# P2.T7.520. Basel 2.5 with stressed VaR, IRC and CRM (Hull)

#### Nicole Seaman

##### Director of FRM Operations
Staff member
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Learning outcomes: Describe and calculate the stressed value-at-risk measure introduced in Basel 2.5, and calculate the market risk capital charge. Explain the process of calculating the incremental risk capital charge for positions held in a bank’s trading book. Describe the comprehensive risk measure (CRM) for positions which are sensitive to correlations between default risks.

Questions:
(Source: John Hull, Risk Management and Financial Institutions, 3rd Edition (New York: John Wiley & Sons, 2012))

520.1. As a risk manager for Transworld Financial Bank, Roger needs to calculate the market risk capital requirement for the bank's trading book. He needs to comply with Basel 2.5. Consequently, he needs to include stressed value at risk (sVar) in addition to the usual VaR. He has calculated the following value at risk (VaR) measures:
• The 95.0% one-day VaR on the previous day is $20,000 • The average 95.0% one-day VaR over the last 60 trading days is$12,000
• The 95.0% one-day stressed VaR (sVaR) on the previous trading day is $188,000 • The average 95.0% one-day stressed VaR (sVaR) over the last 60 trading days is$50,000
Both multiplication factors, m(c) and m(s), are set at the minimum of 3.0. Roger also assumes the return of the bank's trading portfolio is normally distributed. For example, the 10-day 99.0% VaR(t-1) = $20,000 * 2.326/1.645 * SQRT(10) =$89,449. Which is nearest to the market capital requirement?

a. $161,000 b.$188,000
c. $840,800 d.$1.0 million

520.2. About Basel 2.5, Hull says "During the credit crisis, it was recognized that some changes were necessary to the calculation of capital for market risk in the Basel II framework. These changes are referred to as 'Basel 2.5' ... There are three changes involving: 1. The calculation of a stressed VaR; 2. A new incremental risk charge; and 3. A comprehensive risk measure for instruments dependent on credit correlation. The measures have the effect of greatly increasing the market risk capital that large banks are required to hold."
(Source: John Hull, Risk Management and Financial Institutions, 3rd Edition (New York: John Wiley & Sons, 2012))

In regard to the incremental risk charge (IRC) each of the following is true EXCEPT which statement is untrue about the IRC?

a. The IRC was introduced because instruments in the trading books often required less regulatory capital than equivalent instruments in the banking book
b. The IRC is calculated as the one-year 99.9% value at risk (VaR) for losses from credit instruments in the trading book
c. The IRC excludes ratings changes or migrations because a rating change does not itself lead to default within the one year horizon
d. The constant level of risk assumption assumes that the bank will have the opportunity to rebalance its portfolio during the course of the year so that default risk is mitigated

520.3. According to Hull, each of the following is true about the comprehensive risk measure (CRM) EXCEPT which is not accurate?

a. The CRM is a single capital charge replacing the incremental risk charge and the specific risk charge for instruments dependent on credit correlation
b. The CRM can be calculated using a standardized approach which determines a charge based on the credit rating (e.g., BBB+ to BBB-) of the securitization or re-securitization
c. The maximum capital charge under the standardized approach is 28.0% which applies securitization with the lowest credit rating
d. The Basel Committee allows banks, with supervisory approval, to use their internal models to calculate the CRM for unrated positions, but the models developed by banks have to be sophisticated in order to be approved by bank supervisors.

Answers here:

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