Tuesday, October 6, 2015

Two Hundred Year Floods and the Mercedes Maybach

The year is 1950. You are a county commissioner living in a growing suburban area. Your citizens are going to need more water, a lot more water, in the coming years. A plan is proposed to float a bond issue to fund a new reservoir to meet the demand generated by projected population growth for maybe the next twenty years. You have a lot of decisions to make. Being a prudent man, you consult with a professor of civil engineering from a nearby university. The engineer using the best available methods tells you that a properly constructed earthen dam will meet your requirements at a cost of $3 million. When you ask him if the dam will be safe, he might give you this answer, “This dam will have a 98.6% chance of surviving a once in a century flood.” You might ask him if something safer could be built. He might tell you that a reinforced concrete dam would be safer, but would cost $30 million to build.

Since your total budget for the project is capped at $15 million, your decision has already been made for you.

Sixty five years later, a once in 200 year flood hit the Midlands of South Carolina. Several small dams suffered varying types of failure, adding to the region’s difficulties. It will take the state some time to recover from this disaster. Your prayers and assistance for the victims is appreciated.

Risk evaluation is an important skill not only in selecting investments, but for living in this material world. People make statements like, “A once in a hundred year event,” all the time. What does it really mean if your town suffered a once in a thirty year flood twice in one year as happened in Maryland not so many years ago.

In The Plight of the Fortunetellers by Riccardo Rebonato, the author analyzes why the quants, some of the brightest mathematicians on the planet armed with the largest computers money could buy failed to properly evaluate risk during the real estate crash of 2006 and the subsequent stock market crash of 2008. In short, they were applying statistical methods that while mathematically correct were treating all available data, say 200 years worth, as equally valuable then using that data to predict events that might only happen once in 1,000 years. Such an approach is deeply flawed. While we can make such statements about events like flipping a fair coin with a limited data set, the stock market is not as predictable, since it is driven by human greed and fear more than by rational behavior.

Not only do we live in a world that contains an element of randomness, it is also at times a very nonlinear world. Very small differences in initial conditions, such as the exact date you choose to buy a particular stock, can produce radically different results over an extended period of time. Modern portfolio theory (MPT), the best investment tool available to the normal prudent investor, assumes that changes in the stock market can be described by a Gaussian distribution. The theory assumes that the probability of a share price moving more than 10 or 20 times the average daily move in a particular day is diminishing small. Even excluding events like the declaration of war or fraudulent activities such as insider trading, Benoit Mandelbrot has demonstrated that the market is a much more dangerous place than can be predicted by MPT. The truth is we can expect a significant stock market crash about once every ten years, more often than can be explained by MPT. The bottom line is that the market can and does move as much in a matter or minutes or even seconds as one would expect in years.

Such decisions are not limited to engineers, politicians, and investors. We all make such decisions all the time. All of us wish to drive around in a safe car. However, there is that pesky question, “How safe at what cost?” Most years, the safest production car in the world will be the flagship of the Mercedes Benz line. This year that would be the Maybach, a car that can be had for around $200,000 depending on the options selected. Yet most of us drive around in cars that cost $28,000 or less when new. They aren’t as safe as a Mercedes, but we judge them as “safe enough.”

Predicting the future is at best a risky proposition, but it is something that must be done both implicitly when we open our garage door and drive our Toyota Corolla out into rush hour traffic and explicitly when choose to invest in a particular mix of low cost index funds. Most mornings, most of us make it to work without incident. Just as we know that market crashes occur from time to time, we also know that Jeremy Siegel has demonstrated that investing in American equities has produced a remarkably steady return of about 7% after inflation and taxes over any sufficiently long period of time.

Now, Lets be careful out there.

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