Felix Salmon and Phorgy Phynance have a couple of very interesting posts on VaR.
Value at Risk models, which are meant to measure risk loss on a portfolio, have been grabbing headlines of late. Goldman’s VaR increased to $245m in the second-quarter of 2009. Barclays, we also note, appear to be ratcheting up the risk, upping its one-day VaR to a high of £118.7m in the first-half of this year.
However the counter-argument to this — which we’ve also witnessed here on FT Alphaville — is that since VaR is partly calculated using historical volatility it’s wholly unsurprising that banks’ VaR numbers have increased in recent months. VaR, so it goes, naturally increases following a period of unrest — and that would be the latter-half of 2008. Thus it’s inaccurate to say that Barclays or Goldman are getting riskier just because their VaR has increased.
Here’s Salmon’s commentary:
Whenever I write about banks’ rising Value-at-Risk, a bunch of commenters tells me that duh of course VaR is rising, because VaR is a function of volatility, and volatility has gone up. So here’s my question: can someone come up with a baseline VaR chart, for a hypothetical bank which had, say, a fixed $1 million investment in the S&P 500. What would its quarterly Value-at-Risk have looked like over the past couple of years?
Would the decrease in volatility this year have shown up as decreased VaR in say the second quarter? Or do the volatility calculations go back so far that only now are we losing the Great Moderation datapoints and using volatility numbers only from the era of increased volatility?
Armed with that kind of baseline chart, we’ll be able to tell much more easily, for any given bank, whether it’s actually increasing the size of its bets, or whether increased VaR is simply a statistical necessity given the recent history of volatility. Does such a chart exist?
Et voila — Phorgy Phynance has come through with a set of three charts, showing 80 years of daily S&P 500 VaR estimates.
Here’s one of the charts, which highlights the movement of that VaR value so far this year.
What the chart suggests to Salmon is that since ‘baseline VaR’, if you will, declined a bit in the second quarter of 2009, one would have expected a decline in the likes of Goldman’s Q2 VaR as well. Instead it ticked up, which suggests to Salmon a much more conscious increased level of risk-taking.
Only, Goldman’s VaR, of course, takes into account stuff other than equities — interest rates, credit spreads, currency changes, etc. Phorgy’s chart is also of a 99 per cent one-day VaR and Goldman’s VaR is calculated at the one-day 95 per cent level. So this is clearly an imperfect, albeit interesting, comparison.
Going back to the main argument at hand, however, for all its faults, VaR is one of the few indicators of risk-taking we actually have at banks like Goldman.
While VaR models themselves are pretty set, the banks have a lot of control over the actual inputs used in the calculations themselves; if VaR increases we have to assume, almost by definition, that the bank is consciously increasing its own risk profile.
That doesn’t mean, of course, that the bank will actually make more losses.
Indeed, as we’ve noted before, despite Goldman’s stated VaR probabilities, reprinted below from its latest 10-Q, things have a tendency to turn out rather differently for the bank:
For the VaR numbers reported below, a one-day time horizon and a 95% confidence level were used. This means that there is a 1 in 20 chance that daily trading net revenues will fall below the expected daily trading net revenues by an amount at least as large as the reported VaR. Thus, shortfalls from expected trading net revenues on a single trading day greater than the reported VaR would be anticipated to occur, on average, about once a month. Shortfalls on a single day can exceed reported VaR by significant amounts. Shortfalls can also occur more frequently or accumulate over a longer time horizon such as a number of consecutive trading days.
In actuality, Goldman never lost more than $245m in a one day in the second-quarter of 2009. The closest it came was a single day when it made a loss of between $100m and $75m. 2008 told much the same story. Clearly VaR is pretty useless as a predictive measure of risk.
But again, until the banks replace it with something more meaningful, it is basically all we have. And it is, for better or worse, the bank’s own measure of their own risk based largely on their own inputs. If Goldman’s or Barclays’ VaR is increasing — they know about it and are happy to have it advertised. It sets them apart from banks that are, or want to be seen as, derisking.
In short, VaR, we think, is very useless but it’s not very irrelevant.
Related links:
No sense in reforming VaR - FTfm
Sky’s the limit as banks rediscover their taste for risk - Independent
Basel Committee ramps up VaR model - eFinancial News
Stressed-out VaR - FT Alphaville
