LO 60.2: Compare the various liquidity horizons proposed by the Fundamental Review of the Trading Book (FRTB) for different asset classes and explain how a bank can calculate its expected shortfall using the various horizons.

According to the Basel Committee, a liquidity horizon (LH) is the time required to execute transactions that extinguish an exposure to a risk factor, without moving the price of the hedging instruments, in stressed market conditions. The standard 10-day LH was not deemed appropriate given the actual variations in liquidity of the underlying transactions. Five different liquidity horizons are now in use: 10 days, 20 days, 60 days, 120 days, and 250 days. Consider the 60-day horizon, which is essentially three months worth of trading days. The calculation of regulatory capital for a 60-day horizon is intended to shelter a bank from significant risks while waiting three months to recover from underlying price volatility.

Under FRTB proposals, every risk factor is assigned a liquidity horizon for capital calculations. For example, investment grade sovereign credit spreads are assigned a 20- day horizon, while non-investment grade corporate credit spreads are assigned a 120-day horizon and structured products have a 250-day horizon. See Figure 2 for a sample listing of liquidity horizons.

Figure 2: Allocation of Risk Factors to Liquidity Horizons

Risk Factors

Horizon (in Days)

Interest rate (EUR, USD, GBP, AUD, JPY, SEK, and CAD) Interest rate (other) Interest rate at-the-money (ATM) volatility Credit spread: sovereign, investment grade Credit spread: sovereign, non-investment grade Credit spread: corporate, investment grade Credit spread: corporate, non-investment grade Credit spread: structured products Equity price: large cap Equity price: small cap Equity price: large cap ATM volatility Equity price: small cap ATM volatility FX rate (liquid currency pairs) FX rate (other currency pairs) FX volatility Energy price Precious metal price Energy price ATM volatility Precious metal ATM volatility

10 20 60 20 60 60 120 250 10 20 20 120 10 20 60 20 20 60 60

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The Basel committees original idea was to utilize overlapping time periods for stress testing. They initially wanted to find a time periods expected shortfall (ES) by scaling smaller time periods up to longer time periods using a series of trials. Consider a bank that has a 10- day risk asset, like large-cap equity, and a 120-day risk asset, like a non-investment grade corporate credit spread. In the first trial, they would measure the stressed P&L changes from Day 0 to Day 10 for the large-cap equity and also the value change from Day 0 to Day 120 for the non-investment grade corporate credit spread. The next trial would measure the change from Day 1 to Day 11 on the large-cap equity and from Day 1 to Day 121 for the credit spread. The final simulated trial would measure Day 249 to Day 259 for the large- cap equity and Day 249 to Day 369 for the credit spread. The ES used would then be the average loss in the lower 2.5% tail of the distribution of the 250 trials.

After the initial idea was submitted for comments, it was revised in December 2014 to incorporate five categories. The rationale was to reduce implementation costs. The updated categories are as follows: Category 1 is for risk factors with 10-day horizons. Category 2 is for risk factors with 20-day horizons. Category 3 is for risk factors with 60-day horizons. Category 4 is for risk factors with 120-day horizons. Category 5 is for risk factors with 250-day horizons. Using this revised, categorical process attempts to account for the fact that risk factor shocks might not be correlated across liquidity horizons.

This proposed new process is formally known as the internal models-based approach (IMA). In the internal models-based approach, expected shortfall is measured over a base horizon of 10 days. The expected shortfall is measured through five successive shocks to the categories in a nested pairing scheme using ES15. ESj is calculated as a 10-day shock with intense volatility in all variables from category 15. ES2 is calculated as a 10-day shock in categories 25, holding category 1 constant. ES3 is calculated as a 10-day shock in categories 35, holding category 1 and 2 constant. ES4 is calculated as a 10-day shock in categories 45, holding categories 13 constant. The final trial, ES5, is calculated as a 10-day shock in category 5, holding categories 14 constant. The idea is to measure the hit to the banks P&L for ES15. The overall ES is based on a waterfall of the categories, as described above, and is scaled to the square root of the difference in the horizon lengths of the nested risk factors. This relationship is shown in the following formula:

Until the internal models-based approach has been formally approved, banks must continue to use what is known as the revised standardized approach. This process groups risk assets with similar risk characteristics into buckets, which are essentially just organized around

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liquidity horizons. The standardized risk measure for each bucket is then calculated using the following formula:

+ 2 ^ y ^ p ijw iw jv iv j

i

i

j*
*

# LO 60.2: Compare the various liquidity horizons proposed by the Fundamental