Choosing Risk Measures for Equity Portfolio Construction
Summary
The document considers whether value-at-risk or conditional value-at-risk (also called expected shortfall) is better suited to portfolio construction, focusing on a long/short equity portfolio without options. It summarizes a debate over risk measure properties: coherent measures satisfy conditions such as subadditivity, translation invariance, positive homogeneity, and monotonicity. The text notes that expected shortfall meets these criteria while VaR does not, but also cites research arguing that VaR procedures can be more robust.
A response proposes variance as a practical choice for an option-free equity portfolio, on the grounds that it uses information across the return distribution rather than focusing only on its tail. It also observes that equity returns may be approximately symmetric, while downside-only measures can give misleadingly low risk readings during sustained rises. The discussion is brief and does not provide comparative empirical tests or settle the broader debate. It suggests that tail-focused alternatives become more relevant when options create asymmetric or nonlinear outcomes.
Key ideas
- Coherent risk measures satisfy properties including subadditivity, translation invariance, positive homogeneity, and monotonicity.
- Expected shortfall satisfies the cited coherence criteria, whereas VaR does not.
- The document notes an argument that VaR can yield more robust risk measurement procedures.
- For an option-free equity portfolio, variance is suggested as a measure that uses the full return distribution.
- Tail-focused measures may warrant more attention when options make portfolio returns asymmetric.
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Full text
# Which is a more appropriate choice of risk measurement in a utility function, CVaR or VaR? # Which is a more appropriate choice of risk measurement in a utility function, CVaR or VaR? 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? ## Answer by Patrick Burns (score 1) https://quant.stackexchange.com/a/2245 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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