Introduction

•In May 2012, the Basel Committee on Banking Supervision issued a consultative document  proposing major revisions to the way regulatory capital for market risk is calculated. This is  referred to as the “Fundamental Review of the Trading Book” (FRTB). The Basel Committee  then followed its usual process of  requesting comments from banks, revising the proposals,  and carrying out Quantitative Impact Studies (QISs).

•The final version of  the rules was published by the Basel Committee in January 2016. Initially,  the banks were to implement the new rules by 2019, however, in December 2017, the year by  which implementation is to be completed was revised to 2022.

•FRTB’s approach to determining capital for market risk is much more complex than the  approaches previously used by regulators. The Basel Committee has announced a move to a  situation where total required capital is at least 72.5% of  that  given by standardized  approaches. They will achieve this by 2027 with a five-year phase-in period.

•These changes are a culmination of a trend by the Basel Committee since the 2008 crisis to  place less reliance on internal models and to use standardized models to provide a floor for capital requirements.

•A difference between FRTB and previous market risk regulatory requirements is that most  calculations are carried out at the trading desk level. Furthermore, permission to use the  internal models approach is granted on a desk-by-desk basis. Therefore it is possible that, at a  particular point in time, a bank’s foreign currency trading desk has permission to use the  internal models approach while the equity trading desk does not.

•The way in which capital is calculated for the trading book and for the banking book are quite  different. This potentially gives rise to regulatory arbitrage where banks choose to allocate  instruments to either the trading book or the banking book so as to minimize amount of  capital required.

•However, in Basel II.5, the incremental risk charge made such regulatory arbitrage less  attractive. FRTB counteracts regulatory arbitrage by defining more clearly than previously the  differences between the two books.

Background and Motivations

•The calculation of market risk capital has undergone various changes over the years –

1. The Basel I calculations of market risk capital were based on a value at risk (𝑉𝑎𝑅)  calculated for a 10-day horizon with a 99% confidence level. The 𝑉𝑎𝑅  was “current” in  the sense that calculations made on a particular day were based on the behavior of market  variables during an immediately preceding period of time (typically, one to four years).

2. Basel II.5 required banks to calculate a “stressed 𝑉𝑎𝑅” measure in addition to the current  measure. This is 𝑉𝑎𝑅 where calculations are based on the behavior of market variables  during a 250-day period of stressed market conditions. To determine the stressed period,  banks were required to go back through time searching for a 250-day period where the  observed movements in market variables would lead to significant financial stress for the  current portfolio.

•FRTB changes the measure used for determining market risk capital. Instead of 𝑉𝑎𝑅 with a  99% confidence level, it uses expected shortfall (𝐸𝑆) with a 97.5% confidence level. The  measure is actually stressed 𝐸𝑆 with a 97.5% confidence. This means that, as in the case of  stressed 𝑉𝑎𝑅, calculations are based on the way market variables have been observed to move  during stressed market conditions.

•For normal distributions, 𝑉𝑎𝑅 with a 99% confidence and 𝐸𝑆 with a 97.5% confidence are  almost exactly the same. Suppose losses have a normal distribution with a mean 𝜇  and  standard deviation 𝜎. The 99% 𝑉𝑎𝑅 is 𝜇 + 2.326𝜎 while the 97.5% expected shortfall is

𝜇 + 2.338𝜎.

•For non-normal distributions, they are not equivalent. When the loss distribution has a heavier  tail than a normal distribution, the 97.5% 𝐸𝑆 can be considerably greater than the 99% 𝑉𝑎𝑅.

Liquidity Horizons

•Under FRTB,

1. The 10-day time horizon used in Basel I and Basel II.5 is changed to reflect the liquidity of the market  variable being considered.

2. Changes to market variables (in stressed market  conditions) are considered over periods of time  reflecting their liquidity.

3. The changes are referred to as shocks.

4. The market variables are referred to as risk factors.

5. The periods of time considered are referred to as  liquidity horizons. Five different liquidity horizons are specified: 10 days, 20 days, 40 days, 60 days, and 120 days.

