The original paper defining Conditional Value at Risk = CVaR = Expected Tail Loss.
Pessimism & Probability Distributions
In an interview given to EDGE magazine, Bart Kosko explains how great the
median is. He used to think the
mean was the statistic to look at (cf., Francis Galton’s story of the crowd average guessing correctly the weight of the prize hog to a tenth of a unit) but the
median is more robust and so on.
My opinion is that the most important statistic for many practical purposes is something like the
25% CVaR or
50% CVaR. I think that’s the essence of “What do you stand to lose?” as people mean it in normal English.
In other words, I think the way people think about risk in everyday, non-finance terms, basically boils down to
- the observed
minimumif you’re a lawyer) and
CVaR(expected loss) for some wide-ish (likely) swath of the bad outcomes.
The reason the
CVaR is so intuitive is that it smoothly interweaves both
- egregiously bad, low probability outcomes (“You could die with a .01% probability!” is actually a good reason to avoid something)
- and likely bad outcomes (“After you graduate you might not find a job in your field”).
So obviously there isn’t “one best” question to ask. It depends what you want to know—if it’s the value of the gravitational constant,
median may be a great statistic. On the other hand, if you’re looking at the salaries that might result from your law degree or MBA—that is, if you’re looking for a sensible measure of risk and downside—then I’d suggest a
(I actually emailed Dr Kosko and got a response—but he linked to a 20-page paper he had written and I never got around to reading it and felt bad responding without reading all of his response.)