# Steve Irwin Redux, from Tom Ryan

September 13, 2006 |

One of the problems that I see repeatedly in my work is the confusion over probability regarding a single event, vs. the probability of a sequence or continuum of events. A good example would be Steve Irwin's show stopping stunts, or a question recently posed to us by one of our clients regarding mining safety, or trading, or the topic of this morning's coffee … which was bicycle commuting. Although most people can easily think in terms of probability for a single event (e.g. there is a 50% chance of the roulette wheel hitting black or a .00000001% probability of being hit by a car on my commute) they have a difficult time integrating this probability over a long period of continuous exposure. To do that you have to do a Pulaski/Feynman "invert, always invert" and look at the probability of an event not happening given a certain long period of continuous exposure. Continuing with the bicycling analogy, as long as bikes and cars are sharing the road, and given some basic newtonian physics (F=ma), the mass differential between a car and a human on a bicycle, there is a finite, albeit low probability (lets say 1e-08?) of being hit by a car and getting killed as it goes past you. No matter the speed limit, size of bike lane, cell phone laws etc, there is a chance you will get mowed down from behind, as a good friend of mine found out last year (he survived, barely).

So lets say your exposure is 1e-08 to any one car, and 100 cars pass you on your commute. The probability of being hit by a car for the total exposure must be evaluated by looking at the probability of surviving which can be approximated by (1.0-[1e-08])^100. Which means that for that exposure you have a .999999 probability of survival or a 1e-06 probability of getting hit. This can be expanded for longer and longer periods of exposure. Lets stick with a single event probability of 1e-08 for now, and 100 cars per commute to keep it simple.

1 commute, 1-e06 (.0001%)
10 commutes 1e-05 (.001%)
100 commutes 1e-04 (0.01%)
1000 commutes 1e-03 (0.1%)
10000 commutes 1e-02 (1%)
100000 commutes 1e-01 (10%)

The point is that any one ride is not that risky, but if you look at the risk for longer and longer time periods or more and more continuous exposure the behavior can start to look a bit risky.

This gets back to Steve Irwin, why people should wear their seat belts, and why when you get the 30 year term life insurance there are three pages of fine print about what behaviors are not covered. What can seem responsible behavior for a single event can start to look a bit dangerous given a long enough exposure to the hazard. This is where the media tends to fall down when reporting on things like Steve Irwin's unfortunate incident.

Recently we were examining a mining safety situation and looking at PDI (prob. of individual death) and PDG,n (probability of death for a group of size n). There are no mining industry standards, but some general ranges that are well accepted. Generally PDIs for a one year exposure of less than 3e-05 are considered 'low' risk, 3e-05 to 1e-03 'moderate' risk and anything above 1e-03 'high' risk. People's risk acceptance however tends to vary between voluntary (surfing) and involuntary (my job) tasks. For example when we looked at traffic safety records for the highway between Safford Arizona and the mine at Morenci, we found PDI's (based on miles traveled annually commuting to/from home/work) between 2e-04 and 6e-04. A panel, of which I was a member, could not find any job related position at the mine which had a PDI exceeding 3e-05. Yet both regulatory personnel and the workers considered working "more dangerous" than commuting.

How this relates back to the market is that the markets are in many ways a "perfect trap" for the fund investing public to make poor risk taking decisions over long time horizons. You have relatively low barriers to entry which results in a high level of competition, ever changing cycles which makes it hard to predict long term effectiveness of strategies, and a lack of control which lends itself to an involuntary risk perception. This is a long winded way of saying "stay out of the switches" and focus on the longer term but that is why I think passive index funds are so valuable to the layperson investing for long term horizons … because they allow anyone with a bit of math background to estimate risk in a quantitative fashion, which then allows one to set their own risk levels and create a portfolio that meets their long term goals.

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