Finiteness of variance and its limitations in quantitative finance

For our 4/26 discussion, a paper by Nassim Taleb, with his typical choleric flair:

“Outside the Platonic world of financial models, assuming the underlying distribution is a scalable “power law”, we are unable to find a consequential difference between finite and infinite variance models –a central distinction emphasized in the econophysics literature and the financial economics tradition. While distributions with power law tail exponents α>2 are held to be amenable to Gaussian tools, owing to their “finite variance”, we fail to understand the difference in the application with other power laws (1<α<2) held to belong to the Pareto-Lévy-Mandelbrot stable regime. The problem invalidates derivatives theory (dynamic hedging arguments) and portfolio construction based on mean-variance. This paper discusses methods to deal with the implications of the point in a real world setting.”

Link to paper

Comparing realized and absolute return volatility measures

This paper compares two different ways to measure volatility, with a survey of techniques that analyze their respective probability distribution, mean-reversion, cross-correlation, and long-term memory effects.

Excerpt: “…two nonparametric measurements have emerged and received wide use over the past decade: realized volatility and absolute return volatility. The former is strongly favored in the financial sector and the latter by econophysicists. We examine the memory and clustering features of these two methods and find that both enable strong predictions. We compare the two in detail and find that although realized volatility has a better short-term effect that allows predictions of near-future market behavior, absolute return volatility is easier to calculate and, as a risk indicator, has approximately the same sensitivity as realized volatility.”

Link to paper

An analysis of Warren’s Buffet’s investment strategy

Buffett’s Alpha. by Andrea Frazzini, David Kabiller, and Lasse Heje Pedersen

The authors find that Buffet has been picking low volatility, low beta stocks with consistent earnings, and then levering up his investment using his insurance float.

“Buffett’s returns appear to be neither luck nor magic, but, rather, reward for the use of leverage combined with a focus on cheap, safe, quality stocks. Decomposing Berkshires’ portfolio into ownership in publicly traded stocks versus wholly-owned private companies, we find that the former performs the best, suggesting that Buffett’s returns are more due to stock selection than to his effect on management.”

Link to paper   Slide version


Momentum Crashes. by Kent Daniela, obias J. Moskowitz, Journal of Financial Economics. Volume 122, Issue 2, November 2016, Pages 221–247

From abstract: “An implementable dynamic momentum strategy based on forecasts of momentum’s mean and variance approximately doubles the alpha and Sharpe ratio of a static momentum strategy and is not explained by other factors. These results are robust across multiple time periods, international equity markets, and other asset classes.”

Link to paper