Tuesday, 29 January 2008

'Sucks' is an invariant

If a model sucks today, the strong likelihood is that it will suck tomorrow. VAR sucks. Let's reprise the case.

VAR is procyclical. As markets rise, volatilities and correlations tend to fall so the VAR for a position goes down, encouraging over-leverage. When they crash, VAR goes up, encouraging firms to cut at the worst moment and exacerbating illiquidity.

VAR models are based on history. The better we calibrate to the recent past, the less accurate VAR is likely to be: this is true for both simple variance/covariance VAR models and for more sophisticated historical simulation ones.

(To see this, consider a delightful note to UBS's 2004 account.

Over the past two years, growth in asset-backed securities has outpaced other sectors in the fixed income markets. At the same time, our Investment Bank’s market share in this sector has grown, leading to an increase in exposure. To date these exposures have been represented as corporate AAA securities in VAR, leading to a conservative representation of credit spread risk.

To better reflect the risk in Var, we have increased the granularity of our risk representation of such securitized products. In July 2004, the Swiss Federal Banking Commission (SFBC) gave their approval for this change and we have implemented the revised model during third quarter.

The enhanced model added a number of historical data series, which more closely reflect the individual behavior of products such as US Agency debentures, RMBS & CMBS, and other asset backed securities such as credit card & automobile loan receivables.

Then look what happened:

In other words UBS rightly improved their model. But because the improved model was better calibrated to recent conditions, it reduced the risk shown on ABS. ABS ended up costing UBS billions.)

VAR gives no insight into the tails. Morgan Stanley's $480M loss on a (at most) $110M VAR is evidence enough of that.

Many firms have highly non-linear P/L distributions. This means they respond in a highly non-linear fashion to extreme returns, making VAR at a reasonable (i.e. statistically significant) confidence interval even less useful. The evidence for this is discussed here.

We got very lucky with the timing. VAR for reporting regulatory capital was approved in the 1996 Market Risk Amendment to Basel 1. 1996 came at the end of a relatively quiet period in most markets, with no major equity market or emerging market crashes since the 80s. If the matter had come up for consideration in 1997 (South East Asian Crisis), 1998 (Russia, LTCM), 2000 (high tech crash) or 2001 (Argentina, 9/11), the data supporting the veracity of VAR as a risk measure would have looked a lot less good.

See here for a further discussion on Bloomberg, or here for a longer one from Naked Capitalism.

VAR is a reasonable ordinary conditions risk measure. But it gives somewhere between very little and no insight into stress losses. Yet stress losses occur several times a decade. Perhaps we should move towards a simpler capital regime based on large moves and no benefit for diversification. Like, err, the one we had before 1996.

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