Category Archives: Math and Statistics

"Fat Tails" and implications for risk management

Benoît Mandelbrot passed away last week at the ripe old age of 85. Mandelbrot was most famous for his seminal work in the field of fractal geometry, but is also considered by many (e.g., Nassim Nicholas Taleb, the author of Fooled by Randomness and The Black Swan) as the “intellectual father” behind critiques of efficient markets models. Mandelbrot’s critique of efficient market theory was centered on the notion that actual return distributions are more “fat tailed” than would be implied by the normal distribution. Taleb provocatively argues in chapter 15 of his book The Black Swan that the bell curve (normal distribution), when applied to financial markets, is a “great intellectual fraud”. Taleb has also recently argued that “… the Nobel Prize for Economics (specifically, the 1990 awards to Harry Markowitz, Merton Miller and William Sharpe for their work on portfolio theory and asset-pricing models and the 1997 awards to Myron Scholes and Robert Merton for their work on option pricing theory) has conferred legitimacy on risk models that caused investors’ losses and taxpayer-funded bailouts…”, and that “investors who lost money in the financial crisis should sue the Swedish Central Bank for awarding the Nobel Prize to economists whose theories he said brought down the global economy” (see “`Black Swan’ Author Says Investors Should Sue Nobel for Crisis“). While there is no question that Dr. Taleb’s narrative is brash and provocative, I am not convinced. Of course, he would argue that people like me who received their graduate training in finance during the past 2-3 decades have a vested interest in defending orthodoxy for its own sake. However, it’s only fair to also recognize that Dr. Taleb has a vested interested in defending heterodoxy for its own sake. It seems that Taleb seeks to discredit pretty much anyone who happens to disagree with him, not on the strength of the arguments that they marshall on behalf of “orthodoxy”, but rather on the basis of ad hominem arguments about how they can’t be taken seriously because they are intellectually biased a priori in favor of efficient markets orthodoxy. I couldn’t have explained the implications of Benoit Mandelbrot’s research for financial markets any better than Dr. Ewan Kirk, who is Chief Executive for Cantab Capital Partners in Cambridge, UK, so I quote directly from Dr. Kirk’s letter to the Financial Times entitled “How Mandelbrot Caused Confusion“: “It is true that markets are very difficult to model precisely. Indeed, even after this simple transformation, there continue to be significant non normal features to markets and of course there are always “unknown unknowns” and “black swan” events. However, these issues are considerably more subtle than just presenting the 100-year unscaled daily returns of the stock market and implying that foolish theoreticians and practitioners are modeling the returns as a stationary Gaussian or normal distribution.” Also, the essay by Bob Gillespie entitled “Black Swans and Absurdistan” is worth reading. In closing, I would like to point out two interesting videos from FT.com. The first video, “Inefficient markets and Mandelbrot“, features a debate concerning whether the impact of Mandelbrot’s legacy has been overstated. The other video, “Why ‘efficient markets’ collapse” is an interview with Mandelbrot recorded last year in which Mandelbrot explains his more than 40-year old critique of the “efficient markets” hypothesis and why new (i.e., Mandelbrotian) theories on price movement discontinuities are needed in light of the financial crisis of 2007-????.”]]>

“Fat Tails” and implications for risk management

Yale mathematician and emeritus professor Benoît Mandelbrot passed away last week at the ripe old age of 85. Mandelbrot was most famous for his seminal work in the field of fractal geometry, but is also considered by many (e.g., Nassim Nicholas Taleb, the author of Fooled by Randomness and The Black Swan) as the “intellectual father” behind critiques of efficient markets models. Mandelbrot’s critique of efficient market theory was centered on the notion that actual return distributions are more “fat tailed” than would be implied by the normal distribution. Taleb provocatively argues in chapter 15 of his book The Black Swan that the bell curve (normal distribution), when applied to financial markets, is a “great intellectual fraud”. Taleb has also recently argued that “… the Nobel Prize for Economics (specifically, the 1990 awards to Harry Markowitz, Merton Miller and William Sharpe for their work on portfolio theory and asset-pricing models and the 1997 awards to Myron Scholes and Robert Merton for their work on option pricing theory) has conferred legitimacy on risk models that caused investors’ losses and taxpayer-funded bailouts…”, and that “investors who lost money in the financial crisis should sue the Swedish Central Bank for awarding the Nobel Prize to economists whose theories he said brought down the global economy” (see “`Black Swan’ Author Says Investors Should Sue Nobel for Crisis“).

