# LO 59.1: Describe and calculate the stressed VaR measure introduced in Basel 2.5,

LO 59.1: Describe and calculate the stressed VaR measure introduced in Basel 2.5, and calculate the market risk capital charge.
The implementation of Basel II coincided with the financial crisis of 2007-2009. Some people blamed Basel II because banks using the advanced internal ratings based (IRB) approach to calculate credit risk were allowed to use their own estimates of probability of default (PD), loss given default (LGD), and exposure at default (EAD). Some believed Basel II was a move toward self-regulation and allowed banks to underestimate risks. As a result, the Basel Committee on Banking Supervision implemented a series of changes to the calculation of market risk capital. These changes were part of Basel II.5, implemented December 31, 2011. There were three primary changes, including: 1. The calculation of a stressed value-at-risk (SVaR).
2. The implementation of a new incremental risk change (IRC).
3. A comprehensive risk measure (CRM) for instruments sensitive to correlations between
default risks of various instruments.
In the past, banks used the historical simulation method to calculate the VaR in order to find the market risk capital charge. The assumption in the historical simulation method
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Topic 59 Cross Reference to GARP Assigned Reading – Hull, Chapter 16
is that percentage changes in market variables the next day are random samples of the percentage changes over the previous one to four years. Volatilities of most market variables were low in the pre-crisis period (i.e., 20032006). As such, market risk VaRs were also low during this period and continuing for a time following the start of the financial crisis. To remedy the problem of low VaRs, Basel II.5 required banks to calculate two VaRs, the usual VaR, using the historical simulation method, and a stressed VaR, using a 250-day period of stressed market conditions. Initially, regulators thought the year 2008 would be ideal for stressed market conditions. However, banks are now required to identify a one-year period when their actual portfolios performed poorly. This means the stressed period may be different across banks.
The total market risk capital charge is the sum of the usual bank VaR and the stressed VaR. The formula for the total capital charge is:
Example: Total market risk capital charge
Spartan State Bank has calculated a market risk VaR for the previous day equal to $15.6 million. The average VaR over the last 60 days is$4.8 million. The bank has calculated a stressed VaR for the previous day equal to $17.7 million and an average stressed VaR equal to$18.4 million. Spartan State Bank has an accurate risk measurement model and recorded only two exceptions while backtesting actual losses against the calculated VaR. As such, the multiplicative factors, both mc and ms are set to 3. Calculate the total market risk capital charge.
Answer:
total capital charge = $15.6 million + ($18.4 x 3) = $70.8 million Professors Note: Because the stressed VaR w ill be equal to or\ more likely, greater than, VaR, the capital charge fo r market risk under Basel II.5 w ill be at least double the capital charge under Basel II. 2018 Kaplan, Inc. Page 291 previous days VaR, 10-day time horizon, 99% confidence levelmultiplicative factor, determined by supervisor, minimum value of threethe average stressed VaR over the past 60 days, 10-day time horizon, 99% = previous days VaR, 10-day time horizon, 99% confidence level the average VaR over the past 60 days, 10-day time horizon, 99% confidence = level = multiplicative factor, determined by supervisor, minimum value of three = previous days stressed VaR, 10-day time horizon, 99% confidence level = the average stressed VaR over the past 60 days, 10-day time horizon, 99% confidence level stressed VaR multiplicative factor, determined by supervisor, minimum of = three VaRt – l SVaRavg mS m max(VaRt l, mc x VaRavg) + max(SVaRt l , m$ x SVaRave)avg where: VaRt – l VaRavg
Topic 59 Cross Reference to GARP Assigned Reading – Hull, Chapter 16
I n c r e m e n t a l R i s k C a p i t a l C h a r g e