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What is the consensus on which risk measure to use in measuring portfolio risk? I am researching what is the best risk measure to use in a portfolio construction process for a long/short option-free equity portfolio.

Since the late '90s thru today, it seems that VaR is the dominant risk measure but is losing ground.

Artzner et al. (1997) suggested properties for a risk measure to be coherent: exhibit sub-additivity, translation invariance, positive homogeneity, and monotonicity.

VaR is not a coherent measure whereas conditional value-at-risk (CVaR) or expected shortfall meets these normative requirements.

However, Rama Cont et al (2007) argue in "Robustness and sensitivity analysis of risk measurement procedures" that VaR produces more robust procedure for risk measurement.

One would think the debate is settled then. More recent risk research from Jose Garrido (2009) suggests that new families of risk measures be defined such as "complete" and "adapted" which addresses the fact that CVaR does not account for extreme losses with low frequency, and that VaR only accounts for loss severity as opposed to frequency.

Has there been further empirical research that argues for whether to use VaR or CVaR (or some other measure) in the construction of optimal portfolios?

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Interesting question. I had started to develop a preference for Expected Shortfall in my own thinking. I am not sure what empirical research could say, though, since all this is something of a matter of taste, is it not? –  Brian B Oct 25 '11 at 18:54
    
Starting with a normative definition of "what is risk" makes the most sense to me. In this view, I also have a clear preference for cVaR over VAR. However, the Rama Cont recent research suggests that some normative requirements (namely sub-additivity) conflict with other requirements (robustness). Also, CVAR (nor VAR) use the complete information in the loss distribution which can lead to inconsistent decisions -- well illustrated in the Jose Garrido example 4.1 on page 67. I am surprised this is not receiving much research attention (hopefully I am missing something)! –  Quant Guy Oct 26 '11 at 2:08
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@ QuantGuy : Hi I used to be a not so big fan of VaR compared to ES essentially because VaR is failing axioms of risk measures, but I attended a lecture where Cont has shown duality between robustness/some axioms of risk measures and this has led me to reconsider VaR in the picture as a not so bad but "to handle with care" risk measure. This duality prevents any dynamic axiomatic to be as fancy as static risk measure if you want to get robustness in the picture. There is academic work on dynamic risk measure but they're not "usable" as they are stated right now as too far from pratical matter. –  TheBridge Oct 26 '11 at 8:25
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If your problem is an equity portfolio without options, then I would vote for variance. This uses all the information rather than just looking at the tail. In 1999 the semi-variance became popular because it showed very small risk for telecom, media and tech stocks. They were just going up -- how is that risky?

Equities are pretty close to having symmetric distributions.

If you add options into the mix, then I think wondering about VaR, CVaR, Omega, ... is a useful project.

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This portfolio does not include options. Interesting point on semi-variance. It suggests that we may want to condition our risk estimates on some prior. Equities are close to symmetric distributions, but not necessarily for portfolios (for example, I may create a portfolio with positive skew using a lower partial moments utility function). 2nd issue with Variance is that it upside surprise is a form of "risk". Thank you for your take though I appreciate it! +! –  Quant Guy Oct 26 '11 at 14:26
    
You can get a portfolio that is skewed over a period of time, but I'm not yet convinced that you can deliberately find a skewed portfolio. It certainly isn't definitive, but the blog post portfolioprobe.com/2011/10/03/… suggests that skewness is very hard to predict. –  Patrick Burns Oct 26 '11 at 16:16
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