenly specific risk can become systemic risk.

So everyone just watched when the sub prime systematic risk became a systemic risk to the banking sector.  And watch the specific risk to AIG lead to the largest single firm bailout in history.

Many have proposed the establishment of a systemic risk regulator.  What that person would be in charge of doing would be to identify growing systematic risks that could become large enough to become systemic problems.  THen they are responsible to taking or urging actions that are intended to diffuse the systematic risk before it becomes a systemic risk.

A good risk manager has a systemic risk job as well.  THe good risk manager needs to pay attention to the exact same things – to watch out for systematic risks that are growing to a level that might overwhelm the capacity of the system.  The risk manager’s responsibility is then to urge their firm to withdraw from holding any of the systematic risk.   Stories tell us that happened at JP Morgan and at Goldman.  Other stories tell us that didn’t happen at Bear or Lehman.

So the moral of this is that you need to watch not just your own capacity but everyone else’s capacity as well if you do not want stories told about you.

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Explore posts in the same categories: Assumptions, Black Swan, Financial Crisis, Modeling, Random, Risk, risk assessment, Risk Learning, Risk Limits, Sub prime

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