The Fundamental Review of the Trading Book is a new set of proposals defined by the BCBS (Basel Committee of Banking Supervision) which aims to improve the Market Risk frameworks currently implemented by large Significantly Important Financial Institutions (SIFIs).

The current framework also designed by the BCBS in the Basel 2.5 regulation was aimed as a response to the Financial Crisis in 2007-2008 where capital requirements were not strong enough for some banks to cope with large asset price shocks and defaults.

It outlined the following weaknesses:

- Internal Models are inconsistent across banks in the industry,
- Standardised Approach used was not reliable,
- Transfers from Trading Book to Banking Book and vice versa are too lenient.

## FRTB Explained

The new FRTB overhaul aims to reduce the variability of bank capital levels providing a more comprehensive and easily replicable and consistent model in the industry.

The recommendations in the BCBS regulation ‘Minimum Capital Requirements for Market Risk” (BCBS352) released in January 2016, have been discussed since 2010, with multiple consultation papers and analysis documents being released in between these two dates.

Finally, after intensive discussions between the BCBS, and banks which will need to implement the new regulation, the agreed implementation date for FRTB was set as 1^{st} January 2022.

So what are the key amendments outlined in the Fundamental Review of the Trading Book which would need to be added to the existing market risk management framework?

The new model proposed by the regulation splits capital components into two buckets: FRTB Internal Model Approach (IMA) and FRTB Standardised Approach (SA).

**Internal Model Approach**

The FRTB IMA is the desired approach for banks given that in the majority of cases, the required capital held against its assets is likely to be less than in the FRTB SA.

The high level changes for the FRTB IMA approach are:

Basel 2.5 | FRTB IMA |

VaR + SVaR | Stressed Expected Shortfall |

1 or 10-day Holding Period whether VaR or SVaR | Defined Product Specific Liquidity Horizons |

Full Diversification | Constraints on Diversification, including Non Modellable Risk Factors (NMRF) |

IRC includes Default and Migration Risk | DRC only concerns Jump-to-Default |

Correlation Products included | Correlation Products not permitted in IMA |

Model Eligibility Determined at Bank Level | Model Eligibility Determined at Trading Desk Level |

Eligibility Criteria done with Backtesting | Eligibility Criteria done with Backtesting, and PLA Attribution test |

**Value at Risk vs Expected Shortfall**

For the first point, the VaR which gives us a value which tells us “what is our maximum expected loss in a certain time period?”, is replaced by the Expected Shortfall measure which tells us “if things do get bad, what is the loss we would expect?”

The reason this is preferred is that it gives us more of an indication of what to expect when we breach our expected loss – this is important to understand what the loss outliers look like, and should represent a more conservative measure.

The Stressed Expected Shortfall measure will be calculated on a 97.5% confidence interval calibrated to the most severe 12-month period of stress over the observation horizon (2005+ data).

**Change in Liquidity Horizon for Capital Calculations**

There are a variety of BCBS specified holding periods which will apply to products of different types (depending on risk factor).

These have been designed to reflect the actual holding periods of each asset, where a bank may be calculating their VaR measures previously using other holding periods (to reflect potential illiquidity of products in the market particularly in an economic downturn).

I have included the list of products and their liquidity horizons below:

Risk Factor | Liquidity Horizon (Days) |

Interest Rate | 20 |

Interest Rate ATM Volatility | 60 |

Interest Rate (Other) | 60 |

Credit Spread – Sovereign (IG) | 20 |

Credit Spread – Sovereign (HY) | 60 |

Credit Spread – Corporate (IG) | 60 |

Equity Price (Small Cap) Volatility | 120 |

Equity (Other) | 20 |

FX Rate | 60 |

FX Volatility | 60 |

FX (Other) | 60 |

Energy Price | 20 |

Credit Spread – Corporate (HY) | 120 |

Credit Spread – Structured (CDS and Cash) | 250 |

Credit (Other) | 250 |

Equity Price (Large Cap) | 10 |

Equity Price (Small Cap) | 20 |

Equity Price (Large Cap) Volatility | 20 |

Precious Metals Price Volatility | 60 |

Other Commodities Price Volatility | 120 |

Using the various provided liquidity horizons, the relative risk weight is calculated by applying it to the following formula:

Where:

- T is 10 days
- ES(Qj) is the Expected Shortfall at horizon T where the subset of risk factors Qj which have liquidity horizons at least as long as LHj are simulated (with all other risk factors remaining constant)
- LHj is the liquidity horizon in days for j, with the longer list provided in the table above

**Rules of Diversification**

This requirement outlines that ‘Non Modellable Risk Factors (NMRFs)’ must be removed from the Stressed Expected Shortfall calculation. For something to be deemed ‘non modellable’, it means that the risk factor is not observable by a sufficient number of transactions in the market.

There is a monthly assessment where the time series for the risk factor must have at least 24 price points per year with no more than 1 month between two consecutive prices, and that the price is defined as either an executed price or committed quote (no hypothetical quotes).