Risk Factor	Horizon (Days)
Interest rate (dependent on currency)	10-60
Interest rate volatility	60
Credit spread: sovereign, investment grade	20
Credit spread: sovereign, non-investment grade	40
Credit spread: corporate, investment grade	40
Credit spread: corporate, non-investment grade	60
Credit spread: other	120

•The  allocation of  risk  factors  to  these  liquidity horizons is indicated in this table (which is continued  in next page as well) –

Risk Factor	Horizon (Days)
Credit spread volatility	120
Equity price: large cap	10
Equity price: small cap	20
Equity price: large cap volatility	20
Equity price: small cap volatility	60
Equity: other	60
Foreign exchange rate (dependent on currency)	10-40
Foreign exchange volatility	40

 

Risk Factor	Horizon (Days)
Energy price	20
Precious metal price	20
Other commodities price	60
Energy price volatility	60
Precious metal volatility	60
Other commodities price volatility	120
Other commodities price volatility	120

 

•The horizon days are more for the assets that are more risky.

Internal Models Approach

•The variables are categorized into five categories with overlapping 10-day periods –

1. Category 1 Risk Factors – Risk factors with a time horizon of 10 days

2. Category 2 Risk Factors -Risk factors with a time horizon of 20 days

3. Category 3 Risk Factors – Risk factors with a time horizon of 40 days

4. Category 4 Risk Factors – Risk factors with a time horizon of 60 days

5. Category 5 Risk Factors – Risk factors with a time horizon of 120 days

•Banks are required to calculate various 𝐸𝑆 measures –

1. 𝐸𝑆₁ – Banks are first required to calculate when 10-day changes are made to all risk factors.  This is denoted by 𝐸𝑆₁.

2. 𝐸𝑆₂ – They are then required to calculate 𝐸𝑆 when 10-day changes are made to all risk  factors in categories 2 and above with risk factors in category 1 being kept constant. This  is denoted by 𝐸𝑆₂.

3. 𝐸𝑆₃ – They are then required to calculate 𝐸𝑆 when 10-day changes are made to all risk  factors in categories 3, 4, and 5 with risk factors in categories 1 and 2 being kept constant.  This is denoted by 𝐸𝑆₃.

4. 𝐸𝑆₄ -They are then required to calculate 𝐸𝑆 when 10-day changes are made to all risk factors in categories 4 and 5 with risk factors in categories 1,2, and 3 being kept  constant. This is denoted by 𝐸𝑆₄.

5. 𝐸𝑆₅ – Finally, they are required to calculate 𝐸𝑆₅, which is the effect of making 10-day  changes only to category 5 risk factors.

•The liquidity-adjusted 𝐸𝑆 is calculated as

where,

𝐿𝐻_j is the liquidity horizon for category 𝑗.

•Calculations are carried out for each desk. If  there are six desks, this means the internal  models approach, as we have described it so far, requires 5 × 6 = 30 𝐸𝑆 calculations. As  mentioned, 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 it reduces the effective sample size, making results more noisy than they would otherwise be.

•In FRTB, banks are required to consider changes over periods of 10 days that occurred during  a stressed period in the past. The first simulation trial assumes that the percentage changes in  all risk factors over the next 10 days will be the same as their changes between Day 0 and Day  10 of the stressed period; the second simulation trial assumes that the percentage changes in  all risk factors over the next 10 days will be the same as their changes between Day 1 and Day  11 of the stressed period; and so on.

Revised Standardized Approach(RSA)

•Until internal models are not approved, banks are required to continue using the revised  standardized approach, RSA. Under the RSA, risks (assets) are grouped into “buckets,” which  are created based on the concept of liquidity horizons. After that, the  standardized risk  measure for each bucket is calculated using the following formula –

where

𝑣_i  = value of the 𝑖^th risk factor (or 𝑖^th instrument)

𝑤_i = risk weight of 𝑖^th risk factor (determined by the Basel Committee)

𝜌_ij = the correlation between 𝑖^th and 𝑗^th risk factors (determined by the Basel committee)

•The standardized risk measures are then combined for each bucket to calculate regulatory  capital.

•Regulators may require that capital calculated using the new internal models-based approach be  at least some specified percentage of the RSA.

