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# P2.T7.609. Fundamental Review of the Trading Book: expected shortfall and credit trades (Hull)

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
Learning objectives: Compare the various liquidity horizons proposed by the FRTB for different asset classes and explain how a bank can calculate its expected shortfall using the various horizons. Explain proposed modifications to Basel regulations in the following areas: classification of positions in the trading book compared to the banking book and treatment of credit spread and jump-to-default risk, including the incremental default risk charge.

Questions:

609.1. A key difference between the internal models approach (IMA) under Basel I and II.5 and the Fundamental Review of the Trading Book (FRTB) is the introduction of liquidity horizons: while the Basel I and II.5 calculated market risk capital using a 10-day time horizon, the FRTB uses five different horizons (10, 20, 40, 60, and 120 days) depending on the liquidity of the market variable. For example, investment grade corporate credit spreads and non-investment grade sovereign credit spreads are each Category 3 Variables with an assigned time horizon of 60 days. Due to this, the FRTB requires calculation of ES(1), ES(2), ES(3), ES(4) and ES(5).

Which of the following best summarizes the approach proposed in the Fundamental Review of the Trading Book (FRTB) for the estimation of expected shortfall (ES)?

a. ES(3) is a 10-day shock to all variables in categories 3, 4, and 5 while holding constant categories 1 and 2. Then ES(3)*sqrt(60/10) scales to a 60-day ES for the category variable. For the simulation, total ES is the square root of the sum of the five squared n-day expected shortfalls (ESs). Five simulations constitute the trial. Finally, 250 overlapping trials (each of the five simulations) are generated to produce the historical simulation.
b. ES(3) is a 10-day shock to all variables in categories 3, 4, and 5 while holding constant categories 1 and 2. Then ES(3)*sqrt(60/10) scales to a 60-day ES for the category variable. For the simulation, total ES is the sum of the five squared n-day expected shortfalls (ESs) because the variable changes are assumed to be perfectly correlated which is the most conservative assumption. Five simulations constitute the trial. Finally, 250 overlapping trials (each of the five simulations) are generated to produce the historical simulation.
c. ES(3) is a 60-day shock to the variable in category 3, while each variable is shocked over its own liquidity time horizon; e.g., ES(4) in the first trial is a shock equal to the change between Day 0 and Day 120. As ES(1) to ES(5) do not here require scaling, total ES is the square root of the sum of the five ES(n). Each trial is one simulation. Finally, 250 overlapping trials (each of the five simulations) are generated to produce the historical simulation.
d. ES(3) is a 60-day shock to the variable in category 3, while each variable is shocked over its own liquidity time horizon; e.g., ES(4) in the first trial is a shock equal to the change between Day 0 and Day 120. As ES(1) to ES(5) do not here require scaling, total ES for the simulation is the sum of the five ES(n)^2 because the variable changes are assumed to be perfectly correlated which is the most conservative assumption. Five simulations constitute the trial. Finally, 250 overlapping trials (each of the five simulations) are generated to produce the historical simulation.

609.2. Each of the following true about the internal models-based approach (IMA) under the Fundamental Review of the Trading Book (FRTB) EXCEPT which is false?

a. The FRTB therefore allows the stressed period calculations to be based on a SUBSET of market variables which are scaled up, if the subset of market variables account for at least 75% of the expected shortfall
b. The backtest must be conducted of the 97.5% stressed expected shortfall (ES) measure; that is, just as FRTB switches from Basel I/II.5's 99.0% value at risk (VaR) to 97.5% ES, the backtest must use the same stressed ES measure
c. Although the use of overlapping time periods is less than ideal because changes in successive historical simulation trials are not independent, this does not bias the results, but instead reduces the effective sample size making results more noisy than they would otherwise be.
d. The capital charge is based on a weighted average of (a) the expected shortfall for the whole portfolio and (b) the sum of the partial expected shortfalls. The partial expected shortfalls are determined by shocking the variables in a risk category (i.e., interest rate risk, equity risk, foreign exchange risk, commodity risk, and credit risk) while keeping all other variables fixed

609.3. Basel II.5 introduced the incremental risk charge (IRC) to ensure that banks did not reduce capital requirements by choosing the trading book over the banking book for a credit-dependent instrument; aka, regulatory arbitrage. How does the Fundamental Review of the Trading Book (FRTB) address credit trades?

a. The FRTB makes no changes to the IRC
b. The FRTB edits the IRC to produce a capital charge based on a 10-day, 97.5% confident expected shortfall (ES)
c. The FRTB replaces IRC with the default risk charge (DRC) which recognizes jump-to-default risk and mandates the inclusion of equity products
d. The FRTB replaces IRC with the default risk charge (DRC) which does not recognize jump-to-default risk and explicitly excludes equity products