Monday, October 25, 2010

“The Great Mandelbrot”

That is how Nassim Taleb described his first encounter with the work of Benoit Mandelbrot. My own encounter with his work occurred when I read his book, The (Mis) Behavior of Markets, A Fractal View of Risk, Ruin, and Reward. I was very saddened to learn last week that Mandelbrot died of cancer on October 14th in Cambridge, Massachusetts. He was 85 years old. I have little to no idea how mathematicians and economists are nominated for a Nobel Prize, and recent winners like Paul Krugman lead me to be skeptical about the process. If there is any justice, Mandelbrot will be accorded the honor of the Nobel, even if he made it clear in life that he didn’t exactly revere the prior winners.

Mandelbrot’s genius was his ability to see risk differently from everyone else, and then to be able to express it in a new kind of mathematics called fractal geometry. His book goes into great detail about fractals, but for the purposes of this blog I will simply say that they look beautiful. My key take away from Mandelbrot’s work was to better understand the problems with standard deviation as a measure of risk. Mandelbrot helps us to understand that risk is actually a lot “wilder” than standard deviation implies, and that the odds of “fat tail” occurrences are actually much higher than is generally understood. He gives us a new measure of risk called Power Laws where the odds of an event occurring do not geometrically increase as you get further from the average or the mean, which is exactly what happens when you measure risk using a bell curve. The insight that financial risk (which should be measured by Power Laws) is different from the deviation from the mean found in nature (which can be measured by bell curves and standard deviation) leads to powerful new conclusions about how to manage risk in portfolio management. Today the problems with “fat tails” are part of the lexicon of informed portfolio managers, and “fat tail” investment strategies designed to hedge these risks are approaching the mainstream. I believe Mandelbrot is the “founding father” of our new appreciation of risk as portfolio managers.

His book is coauthored by Richard L. Hudson, and I wonder who should get the credit for writing a book about so difficult a subject that is so easy to read. I often thought that I would have liked to sit in his classes at Yale where he taught since 1987 after a long career at IBM. My best tribute to Mandelbrot is to ask you to read his book, which I quote liberally in my book, Buy and Hold is Dead (Again), The Case for Active Management in Dangerous Markets. Chapter XII is one of my favorites, called Ten Heresies of Finance. Here they are: 1) Markets are Turbulent, 2) Markets are Very Very Risky- More Risky Than the Standard Theories Imagine, 3) Market “Timing” Matters Greatly. Big Gains and Losses Concentrate into Small Packages of Time. 4) Prices Often Leap, Not Glide. That Adds to the Risk. 5) In Markets, Time is Flexible, 6) Markets Will in All Places and Ages Work Alike, 7) Markets are Inherently Uncertain, and Bubbles Are Inevitable, 8) Markets Are Deceptive, 9) Forecasting Prices May Be Perilous, but You Can Estimate the Odds of Future Volatility, and 10) In Financial Markets, the Idea of “Value” Has Limited Value. I’m not on the Nobel committee, but I can recognize the passing of a giant when I see it.