Instructor Micky Midha

Updated On - Describe the changes to the Basel framework for calculating market risk capital under the Fundamental Review of the Trading Book (FRTB), and the motivations for these changes.
- 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 the FRTB revisions to Basel regulations in the following areas:
- Classification of positions in the trading book compared to the banking book.
- Backtesting, profit and loss attribution, credit risk, and securitizations.

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•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.

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

- 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.

•Under FRTB,

- 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.

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

- 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 –

- 𝐸𝑆
_{1 }– Banks are first required to calculate when 10-day changes are made to all risk factors. This is denoted by 𝐸𝑆_{1}.

2. 𝐸𝑆_{2 }– 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 𝐸𝑆_{2}.

3. 𝐸𝑆_{3 }– 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 𝐸𝑆_{3}.

4. 𝐸𝑆_{4 }-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 𝐸𝑆_{4}.

5. 𝐸𝑆_{5 }– Finally, they are required to calculate 𝐸𝑆_{5}, 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.

•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.

•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.

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

- 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.

•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.

•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.

•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.