## Riskometers and their inconsistencies

11 April 2021

Risk measurements are quite inconsistent. Does that matter, and how to interpret the results?

We need three layers of analysis for risk:

1. The recognition of what sort of risk is most important;
2. A theory of how to quantify that risk;
3. Statistical technologies for producing the actual risk measurements.

The latter two make up the concept of a riskometer, the choice of which intimately depends on what the riskometer is needed for, the first layer.

It is easy to demonstrate how riskometers disagree. Suppose I take a common riskometer, one that is embedded in Basel III — expected shortfall — and apply it to returns on the S&P 500 index and Amazon stock prices and then estimate the expected shortfall with six of the most common techniques.

symbol HS EWMA GARCH tGARCH EVT
SP500 64.7 25 21 48.5 67.5
AMZN 66.3 42.1 42.6 70.8 71.4

Table: Expected shortfall on a $1000 portfolio, 9 April 2021. The highest risk reading is more than three times that of the lowest. Similar results would obtain for other assets and times, and you can go to my website, extremerisk.org, where I estimate risk every day, for a lot more examples. Does it matter that the riskometers are so inconsistent? In theory, it shouldn’t. A good risk manager knows riskometers are imprecise. They know the strengths and weaknesses of each, treating them as a portfolio of methods, picking the best one for the problem at hand. For example, among the six in the Table above, EWMA is really simple, and nothing can go wrong when implementing it. It reacts quickly to changing information. However, just like an overeager teenager, it can respond way too strongly to new information. HS is opposite, calm, and stable. Nothing ruffles it, like a seasoned bureaucrat. Which do you prefer? It depends. HS’s conservativeness is an asset for day-to-day operations, but when a shock hits, you need a quick reaction, and that is when EWMA can be invaluable. Then, there is the dark horse of EVT, short for extreme value theory, like the wise man who has nothing to say about day-to-day occurrences but tells us what we need to know about the extremes when everything goes wrong. All the riskometers have their good sides, and a good risk manager will be guided by her intuition and experience. Seeing EWMA is$25 and GARCH $21, while HS is$64.7, tells her not only that short term risk has fallen quite a bit recently but is still relatively high by historical standards. Meanwhile, EVT says long-term risk has picked up because of Covid-19.

The risk manager knows each number tells a different part of the story, and by using all of them, she gets a much more complete story.

It is only we we have to pick one riskometer and stick with it, that we get seriously misled.

© All rights reserved, Jon Danielsson, 2021