### Fundamental Review of the Trading Book (FRTB)

After completing this reading you should be able to:

• Summarize the clearing process in OTC derivative markets.
• Describe changes to the regulation of OTC derivatives which took place after the 2007-2009 financial crisis and explain the impact of these changes.

In this chapter, the proposed changes to the Basel Market Risk Capital will be described, including the motives for these changes. The market risk capital will also be computed under this method. There will be a comparison of the various liquidity horizons proposed for different asset classes by the FRTB.

A further explanation will be given on the computation of a bank’s expected shortfall via various methods. Finally, the chapter will explain proposed modifications to the Basel Regulations in various areas, namely:

1. Positions classification in the trading book in comparison to the banking book; and
2. Credit spread and jump-to-default risk treatment.

# New Market Risk Measures

A VaR computed for a 10-day horizon and a confidence level of 99% is the basis of the Basel I computation of market risk capital. Since the computations were based on the recent market variables behavior, then the VaR was current.

In addition to the current measure, banks were required under Basel II.5 to compute a stressed VaR measure whose computations are based on the characteristics of market variables in a 250-day period of stressed market conditions.

A change to the measure applied for determining market risk capital is being proposed by the Fundamental Review of the Trading Book (FRTB). An expected shortfall with a 97.5% confidence level is proposed to replace the 99% VaR. However, the distributions are almost perfectly equivalent under normal distributions.

The computation of the expected shortfall using a 12-month stressed period is the only basis of capital. By searching back through time, a period that would be particularly difficult for the current portfolio of the bank will be chosen, analogously to the determination of the stressed VaR determination for Basel II.5.

Further proposals by the FRTB states that: to mirror the fact that market variables underlying transactions vary according to their liquidity, then the 10-day time horizon applied in the Basel I and Basel II should be changed.

In the implementation of Basel I and Basel II.5, one-day changes in market variables are typically considered by banks for the computation of a one-day VaR, which is then multiplied by the square root of 10 to determine an estimate of the 10-day VaR.

Changes to the market variables are required by the FRTB to be the changes to take place over the periods of time reflecting the differing liquidities of the market variables. Liquidity horizons refer to the periods of time.

The overlapping of time periods is a simple approach in the implementation of varying liquidity horizons. A shock equivalent to the change between Day 0 and Day 10 would be considered for the price of a large-cap stock in the first historical simulation.

For the credit spread of a non-investment-grade corporate bond, the shock should be equal to the change between Day 0 and Day 120. For other market variables, other prescribed shocks would be considered and this would be followed suit by the computation of other market variables and the loss or gain in the portfolio arising from the shocks.

A shock equal to the change between Day 1 and Day 11 for the equity price would be considered by the second trial, the same way it would consider a shock equal to the change between Day 1 and Day 121 for the credit spread and so on.

A shock equivalent to the change between Day 249 and Day 259 for the equity prices would be considered in the final simulation trial, and a shock equal to the change between Day 249 and Day 365 for the credit spread would also be considered.

The average of those losses in the 2.5% tail of the distribution produced by the 250 trials is the calculation of the ES. This approach was rejected in the December 2014 consultative document in favor of an approach having all computations based on the changes in market variables over a 10-day overlapping period.

The computation of ES by banks was only to take place when 10-day changes are effected to all variables. Then, the ES is to be computed when 10-day variations are effected to all categories 2 and above variables. The variables in category 1 should not change.

Afterward, the banks are required to compute ES when 10-day variations are effected to all categories 4 and 5 variables. This time, categories 1, 2 and 3 variables should not change. Finally, the banks should compute ES when 10-day variations are effected to all category 5 variables and all the other variables should not be changing.

The following formula represents the computation of ES:

$$\sqrt { E{ S }_{ 1 }^{ 2 }+\sum _{ j=2 }^{ 5 }{ { \left( E{ S }_{ j }\sqrt { \frac { { LH }_{ j }-{ LH }_{ j-1 } }{ 10 } } \right) }^{ 2 } } }$$

With $${ LH }_{ j }$$ being the liquidity horizon for category $$j$$. Therefore, five historical simulations, with each involving 10-day changes in variables, should be effected. Changes in variables between Day 0 and Day 10 should be considered by the first trial in each historical simulation.

In the second trial, we consider variables between Day 1 and Day 11. The trend continues in a similar fashion. In the final simulation trial, the changes considered are between Day 249 and Day 259.

Due to the lack of dependence in the changes in successive historical simulation trials, the application of overlapping time periods is less than ideal. However, the results do not get biased due to this fact, but rather they become noisier than they are otherwise due to the reduction in effective sample size.

The FTRB contains many details, some of which are:

1. Sometimes, it is difficult for banks to practically search for past stressed periods applying all market variables due to a shortage of historical data for some of the variables. The stressed period computations can thus be based on a subset of market variables, as allowed by the FRTB. The results should then be scaled up by the ratio of the current Expected Shortfall using the full set of risk factors to the current Expected Shortfall measure using the reduced set of factors.
2. The categorization of the market variables should be in various risk categories. The expected shortfall for each risk category should then be computed by the bank, in addition to the computation of its total portfolio’s expected shortfall. The basis of the capital charge is on a weighted average of:
• The whole portfolio’s expected shortfall; and
• The partial expected shortfalls summation.
3. According to FRTB, the back-testing should be done applying a VaR measure computed over a one-day horizon and the data’s latest 12 months. The confidence levels to be applied are both the 99% and the 97.5%.

