http://www.riskmetrics.com/publications/ research_monthly/20081100

http://www.finanalytica.com/en/page/100/ VaR_daily_statistics

Besides you can compare fat-tailed vs. normal VaR.

2/ Suppose the banking universe is closed (it’s not, but suppose it is), so there are some banks which are over-all buyers of volatility/correlation and others which are sellers. (They are delta hedged but not hedged in terms of gamma, vega, etc.) When there is increased volatility/correlation in the market, the Var of the buyers only goes down a little, because there Var gets taken from the calm days, and there’s always some calm days in the historical sample. The Var of the sellers, however, explodes. So over-all in the banking sector the Var explodes.

3/ The banking universe is not closed and as a rule most banks are sellers of catastrophe. If the markets go down a little, they make money; but if they go down a lot, they lose a lot. When catastrophe is not in the historical sample, the Var stays reasonable. But when catastrophe makes it into the historical sample, it gets reflected in the Var, and Var explodes.

I just noticed your “Update” so I added an “Update” on my post to address your “Update”. Meta meta…

In addition they disclose those positions that are NOT included in the VAR calculaton,(p124) which I assume their peers would include, which are sizeable.

The total reported var is 221 million. The risk-10%senstivity (whatever that means)is 1.2 BILLION.
If this sensitivity number can be interpreted as a var equivalent, then including it in any var analysis is a must.

Either way, VAR is of very limited analytical value in GS case since it is so opaquely calculated and disclosed, does not impact its capital requirements (as a result of the exemption), as it does for its peers, and VAR does not reflect intraday risk (, where I believe most of GS exceptional profits originate).

If the excluded market risk is the source of its FI profits, then those numbers should be disclosed and the exception should be revoked immediatedly to require GS to include them in the VAR.

At a minimum GS should be required to disclose their sanctioned VAR vs the VAR they would report if they were not exempt. I’m sure they calculate and monitor it. Its kind of outrageous the SEC or the FED doesn’t require it as a condition of the exemption.

This would be computationally intensive for a single stock and obviously many times moreso for the S&P index, but it is possible. If I had daily call option data (strike price, strike date, and price would be sufficient) for all the stocks, I think I could do it.

What it would tell you is the market’s perception of actual volatility (and thus VaR) for the index. Of course, if the banks are using “dumb” volatility metrics like a trailing average, which it appears they are, then maybe that’s not of much interest. I’d certainly bet that the banks have internal models that are much better than this.

Here you go…

http://phorgyphynance.wordpress.com/2009  /08/06/80-years-of-daily-sp-500-value-a t-risk-estimates/

I added a new chart with 10 years of daily VaR estimates from Aug 1999 to Aug 2009.

Sorry I thought this post was about Goldman’s high VaR numbers instead of banks more generally. Read it too fast before running out the door. :)

Awesome chart. Remember that chart is 1 day, and most banks may (if memory serves) report 10 days, which will be higher. Multiply by sqrt(days) to get a back-of-the-envelope transformation.

http://www.donfishback.com/blog/2008/10/ 27/ironic-the-same-assumptions-that-allo wed-reckless-leverage-have-reversed/

Felix was asking about what a bank’s VaR would look like if it invested in the S&P 500. The chart I provided answers this question.

A deeper (and important) question to ask (which it seems you are looking into) would be about the relationship between this S&P 500 VaR and the bank’s actually VaR. The bank’s P&L is obviously not a linear function of the S&P 500, so the relation should not be 1-to-1, but the sense that Felix seems to be looking for is how they should be related.

I agree that a bank’s VaR will increase as S&P 500 VaR increases, and conversely though the “Great Moderation” we saw VaR decrease. Since bank capital requirements are based on VaR, it is important to understand this. Decreasing VaR means increasing leverage. Increasing VaR means deleveraging.

Here is something I wrote on March 16, 2006 (when we were still in the Great Moderation):

http://phorgyphynance.wordpress.com/2008  /04/05/the-risks-of-risk-management-rev isited/

“When I look out at the world, one of the major risks to the markets that I see is, ironically, risk management. I suspect that one of the primary employers of junior quants in the last 5 years has been in risk analytics. If there is any truth to that, it means there is literally an army of quants who have not lived through a business cycle building risk systems on markets that no one really understands, e.g. CDS/CDOs.

[snip]

If things are at all like what I have seen, then we’ve got a bunch of fairly clueless risk managers out there with an army of fairly green quants developing sophisticated risk models that are probably pretty useless in a crisis. Nonetheless, there seems to be this completely ludicrous false sense of security.

Across the boards, vols seem to be historically low which would mean that most VaR engines are saying “smooth sailing”. What happens if vol increases? Everyone’s VaR model is going to start sending out little red flags. Assets are going to start getting reallocated. Since everyone has almost identical VaR models, the signals will be pretty much identical at all firms. I know it is not an original argument, but this could easily lead to a negative feedback. A small red flag due to increased VaR could signal everyone to make very similar reallocations. If everyone does it at the same time, the market will obviously be affected. In essence, the impact of risk management could actually increase systemic risk in the markets and amplify vol movements.”