Learning objective: 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.
Questions:
608.1 In January 2016 the Basel Committee on Banking Supervision (BCBS) issued its Revised Framework for Market risk Capital Requirements which is also called the Fundamental Review of the Trading Book (FRTB). Compared to Basel I and Basel II.5, each of the following is true about the FRTB EXCEPT which is false?
a. The internal models approach (IMA) under Basel II.5 required the sum of two components, current VaR plus stressed VaR, but the FRTB requires only a single stressed expected shortfall (ES)
b. IMA under Basel I and II.5 calculated market risk capital using a 10-day time horizon, but the FRTB uses five different horizons (10, 20, 40, 60, and 120 days) depending on the liquidity of the market variable
c. IMA under Basel II.5 required the Default Risk Charge (DRC), but the FRTB eliminates this component which implies that the median (and weighted average) total market risk capital requirement is likely to be reduced due to the change from Basel II.5 to the FRTB
d. IMA under Basel I and Basel II.2 calculated the market risk capital requirement based on value at risk (VaR) with a 99.0% confidence level, but the FRTB calculates the market risk capital requirement based on expected shortfall (ES) with a 97.5% confidence level
608.2. In the past, the boundary between the regulatory banking book and the trading book created an opportunity for regulatory arbitrage. As Hull writes, "The FRTB [Fundamental Review of the Trading Book] also addresses the issue of whether instruments should be put in the trading book or in the banking book. Roughly speaking, the trading book consists of instruments that the bank intends to trade. The banking book consists of instruments that are expected to be held to maturity. Instruments in the trading book are marked to market (i.e., revalued) daily while instruments in the banking book are not. Instruments in the banking book are subject to credit risk capital while those in the trading book are subject to market risk capital." (Source: John Hull, Risk Management and Financial Institutions, 4th Edition (New York: John Wiley & Sons, 2012))
Which of the following is TRUE about the treatment of the boundary in the FRTB?
a. The FRTB simply collapses the regulatory banking and trading book into a single book which solves the regulatory arbitrage problem
b. The FRTB makes no change to the boundary between the regulatory banking and trading book but subjects both books to the same exact calculations for the capital requirement
c. The FRTB establishes a more objective boundary between the regulatory banking and trading book, including the assignment when position is initiated and strict limits on subsequent movement between the books
d. The FRTB says that the necessary and sufficient condition for an instrument's inclusion in the trading book is a sincere "intent to trade;" if the position is moved from one book to another, the FRTB imposes the incremental risk capital (IRC) charge as a penalty
608.3. If the distribution is normal, Kevin Dowd (in Managing Market Risk, 2nd Edition) explains that expected shortfall (ES) has an elegant calculation as given by the following:
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(Source: Kevin Dowd, Measuring Market Risk, 2nd Edition (West Sussex, England: John Wiley & Sons, 2005))
For example, if the daily mean, µ, is +1.0% and the daily standard deviation, σ, is 5.0%, then the 99.0% ES = -1.0% + 5.0%*[NORM.S.DIST(2.326, FALSE)/0.010] ~= 12.326%, where NORM.S.DIST(2.326, FALSE) is the standard normal probability density function (pdf) at the quantile, z(99.0%), equal to 2.326.
However, Hull provides the alternative method (see below) which does not require a standard normal lookup. In this function, X is the confidence level and Y is the standard normal quantile; aka, inverse CDF or, as Hull writes "Y is the point on a standard normal distribution that has probability of (1-X) of being exceeded." For example, if X is 99.0%, then Y is 2.326.
