LO 58.4: Calculate VaR and the capital charge using the internal models approach,

LO 58.4: Calculate VaR and the capital charge using the internal models approach, and explain the guidelines for backtesting VaR.
According to the 1996 .Amendment, the market risk VaR is calculated with a 10-trading day time horizon and a 99% confidence level. The market risk capital requirement is calculated as:
max(VaRt l, mc x VaRavg) + SRC multiplicative factor where: VaRt l = previous days VaR VaRavg = the average VaR over the past 60 trading days mc = multiplicative factor SRC = specific risk charge
The multiplicative factor must be at least three, but may be set higher by bank supervisors if they believe a banks VaR model has deficiencies. This means the capital charge will be the higher of either the previous days VaR or three times the average of the daily VaR plus a charge for company specific risks (i.e., the SRC).
Banks calculate a 10-day, 99% VaR for SRC. Regulators then apply a multiplicative factor (which must be at least four) similar to mc to determine the capital requirement. The total capital requirement for banks using the internal model-based approach must be at least 50% of the capital required using the standardized approach.
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Topic 58 Cross Reference to GARP Assigned Reading – Hull, Chapter 15
The banks total capital charge, according to the 1996 Amendment, is the sum of the capital required according to Basel I, described in LO 58.2, and the capital required based on the 1996 Amendment, described in this LO. For simplicity, the RWAs for market risk capital was defined as 12.5 times the value given in the previous equation. The total capital a bank has to keep under the 1996 Amendment is:
total capital = 0.08 x (credit risk RWA + market risk RWA)
where: market RWA = 12.5 x (max(VaRt_1, mc x VaRavg) + SRC) credit RWA = E(RWA on-balance sheet) + E(RWA off-balance sheet)
Example: Market risk capital charge
A bank calculates the previous days market risk VaR as $ 10 million. The average VaR over the preceding 60 trading days is $8 million. The specific risk charge is $5 million. Assuming a multiplicative factor of three, calculate the market risk capital charge.
Answer: $29 million market risk capital charge = 0.08 x {12.5 x [(3 x $8 million) + $5 million]} = $29 million
Backtesting
The 1996 Amendment requires banks to backtest the one-day, 99% VaR over the previous 250 days. A bank calculates the VaR using its current method for each of the 250 trading days and then compares the calculated VaR to the actual loss. If the actual loss is greater than the estimated loss, an exception is recorded. The multiplicative factor (mc) is set based on the number of exceptions. If, over the previous 250 days, the number of exceptions is: Less than 5, mc is usually set equal to 3.
Greater than 10, mc is set equal to 4. The bank supervisor has discretion regarding the multiplier. If the exception is due to changes in the banks positions during that day, the higher multiplier may or may not be used. If the exception is due to deficiencies in the banks VaR model, higher multipliers are likely to be applied. There is no guidance to supervisors in terms of higher multipliers if an exception is simply the result of bad luck.
5, 6, 7, 8, or 9, mc is set equal to 3.4, 3.5, 3.65, 3.75, and 3.85, respectively.
2018 Kaplan, Inc.
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Topic 58 Cross Reference to GARP Assigned Reading – Hull, Chapter 15
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