This approach is known as the internal models-based approach. Instruments with the same risk characteristics are grouped into buckets. The following formula is applied in the computation of a standardized risk measure for each bucket:

$$\sum _{ i }^{ }{ { w }_{ i }^{ 2 }{ v }_{ i }^{ 2 }+2\sum _{ i }^{ }{ \sum _{ j<1 }^{ }{ { \rho }_{ ij }{ w }_{ i }{ w }_{ j }{ v }_{ i }{ v }_{ j } } } }$$

Where $${ v }_{ j }$$ is the $$i$$th instrument’s value and $${ w }_{ j }$$ and $${ \rho }_{ ij }$$ are the weights and the correlations the Basel Committee has specified, respectively. Then, each bucket’s standardized risk measures are combined for the regulatory capital to be determined with some diversification recognition across buckets.

# Trading Book vs. Banking Book

The issue of whether to place trading instruments in the trading book or the banking book is also addressed by the FRTB. Instruments to be traded by the bank are contained in the trading book. Instruments expected to be held to maturity are contained in the banking book. In the trading book, instruments are daily marked-to-market, which is not the case in the banking book.

Furthermore, the banking book instruments are subjected to credit risk capital whereas those in the trading book get subjected to market risk capital. Regulatory arbitrage has, in the past, arisen due to the difference in calculation of these two types of capital.

There are attempts by the FRTB to clearly distinguish between the trading book and the market. The trading intention by the bank will no longer be the sufficient reason to be in the trading book. The bank must demonstrate its trading ability and management of the underlying risks on a trading desk. Equity should be affected by the day-to-day variation in value, therefore posing risks to solvency.

The assigning of instruments to the trading book or banking book should be when they are initiated. To prevent them from being subsequently moved between the two books, strict rules should be set in place. Finally, there should be no capital benefit from items being moved between books.

To ensure capital requirements are not reduced by banks, there was the introduction of the incremental risk charge (IRC) by Basel II.5. A choice of the trading book over the banking book for a credit-dependent instrument, by the banks, could reduce capital requirements. A modification in the IRC is provided by the FRTB.

The two risk types that can be identified for instruments that rely on a particular firm’s credit risk are:

1. Credit spread risk: is the risk of change by a company’s credit spread leading to a change in the mark-to-market value of the instrument; and
2. Jump-to-default risk: is the risk that there will be a default by the company, leading to an immediate loss or gain to the bank.

The handling of the first risk type can be similar to that of other market risks, with the new rules in application. The second risk type is separately handled subject to an incremental default risk (IDR) charge.

Banks are allowed by the Basel II.5 IRC to assume a constant risk level. A liquidity horizon is approximated by the bank for each credit dependent instrument in the trading book and assume that there will be a replacement of deteriorating positions.

# The clearing process in OTC derivatives

In OTC derivative markets, there are no exchanges or some other form of intermediary. Contracts are traded and negotiated directly between two parties. Products include swaps, forwards, and exotic options. The OTC derivative market is the largest market for derivatives. Before the 2007/2009 financial crisis, the OTC market was largely unregulated; traders had the freedom to choose whether or not to post collateral or use a third party in transactions. One could enter into as many contracts as they wished. In the aftermath of the crisis, all that changed. The OTC market is increasingly being monitored with a view to align its regulation with that of the mainstream exchange derivative market.

Clearing is the post-transaction management which ensures that transactions will settle. It can be bilateral or central. In bilateral clearing, market participants clear transactions with each other. Central clearing refers to the use of a central counterparty (CCP) to mitigate risks associated with the default of a trading counterparty.

CCP clearing means that a CCP becomes the legal counterparty to each trading party, providing a guarantee that it will honor the terms and conditions of the original trade even in the event that one of the parties defaults before the discharge of its obligations under the trade. To be able to do this, the CCP collects enough money from each party which goes toward covering potential losses that may be incurred if a party fails to follow through on the initial agreement.

The following view, although a bit simplistic helps to show the role played by CCPs in trading. Each of the six entities denoted B represents a dealer bank.

# Practice Questions

1) Billow Bank has sometimes been finding it difficult to search for past stressed periods using all market variables. This fact can be attributed to shortage of historical data for some of the variables. How does the Fundamental Review of the Trading Book (FRTB) deal with this challenge?

1. The FRTB can allow the stressed period computations to be based on a subset of market variables and the results scaled up by the ratio of the current Expected Shortfall using the full set of risk factors to the current Expected Shortfall measure using the reduced set of factors.
2. One-day changes in market variables are typically considered for the computation of a one-day VaR, which is then multiplied by the square root of 10 to determine an estimate of the 10-day VaR.
3. A shock equal to the change between Day 1 and Day 11 for the equity price would be considered by the second trial, the same way it would consider a shock equal to the change between Day 1 and Day 121 for the credit spread and so on.
4. All the above