Category Archives: Math and Statistics

Financial versus Mathematical literacy

It is rare when I actually take the time to read Baylor’s student newspaper, the Baylor Lariat, and even rarer when I post a critical response to a Lariat article. However, I couldn’t resist commenting on an editorial from earlier this month entitled, “Baylor should implement class to ready students for real world”. In this editorial, the members of the Lariat editorial board opine that Baylor should require a one-hour credit “Life Skills” course in lieu of a basic math course such as “Ideas in Mathematics”. Basically, such a course would be designed to cover very basic personal finance principles, such as budgeting, paying off student loans, buying insurance, saving for retirement, etc. I think this is a manifestly bad idea; let me explain why.

While I am not aware of an empirical literature concerning mandated personal finance courses at colleges and universities, many states have experimented with personal finance and minimum math requirements at the high school level. A recent (2014) Harvard Business School working paper entitled “High School Curriculum and Financial Outcomes: The Impact of Mandated Personal Finance and Mathematics Courses” provides a thorough empirical analysis of personal finance and minimum math requirements and finds that mandated personal finance courses at the high school level do little to improve outcomes that are generally associated with financial literacy (e.g., such as building wealth through asset accumulation, prudent credit management, etc.), whereas “… individuals who were exposed to greater math requirements in high school are more likely to accumulate assets, have more real estate equity, are less likely to be delinquent on their loans, and are less likely to undergo foreclosure.”

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Art meets chemistry meets physics meets finance

This Wired Magazine article provides a layman’s explanation of reaction-diffusion processes, which are characterized by reactive molecules that can diffuse between cells. A special case of a reaction-diffusion process is a “pure” diffusion process, where substances aren’t transformed into each other but nevertheless randomly spread out over a surface. While the reaction-diffusion process makes for much more aesthetically pleasing art, other so-called diffusion processes (e.g., diffusion of thermal energy as characterized by heat equations or movements of speculative asset prices as characterized by Itō diffusions) similarly generate (what appear to the naked eye to be) “patterns” from randomness…

Hypnotic Art

Hypnotic Art Shows How Patterns Emerge From Randomness in Nature

These digital canvases represent British mathematician Alan Turing’s theory of morphogenesis.

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Fibonacci numbers in nature and in finance

My favorite econ blogger, George Mason University’s Russ Roberts, posted the following (short, less than 4 minutes) video called “nature by numbers” yesterday on Cafe Hayek.  This video provides a remarkable and beautiful presentation concerning how Fibonacci numbers appear in nature. 

For more information concerning the math used in this video, go here.  Peter Bernstein (author of the worldwide best seller “Against the Gods: The Remarkable Story of Risk”) traces the origins of risk theory and finance back to a 13th century Italian mathematician by the name of Leonardo Pisano, who was known for most of his life as Fibonacci (see pages 23–26 from Bernstein’s book for historical context on the Fibonacci number series).  For some examples of applications of Fibonacci numbers in finance, go here.

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200 Countries, 200 Years, 4 Minutes (Hat Tip: Donald Marron)

Donald Marron posted this video from BBC on his blog the other day; apparently it is part of a BBC program offering called “The Joy of Stats”.  Hans Rosling, who is Professor of International Health at Karolinska Institute and Director of the Gapminder Foundation, provides a very remarkable presentation, showing in less than 5 minutes how wealth and life expectancy have changed over the course of the past 200 years for 200 countries!

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“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 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-????.”

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