VAR has taken a lot of heat lately, mainly by people who never use it. If you are managing a desk of diverse instruments, it remains the best way to amalgamate risk. Consider you run a trading operation, and your desk has, at the end of the day, the following positions:

$100 Euro (Long Euro)

$100 US 30 year Tbond

$100 SPX stock index

What, other than a Value at Risk, would you use to amalgamate this portfolio of risks in USD risk?

I would say, this basket has a 95% daily VAR of $7.04. This is because the daily standard deviations are {2.74%, 0.97%, 1.58%}, and the correlation matrix is

The basic idea is to take a 95% extremum move in dollars, or whatever you base currency is, and then run it through the correlation matrix. To assume the correlation matrix is filled with ones, that all correlations are perfect, is not 'conservative' because that could be easily gamed, encouraging eople to put on hedges that will not work as well asthe perfect correlation assumes. One should probably apply a bayesian assumption so that a sample correlation is modified by some common sense.

Value at risk is not useful for long maturity assets, (most of what is in a bank portfolio), but is very useful for a trading desk, anything with a liquid daily mark-to-market. It gives you a measure of a worst-case scenario that you should see several times a year. If you see it too much, or too little, you need to adjust your formula. The main advantage of this approach is allowing one to aggregregate different asset types into a common denominator: dollar pnl change. By using the 95% tail, you should capture some of the nonlinearities in your book. Of course, for a highly nonlinear trading desk, like a desk with a lot of credit risk, or optionality, there are other limits and measures that are essential.

Anyway, if someone has an alternative to Value at Risk for such a portfolio, I'd be interested in hearing what it is.

## 6 comments:

Assuming correlations are equal to one usually means calculating the losses on the assumption that any position, long or short - will move against you with a correlation of 1. It doesn't allow for reducing risk via hedging. For a variety of reasons this method may not be advisable but it definitely seems more conservative.

Value at Risk is an answer. More importantly what is the question. VaR gets stretched and misused becuase of it ease of calculation. So before answering the question, what is the alternative to VaR, I would respond with what actionable information are you seeking?

Good question. In my experience, you are managing a trading desk with many different instruments. How do you monitor their risk so that they are taking positions consistent with their business model. I think in that case, you want de minimus residual risk, so they aren't exposed to changes in big indices. Or, if it were a long/short equity strategy, you want to see the net exposure to the equity indices expressed in dollar terms.

very crisp, 2 decimal correlations. why stop at 95% VAR then? why not 100%? what is the relevance of 95%?

get a real job and steer from snake oil. i myself am looking to retrain as dental technician. they say hours are good.

How about C-var?

Well, if I can pick out the relevant conditioning events, it will be in the total var, so I don't have to double count. Exploding risk measures spreads emphasis around, and I don't have any reason to believe events I anticipate are better anticipated if enumerated via C-VAR, or just modeled well within VAR.

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