An audit trail capability is required to identify underlying transaction or quote behind a price. As a result of the audit trail capability, it is required that banks store time series data going back to 2005 (roughly 10 years of data) so that the worst year in this period can be used as the benchmark.

Where the complete set of data is not defined or stored, it may be required to use a suitable proxy time series as the comparison. Furthermore, regression may be necessary to get the specified data.

**Default Risk Charge – Goodbye Migration Risk!**

For the IMA DRC which is replacing the IRC charge, it is essentially removing the need for the calculation of migration risk (defined as the P&L associated with a counterparty rating improvement or downgrade without full default).

As part of the calculation, banks are now required to get their Probability of Default and Loss Given Default factors from the IRB model, and will need 10 years of historical data for the calibration of default correlations between issuers/guarantors.

The scenarios generated which simulate the Jump to Default of all counterparties in the portfolio are ordered, and the DRC metric is taken as the simulation value at the 99.9% level of confidence.

The eligibility for trading desks to use the Internal Model Approach is now changing from a Bank wide assessment done through Backtesting, to a more rigorous approach which now includes P&L attribution, done at the Trading Desk level on a daily basis. The details of the two tests are:

*Risk-based Profit & Loss test (Hypothetical P&L vs Risk Theoretical P&L)*

*Risk-based Profit & Loss test (Hypothetical P&L vs Risk Theoretical P&L)*

The Risk Theoretical P&L must be within a BCBS specified range of the Hypothetical P&L (excluding the impact of new trades during the day). Calculation of the Risk Theoretical P&L should be based on risk models, not the front office pricing systems.

The two P&L Attribution ratios are defined as:

If any desk experiences a mean or variance difference between its Risk Theoretical and Hypothetical P&L greater than the BCBS specified limits on more than 4 occasions over the last 12 months, all of its positions must be capitalized using the standardized approach.

*VaR Backtesting (Actual P&L and Hypothetical P&L vs VaR)*

*VaR Backtesting (Actual P&L and Hypothetical P&L vs VaR)*

The Hypothetical P&L and Actual P&L are both compared to the 1-day holding period VaR (99% and 97.5%) over the past 12 months.

Banks must have the capability to backtest both hypothetical P&L (which is the hypothetical change in the portfolio value that would occur if the end of day positions remained unaffected); and the actual P&L (which is the P&L for actual trading outcomes).

*Desks which experience more than 12 exceptions at 99% or 30 at 97.5% in the most recent 12 month period, all of its positions must be capitalized using the standardized approach*

**Standardised Approach**

The fall-back approach that bank’s need to account for in the case of a trading desk failing the model attribution tests is the Standardised Approach. This is the default for banks that have no internal market risk model, though is still a requirement for reporting for banks even when they pass all of the IMA criteria.

The three metrics that make up the FRTB SA capital charge are:

**Sensitivities Based Calculation**

For this calculation, each asset class calculates risk charge for Delta, Vega and Gamma (curvature) with no diversification benefits gained between the risk classes, which is based on the Variance-Covariance model covered in my previous blog post here.

For each risk charge, three correlation scenarios are defined, and the final charge is the largest value of the three.

**Default Risk Charge – but not as you know it**

There is also a Default Risk Charge in the Standardised model, though this is not the same calculation as in the IMA model.

The Jump-to-Default (JTD) simulations are calculated for three perimeters: Securitised CTP, Securitised non-CTP and Securitised products (CTP = Correlation Trading Portfolio).

To calculate the top of the house value, the JTD simulations are calculated per instrument, netted by instrument, multiplied by the FRTB designated risk weight, aggregated by bucket, and then aggregated there. The nature of the calculation means that there is no diversification realised across the perimeters.

**Residual Risk Add-on**

The final charge for monthly reporting is the Residual Risk Add-on which applies a set percentage of notional on all trades that are defined as having a ‘residual risk’. These risks include (but are not limited to):

- Gap Risk
- Correlation Risk
- Behavioural Risk
- Exotic Risk (such as Natural Disasters)

In order to calculate all of the requirements of the FRTB regulations, a large amount of time series data is required, and it is estimated that banks will have to increase their data processing and file storage capabilities threefold.

The final notable inclusion in the FRTB paper is the way that internal hedging transfers are defined between the banking book (assets purchased to be held by the bank) and the trading book (assets purchased solely to be traded).

The basic outline of the proposal is to minimize the likelihood of banks being able to transfer assets from one book to another with the intention of reducing their capital requirement due to the hedging that the transferred asset would apply.

By creating the new rules, any hedging benefit from an internal transfer will be added as a fixed charge – negating any incentive to carry this out. The final paper once all consultations have completed is due to be released at the end of this year.

Given the large scope and the impact that the proposals will have on banks, the amount of work already taken, and funding that banks have spent has been understandably significant.

With the final deadline fast approaching, we are almost at the point where we will be witnessing the most significant changes in Market Risk Management since the implementation of the Value at Risk model.