Question:

In regard to the Basel Market Risk Charge:

(i) If the 1-day, 95% confidence RiskMetrics VaR is $2 million, what is the equivalent Basel VaR?
(ii) What do you think is the most important QUALITATIVE requirement for the internal models approach (IMA) to market risk in Basel II?
(iii) What is the rationale and role of the multiplicative factor (which equals 3.0)?
(iv) How is the backtesting framework an application of Type I/Type II trade-off?

Answer:

(i) Under Basel IMA Market Risk Charge, the VaR is a 10-day horizon with 99%. The adjustment is therefore:

$2 million * (2.326/1.645) * SQRT (10/1) = $8.95 million

But, as we’ve often noted, scaling VaR (or volatility) with the square root rule assumes normally distributed returns that are independent and identically distributed (i.i.d.)

(ii) This doesn’t necessarily have a correct answer, just meant to provoke thinking.

(iii) The actual VaR is multiplied by a safety factor which cannot be less than 3.0. The rationale was that daily VaR “must be converted into a capital requirement that offers a sufficient cushion for cumulative losses deriving from adverse market conditions for an extended period of time.” In other words, the multiplier is a sort of conservatism to account for adverse market conditions. But also, the backtesting can adjust it, so the adjusted multiplier also attempts to address model risk.

(iv) To backtest is to collect a historical sample. It cannot be declared with certainty that the Bank’s VaR model is good or bad. Rather, the green/yellow/red “traffic light” zones express a trade-off between two types of errors: one error is to find few exceedences and mistakenly declare the model good; the other error is to observe many exceedences and mistakenly declare the model bad.