Re: Ten-day 99% VaR has worked fine.

From: Glyn Holton
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Date: 08 Nov 2006
Time: 08:12:47

Comments

Clearly, banks aren't actually backtesting ten-day 99% VaR measures. A bank will only suffer losses in excess of ten-day 99% VaR only two or three times every ten years. That doesn't give them enough data points for a meaningful backtest. Here is what is actually going on. Basel gives banks permission to calculate their ten-day 99% VaR as one-day 99% VaR calculated with ten-day standard deviations. I know this sounds bizarre. What it does is save the banks from having to account for events that transpire during a ten-day VaR horizon (like options expiring, coupons being paid, floating rates being reset, dividends being paid). That stuff would make calculating ten-day VaR very complicated. Instead, Basel says the banks can calculate one-day VaR but do so assuming standard deviations that you would use for ten-day VaR. Now, such a VaR measure is impossible to validate because it makes no predictions whatsoever about the actual losses the bank will incur. Banks do not (and cannot) realize one-day losses arising from ten-day standard deviations. The notion is meaningless. So what do banks do to backtest their VaR measures? That is between them and their regulators. I suppose different banks do different things. In most cases, I suspect, the banks are validating their one-day 99% VaR measures (i.e. their VaR measures using one-day standard deviations) and representing that as a valid backtest for their ten-day 99% VaR measure (i.e. the same VaR measure but with ten-day standard deviations). There are two problems with this. One is that most banks have inadequate data for even a one-day 99% VaR backtest. The other is a HUGE problem. It is that a backtest of the one-day 99% VaR measure is not a backtest of the corresponding ten-day 99% VaR measure. The assumption that ten-day 99% VaR can be calculated as one-day 99% VaR using standard deviations scaled up by the square root of is simply wrong. The square root of time rule may be reasonable for calculating 90% VaR. It is not reasonable for calculating 99% VaR. The reason is volatility clustering. If the markets experience a 99% quatile move one day, they are far more likely than is typical to experience another one the following day, and the day after that. What this means is large ten-day market moves are far more likely than the square root of time rule applied to one-day standard deviations would imply. Ten-day 00% VaR figures calculated according to the Basel simplification substantially under-represent the actual ten-day risk. In summary, whatever the banks are doing to "backtest" their ten-day 99% VaR measures is TOTALLY MEANINGLESS.

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