CVaR Mean Conditional Value At Risk

CVaR is a variant of VaR,  Variance at Risk.


VaR was developed by JPMorgan risk group in the early 1990s. Most of that risk group left to start a consultancy to sell the risk management calculation to other banks. It was originally developed because the executives at JPMorgan wants a simple way to wrap up all of the risk into a single number. VaR is the amount in dollars that the institution is expected to lose before trading begins the following day, and therefore required to borrow overnight. The calculation was inserted into a report called the 4:15 Report, which was a report that came up at, you guessed it, 4:15 PM, or fifteen minutes after each trading day. The tool became very effective and useful, so much so that Basel II Accord incorporated it.

CVaR is nothing more than taking the various risk variables and then weighting them for what a risk manager believes is a more accurate view of the market risk. Obviously this has some subjectivity to it. The idea is that VaR doesn’t weigh risks from, say, lending equities differently from trading on the bank’s books.


There has been a long running controversy over VaR, and therefore CVaR. VaR is a probability calculation and therefore it doesn’t tell its reader how much the firm could lose. It tells the reader how much the firm will likely lose. The qualitative difference between the statements is the former is a definitive number while the latter is a forecast. The former is accurate and the latter is prediction, which is inherently inaccurate. The quantitative difference is $0 and infinity. Since VaR is used to either insure against losses through borrowing or hedging, it is merely spreading the risk of loss and therefore, making the whole capital markets system bear the risk of a firm. The benefit is that because it is probability-based, it is very good when the markets are normal. VaR opponents says there is no such thing as normal.


Both sides are right. VaR is an effective tool to manage risks that stem from business-as-usual. But management rely heavily on it, and the system gradually build up risks for firms and eventually implodes. And it is a poor way to forecast extraordinary large risks, also known as tail risk. As a matter of fact, it is specifically designed to truncate the tail risk so that it can arrive at a dollar figure. One way to think about how this cannot work in all situations is to think about shorting a stock. If you buy a share of XYZ for $10, the most you can lose is $10 because the value of the shares cannot go below $0 and shareholders are not liable for debts beyond the the value of equity and assets. But if you short XYZ, it means you lose money every time XYZ’s price goes up. Well, there is no upper limit to how high the stock price can go. This is the reason why, as long as a bank holds shorts of any sort, it can lose infinite amount of money. Not likely, but possibly.

So, while both sides are right, only the side in favor is wrong. Easy to say, but hard to swallow if you are managing a bank and you need some way to reduce market risk for your bank. VaR is a very useful tool.

About the Author: Marcus Maltempo is a compliance professional with more than a decade of experience helping banks, law firms and clients manage investigations and regulatory responses. He is the author of the forthcoming book History of Money Laundering: How criminals got paid and got away.

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