While there is no question that Dr. Taleb’s narrative is brash and provocative, I am not convinced. Of course, he would argue that people like me who received their graduate training in finance during the past 2-3 decades have a vested interest in defending orthodoxy for its own sake. However, it’s only fair to also recognize that Dr. Taleb has a vested interested in defending heterodoxy for its own sake. It seems that Taleb seeks to discredit pretty much anyone who happens to disagree with him, not on the strength of the arguments that they marshall on behalf of “orthodoxy”, but rather on the basis of ad hominem arguments about how they can’t be taken seriously because they are intellectually biased a priori in favor of efficient markets orthodoxy.

I couldn’t have explained the implications of Benoit Mandelbrot’s research for financial markets any better than Dr. Ewan Kirk, who is Chief Executive for Cantab Capital Partners in Cambridge, UK, so I quote directly from Dr. Kirk’s letter to the Financial Times entitled “How Mandelbrot Caused Confusion“: “It is true that markets are very difficult to model precisely. Indeed, even after this simple transformation, there continue to be significant non normal features to markets and of course there are always “unknown unknowns” and “black swan” events. However, these issues are considerably more subtle than just presenting the 100-year unscaled daily returns of the stock market and implying that foolish theoreticians and practitioners are modeling the returns as a stationary Gaussian or normal distribution.” Also, the essay by Bob Gillespie entitled “Black Swans and Absurdistan” is worth reading.

In closing, I would like to point out two interesting videos from FT.com. The first video, “Inefficient markets and Mandelbrot“, features a debate concerning whether the impact of Mandelbrot’s legacy has been overstated. The other video, “Why ‘efficient markets’ collapse” is an interview with Mandelbrot recorded last year in which Mandelbrot explains his more than 40-year old critique of the “efficient markets” hypothesis and why new (i.e., Mandelbrotian) theories on price movement discontinuities are needed in light of the financial crisis of 2007-????.”

Assorted Links (7/19/2010)

Here’s a list of articles that I have been reading lately:

David Cameron: A Staunch and Self-Confident Ally – WSJ.com

online.wsj.com

“British Prime Minister David Cameron writes in The Wall Street Journal that the U.S. and Britain have a clear common agenda: succeeding in Afghanistan, securing economic growth and fighting protectionism.”

You Don’t Have to Pay for Cable TV

www.moneytalksnews.com

“The average cable subscription costs $900 a year, but you can radically reduce that amount and still watch everything you want.”

Leeds: Chew on this: There is no surplus fairy for Social Security

www.statesman.com

Here’s the bottom line from Sandy Leeds’ editorial, published in today’s Austin American Statesman:

“The bottom line is that we’re in trouble. Social Security is woefully underfunded and Medicare is an even larger problem. This is going to increase the amount that we’re going to have to borrow from investors – and there’s no certainty that investors will always be willing to lend to us. Most importantly, we’re never going to solve these problems until the electorate understands the issues and starts to pressure our elected officials into making the hard (but right) decisions. We’re not doing anyone any favors by convincing them that we have “built up a big trust fund.””

Economics One: New Data Show the Debt Problem Is Spending (not Taxes) and Obamacare Worsens the Problem

johnbtaylorsblog.blogspot.com

Quoting from Stanford Professor John Taylor’s Blog (Economics One): “Everyone now seems to agree that the exploding federal debt is a serious problem that must be addressed. But how? The following … charts provide some data to help answer that question.”

Review & Outlook: A Climate Absolution? – WSJ.com

online.wsj.com

“A Wall Street Journal editorial says the global warming alarmists still won’t separate science from politics.”

Firms cancel health coverage

www.boston.com

Here’s what we have to look forward to as Obamacare starts to come “on line” (Massachusetts passed so-called Romneycare in 2006, and Obamacare structurally closely resembles Romneycare, only on a national as opposed to individual state level)… “The relentlessly rising cost of health insurance is prompting some small Massachusetts companies to drop coverage for their workers and encourage them to sign up for state-subsidized care instead, a trend that, some analysts say, could eventually weigh heavily on the state’s already-stressed budgets”.

Studying a Suicide Cluster at Foxconn – The Numbers Guy – WSJ

blogs.wsj.com

“To analyze whether a recent spate of suicides at a set of Chinese manufacturing facilities represents an unusual outbreak, it helps to make the right comparisons.”