Oh DEaR!

Traders live and die off their DEaR limits. Today we delve into the details of the DEaR limit.

DEaR is calculated differently at every firm. A very common method is taking three years (750 trading days) of data and finding the desired percentile worst day. So if you're looking for a 95% DEaR, you line up your portfolio's simulated performance on those 750 days and take the 37th worst one as your current DEaR. It's a measure of how much you have at risk on a given day.

Trading desks at banks tend to use DEaR as the limiting factor in taking on risk, while at many hedge funds the limiting factor is balance sheet as opposed to DEaR. If a desk is allocated $5M in DEaR, then the simulated portfolio cannot exceed $5M of draw-down on that simulated 37th worst day. So effectively your risk is simulated and you are held at a loss limit based upon historical catastrophes.

DEaR simulations are used for the portfolio because of the off-setting effects your portfolio can have. Let's say you are long $100M 10year on-the-runs (On the runs are the latest issue of government bonds, not surprisingly the old issues are called "off the run.") and short $100M 10year off-the-runs. Well, we can't add the risk off the long position (say it has a DEaR of $129M) and the short position (say it has a DEaR of $152M). Clearly the combined position will off-set a lot of the risk involved, namely duration risk. If rates go up or down, you should be quite well hedged. This is an example of a spread trade.

For those of you who are interested, this is exactly the sort of spread trade that got LTCM (Long Term Capital Management) in trouble. They were a huge hedge fund founded by Meriwether and included Merton and Scholes (yes, from the Black-Scholes-Merton model of options pricing). These spread trades tend to be low risk and fairly low reward, but when shit hits the fan you can lose a lot of money. If you're curious about LTCM you should read "When Genius Failed."

So what happens when you bust your DEaR limit? The risk guys get all over you and require a reduction of position. This can really suck if your positions aren't going your way since you have to unwind at a loss. It gets even worse if your position is so big that the whole street knows you're unwinding and starts trading against you (this happened to LTCM, the late Amaranth, and probably a lot of others big funds that no longer exist). So most desks try to keep a good bit of gap between their DEaR limit and actual DEaR. You'll see prop desks skimming really close to their DEaR limits when they think something is so astronomically mispriced in the markets that they have to take a huge position in it due to the risk-reward tradeoff.

As long as we're discussing DEaR, we should look at some of it's shortcomings. For one, DEaR often missed the real "catastrophe" events. Things like Russia defaulting, 9/11, etc usually fall in the 99th percentile or worse. These are the times when a lot of these big risk takers lose liquidity. The most common answer to this shortfall is to use a new measure called CVAR (as opposed to VAR).

VAR and DEaR are really identical. VAR stands for Value At Risk and is calculated the same way as DEaR. CVAR stands for Conditional Value At Risk. This measure is sometimes also known as Expected Shortfall, a name I tend to use because it describes the measure better. Expected Shortfall is the expected value of a loss beyond a certain threshold. So let's say we take 95% CVAR. That means we calculate the expected value (read: average loss) of all the scenarios past the 95th percentile. This method of risk calculation has become rather common in credit markets (since default scenarios are fairly rare, and correlated default scenarios even more rare). As such, some idiots think CVAR stands for Credit Value at Risk. Make sure to let them know that they are idiots if you meet any of them, especially if one them starts talking about CVAR like they know what they are talking about.

Well, that ends my discussion of DEaR, VAR and CVAR risk limits. Let me know if there are questions.