VaR/ES forecasting/measurement: parametric vs non-parametric

[nnja]

Ideally your risk managers should be just as talented, and just as well paid, as your traders.



I'm not sure about that - I'm with scfa. If your risk management is just a super-trader who can override the decision of the trader using the exact same tools and methods as your trader, just different parameterizations and judgment, then why not just set up the risk manager as a trader with his own P&L?



It seems to me that you want your risk managers to use coarser tools, like historical VaR, because even though they don't "work" when "work" is defined as accurately modeling the distribution, e.g. failing a backtest a random 5% of the time, they "work" from a perspective of providing a level of transparency to senior management, or even outside investors. Other important risk management tools, like position and counterparty limits, are effective precisely because they are so coarse - they are difficult to game.



I have read a lot of Aaron's writings on risk management and I am really attracted to the idea of trader = position optimizer, RM = capital allocator, but I think that the most important de facto job of the risk manager is to try to reduce the agency problems between traders and management, or traders and investors. And although there is no direct conflict between these two definitions of the risk management role, asking one functional area to do both might stretch it too thin.

[aaron]

I agree that historical simulation VaR is a useful number to compute. I do it myself. I think of it as a one-dimensional measure of position size. It's not a perfect measure but it's far better than gross notional exposure or other accounting metrics, and it does not reply on input from the front office. I also use Monte Carlo VaR (percentile of the distribution of P&L of current positions under a set of equally-likely future scenarios chosen to be consistent with market underlying and option prices) and Stress VaR (percentile of the distribution of P&L under a set of historical extreme market moves).



These are reasonable stable and predictable numbers, and you can explain deviations. If any of them get large relative to the volatility you think you're exposed to, you think hard about the reliability of your volatility expectation, also you plan for surviving the tail scenarios identified by the VaR process. And, as sfca says, these VaRs are good for communication because they do not require anyone to learn the intricacies of complex risk models. The meaning of, "Your current positions will bankrupt the firm if we get a repeat of October 2008 or September 1998," is clear and not strongly model-dependent.



However, none of these are VaRs. That is, none of them represent the true point such that there is a 5% chance of a larger loss tomorrow. I don't see much debate on that point. Some posters are contending, I think, that getting a true VaR is not very useful.



My reply is mainly empirical. Struggling to get a VaR you would bet on is tremendously useful. You discover all kinds of things about your systems and your central risk that only rigorous insistence on backtest reveals. Of course, it doesn't tell you anything about tail risk, it can't. And it can't tell you how much capital to hold. All it can do in this respect is to filter your data into normal days and VaR breaks, so you can hone in on what happens when you get outside the normal range. That is useful because the VaR breaks from a good VaR are not the largest losses, the ones that everyone pays attention to you. You can learn a lot by studying the day you lost a nickel when you expected to lose no more than a penny, instead of the day you lost $101 million when you expected to lose no more than $100 million.



My other empirical claim is that once you get a good VaR system, changes in the level of VaR (up or down) and VaR breaks turn out to be extremely useful warnings. I have no good theoretical explanation of why that's true, but I thoroughly believe it. It's been my foghorn for 20 years.

[zee4]

Aaron wrote:

"Real VaR systems people rely on, in all cases of my experience, have some kind of (a) internal triggers that push the VaR up sharply when unusual data comes in (or frequently, doesn't come in); and also (b) use forward-looking and non-price data. The market usually does signal before dramatic things happen, but you have to look very carefully to find these signals. If you don't, the VaR is worthless."



Can anybody elaborate these (a,b) points for me please? I have tried to search, but no result. Perhaps, I am not using the correct lingo. I would appreciate any reference (papers, book chapters etc.).

[aaron]

I wish I could point you to a good book or article on the subject. As far as I know, the only place to learn about these is the shops that compute it.

[Corey]

This question may be more directed at Aaron, but I am hoping someone could provide some insight.



In this thread, and Red Blooded Risk (absolutely loved the book, by the way), Aaron discusses a system that has a "VaR" multiplier and a "decay" factor which is a simple methodology of getting our VaR number to conform to the statistically expected behavior (namely: independence of VaR breaks, frequency of VaR breaks, conditionality of VaR break on VaR size).



But it has always been my interpretation that VaR does nothing other than try to identify the region past which "thar be dragons" (i.e. our statistics no longer mean jack-shit).



It seems to me that while Aaron's method will get you the statistical properties we desire for VaR, it breaks my intuitive definition: if I scale my VaR immediately after the first break to represent the new market regime (in the attempt to prevent clustered breaks), I actually only have 1 more piece of information between my old VaR and my new VaR -- namely, the break we just witnessed -- which to me isn't quite enough information to keep saying "my statistics work reasonably well within this region less than VaR."



Instead, VaR simply seems to become the method of identifying the region in which I can reasonably expect 95% of days to fall -- but not necessarily where the statistics on my data is any good. In fact, I think the argument could be made that with each VaR break, the old data is likely instantaneously out-dated since there is a high probability of a regime change.



I would love some feedback and thoughts (even if they are purely philosophical) on resolving these two intuitive needs: (1) having VaR conform to the statistical properties we expect it to and (2) having a meaningful, and hopefully "actionable" takeaway from the VaR level.