VAR Backtesting - Notes pages 11 and 13

[QuantFFM]

Hi David,

why are there two sets of VAR used in the IMA? See below the picture from your Notes.

On page 11 you say it is: 1% 10-day VAR for VAR calculation
On page 13 it is said to use 1% daily VAR for VAR calculation and 1% 10-day VAR for riks charge computation.

For what do we use 1% 10-day VAR and for what do we use 1% daily VAR?

Page 11

Page 13


Many thanks in advance.

 

[David Harper CFA FRM]

Hi @QuantFFM Yes but notice that the 1-day references are to "verification" and "backtest:" while the backtest of VaR can be 10-day, it is more typical to conduct the backtest of the 1-day VaR because that is the primary unit of collection (although it could be any timeframe). So, at least in our typical study in the FRM, in the case of market risk, the firm tends to estimate a one-day VaR; e.g., if the approach is historical simulation, then maybe that is a collection of the last 250 or 500 daily P/L; or if parametric, then compute the daily volatility and multiply it by some deviate (2.33). For purposes of a backtest, it is natural to compare daily exceptions with the daily VaR.

However, with respect to IMA in Basel I, II, II.5 and III and the regulatory capital charge for market risk the requirement is (was) to determine capital based on a 10-day VaR (and, as of II.5, a 10-day stressed VaR). This is typically achieve by scaling the one-day VaR with: one-day VaR * SQRT(10) which importantly assumes i.i.d.. In this way, in most cases, the same one-day VaR that was verified with the backtest is the essential input into the 10-day VaR required for regulatory capital. Please also note that the FRTB (aka, Basel IV) replaces 10-day 99.0% VaR with 97.5% ES and variable horizons (as discussed in Hull RM&FI Chapter 17). I hope that's helpful!