Learning outcomes: Calculate VaR and the capital charge using the internal models approach , and explain the guidelines for backtesting VaR according to the 1996 Basel guideline.
Questions:
(Source: John Hull, Risk Management and Financial Institutions, 5th Edition (New York: John Wiley & Sons, 2018))
516.1. Basel's 1996 Amendment allows more sophisticated banks with well-established risk management functions to use an internal model-based approach (IMA) for setting market risk capital. Most large banks preferred to use the internal model-based approach because it better reflected the benefits of diversification and led to lower capital requirements. About this capital charge for market risk under the internal models approach (IMA), including 2009 revisions to the original Amendment, each of the following is true EXCEPT which is not?
a. The value-at-risk (VaR) measure used in the internal model-based approach is calculated with a 10-day time horizon and a 99.0% confidence level, and regulators explicitly stated that the 10-day 99.0% VaR can be calculated as the one-day 99.0% VaR multiplied by the square root of ten; i.e., 10-day 99.0% VaR = one-day 99.0% VaR * sqrt(10)
b. The capital requirement is equal to max[VaR(t-1), m(c)*VaR(avg) + SRC, where m(c) is a multiplicative factor with a minimum value of 3, SRC is a specific risk charge, VaR(t-1) is the previous day's value at risk, and VaR(avg) is the average value at risk over the past 60 days
c. The capital requirement adds two terms: value-at-risk(VaR) and specific risk charge (SCR). In a corporate bond security, for example, the credit risk is captured by the VaR term and the interest rate risk is captured by the SRC term
d. The bank's VaR risk model must contain a "sufficient" number of risk factors and the bank must justify the omission of any risk factors that are otherwise used in pricing (valuation)
516.2. As a risk manager for Bank ABC, Mary is asked to calculate the market risk capital charge of the bank's trading portfolio under the 1996 internal models approach. The 95.0% one-day value at risk (VaR) of the last trading day is USD 70,000; the average 95.0% one-day VaR for the last 60 trading days is USD 30,000. The multiplier is k = 3. Assume the return of the bank's trading portfolio is normally distributed, which is nearest to the market risk capital charge of the trading portfolio? (please note: this is a variation on FRM handbook Example 28.18)
a. USD 127,300
b. USD 284,600
c. USD 313,100
d. USD 402,500
516.3. The BIS Amendment requires the one-day 99% VaR that a bank calculates to be backtested over the previous 250 days. This involves using the bank’s current procedure for estimating VaR for each of the most recent 250 days. If the actual loss that occurred on a day is greater than the VaR level calculated for the day, an “exception” is recorded. If the number of exceptions during the previous 250 days is less than 5, m(c) is normally set equal to 3. If the number of exceptions is 5, 6, 7, 8, and 9, the value of the m(c) is set equal to 3.4, 3.5, 3.65, 3.75, and 3.85, respectively. If the bank's value at risk (VaR) model is accurate, which is nearest to the chance of ten (10) or more exceptions? (please note this requires a binomial calculation which is a bit more tedious than you are likely to encounter on the exam)
a. infinitesimal; i.e., effectively zero
b. 0.0250%
c. 0.4025%
d. 10.7812%
Answers here:
Questions:
(Source: John Hull, Risk Management and Financial Institutions, 5th Edition (New York: John Wiley & Sons, 2018))
516.1. Basel's 1996 Amendment allows more sophisticated banks with well-established risk management functions to use an internal model-based approach (IMA) for setting market risk capital. Most large banks preferred to use the internal model-based approach because it better reflected the benefits of diversification and led to lower capital requirements. About this capital charge for market risk under the internal models approach (IMA), including 2009 revisions to the original Amendment, each of the following is true EXCEPT which is not?
a. The value-at-risk (VaR) measure used in the internal model-based approach is calculated with a 10-day time horizon and a 99.0% confidence level, and regulators explicitly stated that the 10-day 99.0% VaR can be calculated as the one-day 99.0% VaR multiplied by the square root of ten; i.e., 10-day 99.0% VaR = one-day 99.0% VaR * sqrt(10)
b. The capital requirement is equal to max[VaR(t-1), m(c)*VaR(avg) + SRC, where m(c) is a multiplicative factor with a minimum value of 3, SRC is a specific risk charge, VaR(t-1) is the previous day's value at risk, and VaR(avg) is the average value at risk over the past 60 days
c. The capital requirement adds two terms: value-at-risk(VaR) and specific risk charge (SCR). In a corporate bond security, for example, the credit risk is captured by the VaR term and the interest rate risk is captured by the SRC term
d. The bank's VaR risk model must contain a "sufficient" number of risk factors and the bank must justify the omission of any risk factors that are otherwise used in pricing (valuation)
516.2. As a risk manager for Bank ABC, Mary is asked to calculate the market risk capital charge of the bank's trading portfolio under the 1996 internal models approach. The 95.0% one-day value at risk (VaR) of the last trading day is USD 70,000; the average 95.0% one-day VaR for the last 60 trading days is USD 30,000. The multiplier is k = 3. Assume the return of the bank's trading portfolio is normally distributed, which is nearest to the market risk capital charge of the trading portfolio? (please note: this is a variation on FRM handbook Example 28.18)
a. USD 127,300
b. USD 284,600
c. USD 313,100
d. USD 402,500
516.3. The BIS Amendment requires the one-day 99% VaR that a bank calculates to be backtested over the previous 250 days. This involves using the bank’s current procedure for estimating VaR for each of the most recent 250 days. If the actual loss that occurred on a day is greater than the VaR level calculated for the day, an “exception” is recorded. If the number of exceptions during the previous 250 days is less than 5, m(c) is normally set equal to 3. If the number of exceptions is 5, 6, 7, 8, and 9, the value of the m(c) is set equal to 3.4, 3.5, 3.65, 3.75, and 3.85, respectively. If the bank's value at risk (VaR) model is accurate, which is nearest to the chance of ten (10) or more exceptions? (please note this requires a binomial calculation which is a bit more tedious than you are likely to encounter on the exam)
a. infinitesimal; i.e., effectively zero
b. 0.0250%
c. 0.4025%
d. 10.7812%
Answers here:
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