.jpg)
(Source: John Hull, Risk Management and Financial Institutions, 4th Edition (New York: John Wiley & Sons, 2012))
Using Hull's expression and assuming returns are normally distributed where the daily mean return is +1.0% and the daily standard deviation is 5.0%, which of the following is nearest to the daily 97.5% expected shortfall (ES)?
a. 4.00%
b. 7.22%
c. 8.80%
d. 10.69%
Answers:
Questions:
608.1 In January 2016 the Basel Committee on Banking Supervision (BCBS) issued its Revised Framework for Market risk Capital Requirements which is also called the Fundamental Review of the Trading Book (FRTB). Compared to Basel I and Basel II.5, each of the following is true about the FRTB EXCEPT which is false?
a. The internal models approach (IMA) under Basel II.5 required the sum of two components, current VaR plus stressed VaR, but the FRTB requires only a single stressed expected shortfall (ES)
b. IMA under Basel I and II.5 calculated market risk capital using a 10-day time horizon, but the FRTB uses five different horizons (10, 20, 40, 60, and 120 days) depending on the liquidity of the market variable
c. IMA under Basel II.5 required the Default Risk Charge (DRC), but the FRTB eliminates this component which implies that the median (and weighted average) total market risk capital requirement is likely to be reduced due to the change from Basel II.5 to the FRTB
d. IMA under Basel I and Basel II.2 calculated the market risk capital requirement based on value at risk (VaR) with a 99.0% confidence level, but the FRTB calculates the market risk capital requirement based on expected shortfall (ES) with a 97.5% confidence level
608.2. In the past, the boundary between the regulatory banking book and the trading book created an opportunity for regulatory arbitrage. As Hull writes, "The FRTB [Fundamental Review of the Trading Book] also addresses the issue of whether instruments should be put in the trading book or in the banking book. Roughly speaking, the trading book consists of instruments that the bank intends to trade. The banking book consists of instruments that are expected to be held to maturity. Instruments in the trading book are marked to market (i.e., revalued) daily while instruments in the banking book are not. Instruments in the banking book are subject to credit risk capital while those in the trading book are subject to market risk capital." (Source: John Hull, Risk Management and Financial Institutions, 4th Edition (New York: John Wiley & Sons, 2012))
Which of the following is TRUE about the treatment of the boundary in the FRTB?
a. The FRTB simply collapses the regulatory banking and trading book into a single book which solves the regulatory arbitrage problem
b. The FRTB makes no change to the boundary between the regulatory banking and trading book but subjects both books to the same exact calculations for the capital requirement
c. The FRTB establishes a more objective boundary between the regulatory banking and trading book, including the assignment when position is initiated and strict limits on subsequent movement between the books
d. The FRTB says that the necessary and sufficient condition for an instrument's inclusion in the trading book is a sincere "intent to trade;" if the position is moved from one book to another, the FRTB imposes the incremental risk capital (IRC) charge as a penalty
608.3. If the distribution is normal, Kevin Dowd (in Managing Market Risk, 2nd Edition) explains that expected shortfall (ES) has an elegant calculation as given by the following:
(Source: Kevin Dowd, Measuring Market Risk, 2nd Edition (West Sussex, England: John Wiley & Sons, 2005))
For example, if the daily mean, µ, is +1.0% and the daily standard deviation, σ, is 5.0%, then the 99.0% ES = -1.0% + 5.0%*[NORM.S.DIST(2.326, FALSE)/0.010] ~= 12.326%, where NORM.S.DIST(2.326, FALSE) is the standard normal probability density function (pdf) at the quantile, z(99.0%), equal to 2.326.
However, Hull provides the alternative method (see below) which does not require a standard normal lookup. In this function, X is the confidence level and Y is the standard normal quantile; aka, inverse CDF or, as Hull writes "Y is the point on a standard normal distribution that has probability of (1-X) of being exceeded." For example, if X is 99.0%, then Y is 2.326.
(Source: John Hull, Risk Management and Financial Institutions, 4th Edition (New York: John Wiley & Sons, 2012))
Using Hull's expression and assuming returns are normally distributed where the daily mean return is +1.0% and the daily standard deviation is 5.0%, which of the following is nearest to the daily 97.5% expected shortfall (ES)?
a. 4.00%
b. 7.22%
c. 8.80%
d. 10.69%
Answers:
