Thursday, September 24, 2015

Fundamental Review of the Trading Book: Methodology for Default Risk Capital Calculation



Regulatory Framework

Regulatory  framework for Default Risk capital for market risk in the trading books can be determined by application of either:
• The standardised approach: a set of regulatory mandatory calcu lation and measurement techniques to quantify minimum regulatory required capital for Default Risk. Or,
• The internal model approach: a set of calculation and measurement techniques to quantify minimum regulatory required capita for Default Risk  that is developed by a bank itself. Banks can only use this approach with approval from their regulator.

The scope of this blog Article limited to the standardised approach to calculate the Default Risk Charge (DRC).

Methodology Standardised Approach

A capital charge is calculated for each asset class category as prescribed by regulators. The categories for this purpose are corporates, sovereigns, local governments/municipalities.  The procedure involves determining jump-to-default (JTD) loss amounts by applying loss-given-default (LGD) risk weights to positions, determining hedging and offsetting benefit, and applying default risk weights. For the calculation of JTD loss amounts, the representation of positions uses notional amounts and market values. 

The starting point in the calculation of the DRC is the notional amount and mark-to-market loss already taken on a credit position. The notional amount is used to determine the loss of principal at default, and the mark-to-market loss is used to determine the net loss so as to not double-count the mark-to-market loss already recorded in the P&L.

Gross Jump-to-default risk positions (Gross JTD)

Next, JTD long and JTD short are calculated separately. Specifically , a long (res. short) position is one in which the default of the underlying obligor results in a loss (res. gain). E.g. default of the obligor on sold protection via CDS (written CDS) will result in loss, thus written CDS is a long position in the underlying.
Gross JTD calculations are performed by assigning LGD risk weights to positions.
Gross JTD (long) = max [LGD × notional + P&L, 0]
Gross JTD (short) = min [LGD × notional + P&L, 0]
where notional is the bond-equivalent notional (or face value) of the position and P&L is the cumulative mark-to-market loss (or gain) already taken on the exposure. In more detail,
P&L=market Value – notional,
where market value is the current market value of the position.
Equity instruments and non-senior debt instruments are assigned an LGD of 100%. Senior debt instruments are assigned an LGD of 75%. Covered bonds are assigned an LGD of 25%.
To account for defaults within the one year capital horizon, the JTD for all exposures of maturity less than one year are scaled by a fraction of a year. No scaling is applied to the JTD for exposures of one year or greater. For example, the JTD for a position with a six month maturity would be weighted by one-half, while the JTD for a position with a one year maturity would have no scaling applied to the JTD. Equity positions (i.e. stock) are assigned maturities of greater than one year. The maturity weighting applied to the JTD for short term lending is floored at a weighting factor of one-fourth or, equivalently, 3 months.

Net Jump-to-default risk positions (Net JTD)

The JTD amounts of long and short positions to the same obligor may be offset where the short position has the same or lower seniority relative to the long position. For example, a short position in an equity may offset a long position in a bond, but a short position in a bond cannot offset a long position in the equity.
Exposures of different maturities that meet this offsetting criterion may be offset as follows. Exposures with maturities longer than the capital horizon (one year) may be fully offset, but in the case of longer-than-one-year vs less-than-one-year exposures the offset benefit of the less than one year exposure must be reduced as follows. An exposure to an obligor comprising a mix of long and short positions with a maturity less than the capital horizon (equal to one year) should be weighted by the ratio of the position’s maturity relative to the capital horizon.
For example, with the one-year capital horizon, a three-month short position would be weighted so that its benefit against long positions of longer-than-one-year maturity would be reduced to one quarter of the position size.
In the case of long and short offsetting positions where both have a maturity under one year, the scaling can be applied to both the long and short positions. Finally, the offsetting may result in net long JTD amounts and net short JTD amounts. The net long and net short JTD amounts are aggregated separately as described below.
Equity positions (i.e. stock) are assigned maturities of greater than one year. For derivative exposures, the maturity of the derivative contract is considered in determining the offsetting criterion, not the maturity of the underlying position.
Default risk weights are assigned to net JTD by credit quality categories (ie rating bands), irrespective of the type of counterparty, as in the following graph for illustration only. 

 


The weighted net JTD are then allocated to buckets. The three buckets for this purpose are corporates, sovereigns, and local governments/municipalities.
In order to recognise hedging relationship between long and short positions within a bucket, a hedge benefit ratio is computed as below.


The overall capital charge for each bucket should then be calculated as the combination of the sum of the risk-weighted long net JTD, where the summation is across the credit quality categories (ie rating bands), the WtS, and the sum of the risk-weighted short net JTD, where the summation is across the credit quality categories (ie rating bands): 


Where DRC stands for “default risk charge”, and i refers to an instrument belonging to bucket b.
No hedging is recognised across different buckets. Therefore, the total capital charge for default risk non-securitisations must be calculated as a simple sum of the bucket-level capital charges. For example, no hedging or diversification is recognised across corporate and sovereign debt, and the total capital charge is the sum of the corporate capital charge and the sovereign capital charge.

Concluding Remarks

The main concern of the above methodology is the way the hedge ratio WtS is prescribed. This is calculated across the rating bands. For example, if a long AAA bond position is hedged either with AAA short bond position or CCC short bond position, this approach do not make distinction between the two. This really distorts the hedges and thus create disincentives for effective hedging and risk management.









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