Trading Book vs Banking Book

•The FRTB addresses whether instruments should be put in the trading book or 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 banking book are subject to credit risk capital whereas those in the trading  book are subject to market risk capital. The two sorts of capital are calculated in quite different  ways.

•This has in the past given rise to regulatory arbitrage. For example, banks have often chosen to  hold credit-dependent instruments in the trading book because they are then subject to less  regulatory capital than they would be if they had been placed in the banking book.

•The FRTB attempts to make the distinction between the trading book and the banking book  clearer and less subjective. To be in the trading book, it will no longer be sufficient for a bank  to have an ‘intent to trade’. It must be able to trade and manage the underlying risks on a trading desk.

•The day-to-day changes in value should affect equity and pose risks to solvency. The FRTB  provides rules for determining for different types of instruments whether they should be  placed in the trading book or the banking book.

•An important point is that instruments are assigned to the banking book or the trading book  when they are initiated and there are strict rules preventing them from being subsequently  moved between the two books.

•Transfers from one book to another can happen only in extraordinary circumstances  (Examples given of  extraordinary circumstances are the closing of  trading desks and a change  in accounting standards with regard to the recognition of fair value). Any capital benefit as a  result of moving items between the books will not be allowed.

Backtesting Modifications

•FRTB does not back-test the stressed 𝐸𝑆 measures that are used to calculate capital under the  internal models approach for two reasons-

1. First, it is more difficult to back-test 𝐸𝑆 than 𝑉𝑎𝑅.

2. Second, it is not possible to back-test a stressed measure at all. Statistically, the stressed data  are not expected to be observed with the same frequency in the future as they were during  the stressed period.

•FRTB back-tests a bank’s models by asking each trading desk to back-test a 𝑉𝑎𝑅 measure  calculated over a one-day horizon and the most recent 12 months of  data. Both 99% and  97.5% confidence levels are to be used. If there are more than 12 exceptions for the 99%

𝑉𝑎𝑅 or more than 30 exceptions for the 97.5% 𝑉𝑎𝑅, the trading desk is required to calculate  capital using the standardized approach until neither of these two conditions continues to exist.

•Banks may be asked by regulators to carry out other back-tests. Some of these could involve  calculating the 𝑝‐value of the profit or loss on each day. This is the probability of observing a  profit that is less than the actual profit or a loss that is greater than the actual loss. If the model is working perfectly, the 𝑝‐values obtained should be uniformly distributed.

Profit and Loss Attributions Modifications

•Another test used by the regulators is known as profit and loss attribution. Banks are required  to compare the actual profit or loss in a day with that predicted by their models.

•Two measures must be calculated. The measures are:

where,

𝑈 denotes the difference between the actual and model profit/loss in a day.

𝑉 denotes the actual profit/loss in a day.

•Regulators expect the first measure to be between and —10% and +10% and the second  measure to be less than 20%. When there are four or more situations in a 12-month period  where the ratios are outside these ranges, the desk must use the standardized approach for  determining capital.

Revisions To Credit Risk

•As mentioned, FRTB distinguishes two types of credit risk exposure to a company:

1.Credit spread risk is the risk that the company’s credit spread will change, causing the  mark-to-market value of the instrument to change.

2.Jump-to-default risk is the risk that there will be a default by the company.

•Under the internal models approach, the credit spread risk is handled in a similar way to other  market risks.

•The liquidity horizon for credit spread varies from 20 to 120 days and the liquidity horizon for  a credit spread volatility is 120 days.

•The jump-to-default risk is handled in the same way as default risks in the banking book. In the  internal models approach, the capital charge is based on a 𝑉𝑎𝑅 calculation with a one year time  horizon and a 99.9% confidence level.

Revisions To Securitization

•The comprehensive risk measure (CRM) charge was introduced in Basel II.5 to cover the risks  in products created by securitizations such as asset-backed securities and collateralized debt  obligations. The CRM rules allow a bank (with regulatory approval) to use its own models. The  Basel Committee has concluded that this is unsatisfactory because there is too much variation  in the capital charges calculated by different banks for the same portfolio. It has therefore  decided that under FRTB the standardized approach must be used for securitizations.