A common misconception maintains that different notions of risk capture the same concept: VaR, ES and volatility all measure the same “true” risk”. In the same way as like Celsius, Fahrenheit and Kelvin all tell the same thing, only on a different scale. Not true.
The riskometer is a combination of two things: some concept of what risk is and a statistical apparatus to produce a risk measurement. Start with the concept.
With temperature, we have three units of measure Celsius, Fahrenheit, and Kelvin. However, they all measure the same thing, temperature, and we know exactly how to go from one to the other. 100° Celsius is 212° Fahrenheit and 373.15° Kelvin.
It is not the same with risk, where we have multiple concepts, all sending different signals.
When it comes to an individual stock’s risk, I may consider volatility, Value-at-Risk, or Expected Shortfall, just to mention the three most popular. These are not just three measurements of the same thing like Celsius, Fahrenheit, or Kelvin. They capture different aspects of risk. Aspects that are not directly comparable.
The user has to pick the concept of risk most appropriate to her, and if she uses a generic one — a one-size-fits-all riskometer — the result will not be as good as if she picked the best riskometer for her purpose.
If only someone could convince the regulators of that, they would get much closer to meet their objectives. Alas, the pull of scientific risk management is too strong.