Value at Risk (VaR)


Fully Flexible Extreme Views

Figure 1: View on CVaR: extensive search of minimum relative-entropy posteriorThe combination of subjective views within a broadly accepted risk model is one of the main challenges in quantitative portfolio management. Indeed, any risk model, be it based on historical scenarios, parametric fits, or Monte Carlo scenarios generated according to a given distribution, is subject to estimation risk and thus it is inherently flawed. Therefore, it is important to provide a framework that allows practitioners to overlay their judgement to any risk model in a statistically sound way.

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Humor: Geometric vs. Arithmetic Attribution

NYSSA member and FPP contributor David Spaulding put together this humorous little cartoon about the debate over geometric versus arithmetic attribution. 

Check out David's primer on value at risk and his article about its pitfalls.


Recent Research: Highlights from January 2011

The StressVaR: A New Risk Concept for Extreme Risk and Fund Allocation.” The Journal of Alternative Investments (Winter 2011). Cyril Coste, Raphaël Douady, and Ilija I Zovko.

In this article the authors introduce an approach to risk estimation based on nonlinear factor–models—the “StressVaR” (SVaR). Developed to evaluate the risk of hedge funds, the SVaR appears to be applicable to a wide range of investments. The computation of the StressVaR is a three-step procedure whose main component is to use the fairly short and sparse history of the hedge fund returns to identify relevant risk factors among a very broad set of possible risk sources. This risk profile is obtained by calibrating a polymodel, which is a collection of nonlinear single-factor models, as opposed to a single multi-factor model. The authors then use the risk profile and the very long and rich history of the factors to assess the possible impact of known past crises on the funds, unveiling their hidden risks and so called “black swans.”

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Proceed with Caution: The Pitfalls of Value at Risk

Value at Risk, or VaR, continues to garner a great deal of attention from the investment community, the media, and academia. While it is commonly used at banks, in trading depart-ments, and by many asset managers, we must ask how reliable it is. In Lecturing Birds on Flying (2009), Pablo Triana criticizes it amply; however, there may be more objective ways to grasp its shortcomings.

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In Defense of a Quant (Part II): The Ups and Downs of the Normal Distribution

In my previous column, I mentioned that particular attacks on the deficiency of mathematical finance are centered on the alleged misuse of “simplistic” normal distribution by the quants. Nassim Taleb never fails to contrast the disdainful and primitive “Brownian” paradigm with the supposedly more sophisticated “fractal” point of view, which he attributes to Benoît Mandelbrot. I quote only two passages from the Black Swan: “I find it ludicrous to present the uncertainty principle as having anything to do with uncertainty. Why? First, this uncertainty is Gaussian.” Or another pick: “So selecting the Gaussian while invoking some general law appears to be convenient. The Gaussian is used as a default distribution for that very reason.”

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In Defense of a Quant (Part I)

The public likes simple explanations, especially if they are argued with bombast. For instance, the financial crisis happened because “the young boys with PhDs in physics were conceiving a financial hydrogen bomb” (attributed to F. G. Rohatyn of Lazard Fréres). To me, it sounds like “the laws of fluid mechanics sunk the Titanic.” This is literally true, of course, but the substantive reason was much more mundane (and universal): hubris and the human propensity to throw all caution to the wind—literally and idiomatically—when big money is involved.

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Commentary: From Risk to Uncertainty

Stress-test complacency will be a cause of the next financial meltdown.

Economic commentators have been increasingly using the word “uncertainty” as of late. The context has included the business climate, the stimulate vs. austerity debate, and forecasting the investment outlook across capital markets. 

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Book Review: Managing Hedge Fund Managers

Managing Hedge Fund Managers Book Cover Edward Stavetski’s Managing Hedge Fund Managers provides a thorough analysis of the factors to be considered when investing in hedge funds. The book is particularly relevant now, at a time when less capital (due to deleveraging and redemptions) is chasing more alpha (due to market dislocations), making the hedge fund space more attractive. It is all the more compelling in our post-Madoff environment, as due diligence gains new significance, and investors are forced to play detectives.

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The Greater Fool Theory: Managing and Modeling Risk

The most dramatic financial meltdown since the Great Depression occurred despite recent advances in risk management techniques. Because of a fervent but unfounded belief in some quarters that VaR (value at risk) measures worst-case scenarios, financial institutions were exposed to crippling losses when VaR models failed to anticipate the extent of potential price movements, in some cases by whole orders of magnitude. 

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Recent Research: Highlights from June 2010

"A Valuation Study of Stock Market Seasonality and the Size Effect." The Journal of Portfolio Management, Spring 2010. Zhiwu Chen and Jan Jindra.

Existing studies on market seasonality and the size effect are largely based on realized returns. In this article, Chen and Jindra investigate seasonal variations and size-related differences in a cross-stock valuation distribution. They use three stock valuation measures, two derived from structural models and one from the book-to-market ratio. The authors find that the average valuation level is highest in mid-summer and lowest in mid-December. Furthermore, the valuation dispersion (kurtosis) across stocks increases toward year-end and reverses direction after the turn of the year, suggesting increased movements in both the underand overvaluation directions. Among size groups, small-cap stocks exhibit the sharpest decline in valuation from June to December and the highest rise from December to January. For most months, small-cap stocks have the lowest valuation among all size groups and show the widest cross-stock valuation dispersion, meaning that they are also the hardest to value. Overall, large-cap stocks enjoy the highest valuation uniformity and are the least subject to valuation seasonality. 

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A Primer on Value at Risk

Value at risk, or VaR, is viewed by some as a massively important measure. It is unique in how it characterizes risk. Most measures show risk either as a percentage (as standard deviation and tracking error do) or in units (as the Sharpe and Treynor risk-adjusted measures do). VaR shows risk in terms of money—that is, the money that might be lost.

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