Value at Risk for Algorithmic Trading Risk Management – Part I | Hacker News Reader

Value at Risk for Algorithmic Trading Risk Management – Part I

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30 pointsshogunmike7 comments

I've always preferred Conditional Value at Risk (CVaR) to regular VaR. While VaR is the 5% (say) value of loss, CVaR is the average of the loss of the bottom 5%. That way it captures the size of the tail risk.

The other really big advantage is that you can optimize over CVaR. You can formulate it in a linear program (LP), so you can maximize expected return subject to a limit on CVaR. [1] You can have several CVaR constraints at 1% and 5% say.

In contrast, VaR isn't convex, and is difficult to optimize over.

[1] http://www.ise.ufl.edu/uryasev/publications/

Edit: there is an interesting presentation comparing CVaR and VaR by Stan Uryasev, the main academic that has worked on CVaR formulations here:

http://www.ise.ufl.edu/uryasev/files/2011/11/VaR_vs_CVaR_CAR...

The article does mention the downsides but doesn't really cover how devastating they can be. VaR was the common calculation persuading the banks that everything was nice and safe in 2007 and 2008.

From the article

VaR does not discuss the magnitude of the expected loss beyond the value of VaR, i.e. it will tell us that we are likely to see a loss exceeding a value, but not how much it exceeds it.

It does not take into account extreme events, but only typical market conditions.

Since it uses historical data (it is rearward-looking) it will not take into account future market regime shifts that can change volatilities and correlations of assets.

I always laugh when people use VaR for exactly that reason. In reality for most investors the true actual value at risk is however much money isn't in cash.

I know you can say "well what about hyper-inflation!" and you're right; someone in cash would get wiped out in hyper-inflation.

But considering how infrequent hyper-inflations are and how badly VaR led many folks astray really all over the developed world, perhaps re-defining it that way wouldn't be so terrible.

You're quite right actually! I probably haven't been as explicit as how hidden the risks are when using VaR. Although, within other articles I've tried to make the point that any risk management strategy should be utilised as part of a larger framework.

It is a shame that risk management often takes a back-seat to "alpha generation", as solid implementation of the former is what keeps funds (and retail traders) in business.

At least you put them in there. It is always worth knowing the limits of models and where and how the assumptions behind them breakdown. VaR is something with limits that the real world has reached on numerous occasions which I thought was worth highlighting and when it breaks it can do so in a catastrophic manner so that it essentially no longer functions.

Traders working in banks all knew that VaR was a pretty poor risk metric - at least definitely by 2007 and probably years before that.

Even the regulators "knew" that VaR did not cover everything.

I know this because I was building a CDO VaR Risk System for Royal Bank of Canada in which the regulator also required us to report the impact of "shock" scenarios because of the knowledge that VaR did not capture "tail risk".

It's not like people were completely stupid.

It's simply that while everybody knew about tail risk, they massively underestimated it.

Anybody who was anybody "knew" that a senior AAA rated tranch of a CDO was not a safe as US government debt no matter what that AAA S&P rating might say - but they probably didn't think that a AAA asset would ever be completely worthless either (i.e. every single name in the CDO would default, or that they would effectively have to "mark-to-market" it as worthless for the purposes of reserve requirements).

The real problem was that because they were rated AAA, regulators allowed their use as tier-1 capital (used to calculate the total amount of leverage the bank can take on).

Once it started having to be marked down at all, banks were forced to reduce their leverage to meet the regulator requirements, often by force-selling other assets, which in turn caused more mandatory mark-to-market write-downs, which cascaded into the financial crisis.

P.S. What saved RBC was simply that they were late into the CDO game and did not have a very large CDO exposure.

So everyone "knew" it wasn't doing the job but they (at least in some banks) carried on using it anyway because...have hammer, use hammer. That or they were deliberately using it because of its deficiencies that let them take bigger risks than they knew were wise or at least would be allowed under other approaches.

The reduction of leverage, cascading down of asset prices is exactly the sort of correlated event that VaR doesn't cover at all and does happen every couple of decades. It isn't really some bizarre outlying event. The moment it matters (almost) all asset prices suddenly correlate.

If you use VaR as "the number that runs the bank" (I can't remember where but I'm sure I've heard it referred to as something like that possibly with respect to Lehman) then you are going to get into trouble.

The "shock" scenarios approach sounds useful provided the imagination is open to really shocking outcomes.

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