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).
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.
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.
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.
