LO 60.1: Describe the proposed changes to the Basel market risk capital

LO 60.1: Describe the proposed changes to the Basel market risk capital calculation and the motivations for these changes, and calculate the market risk capital under this method.
In May 2012, the Basel Committee on Banking Supervision began considering the next round of changes to market risk capital calculations for banks. This process is known as the Fundamental Review of the Trading Book (FRTB). After receiving comments on proposals and seeing the results of a formal study, the rules were further refined in December 2014. It is important for risk managers to understand the nature of the proposed changes and the new calculation methodology.
In order to properly understand the changes, it is necessary to first understand the previous market risk requirements. The Basel I calculations for market risk capital involved a 10-day value at risk (VaR) calculated with a 99% confidence interval. This process produced a very current result because the 10-day horizon incorporated a recent period of time, which typically ranged from one to four years. The Basel II. 5 calculations required banks to add a stressed VaR measure to the current value captured with the 10-day VaR. The stressed VaR measures the behavior of market variables during a 250-day period of stressed market conditions. Banks were required to self-select a 250-day window of time that would have presented unusual difficulty for their current portfolio.
The FRTB researched if the 10-day VaR was really the best measurement for a banks true risk. The value at risk measure has been criticized for only asking the question: Flow bad can things get? VaR communicates, with a given level of confidence, that the banks
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Topic 60 Cross Reference to GARP Assigned Reading – Hull, Chapter 17
losses will not exceed a certain threshold. Consider a bank that uses a 10-day VaR with a 99% confidence interval and finds that losses will only exceed $25 million in 1% of all circumstances. What if the 1% chance involves a $700 million loss? This could be a catastrophic loss for the bank. Therefore, the FRTB has proposed an alternate measure using expected shortfall (ES), which is a measure of the impact on the profit and loss statement (P&L) for any given shock of varying lengths. The expected shortfall asks the question: If things get bad, what is the estimated loss on the banks P&L?
Consider the following example that illustrates the difference between value at risk and expected shortfall. A bank has a $950 million bond portfolio with a 2% probability of default. The default schedule appears in Figure 1.
Figure 1: Example Default Schedule for $950 Million Bond Portfolio
Confidence Level
Default
95% 96% 97% 98% 99% 99.9%
No No No No Yes Yes
Loss $0 $0 $0 $0
$950 million $950 million
At the 95% confidence interval, there is still no expected loss, so the 95% VaR would imply a $0 of loss. However, the expected shortfall measure accounts for the potential dollar loss conditional on the loss exceeding the 95% VaR level. In this case, three out of five times the expected loss is still $0, but two out of five times the expectation is for a total loss of the $950 million bond portfolios value due to default. This means that 40% of the tail risk would yield a loss, so the expected shortfall is $380 million (i.e., 40% x $950 million). This presents a very different risk perspective than using the VaR measure alone.
Instead of using a 10-day VaR with a 99% confidence interval, the FRTB is proposing the use of expected shortfall with a 97.5% confidence interval. For a normal distribution, with mean of p and standard deviation of a, these two measures yield approximately the same result. The 99% VaR formula is p + 2.326a, and the 97.5% expected shortfall formula is p + 2.338a. However, if distributions have fatter tails than a normal distribution, then the 97.5% expected shortfall can be considerably different from the 99% VaR.
Under this FRTB proposal, banks would be required to forgo combining a 10-day, 99% VaR with a 250-day stressed VaR, and instead calculate capital based on expected shortfall using a 250-day stressed period exclusively. Just as with the 250-day stressed VaR, banks would be charged with self-selecting a 250-day window of time that would be exceptionally difficult financially for the banks portfolio.
Professors Note: There are approximately 250 trading days in a 12-month time period. This is why 250-day tim e windows are used. Following the same logic, a 120-day window equates to six months, a 60-day window equates to one quarter (three months), a 20-day window equates to one month, and a 10-day window is essentially two weeks.
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Topic 60 Cross Reference to GARP Assigned Reading – Hull, Chapter 17
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