1.Calculating the General Market risk charge

Calculate the general market risk capital charge for XYZ bank’s interest rate positions using the maturity method.

Long position in a qualifying bond: Market value AED 13.33m. Residual maturity 8 years & coupon 8%

Long position in a government bond: Market value AED 75m. Residual maturity 2 months & coupon 7%

Interest rate swap: Notional value AED 150m. Residual life of swap 8 years & bank receives floating rate interest and pays fixed. Next interest fixing after 9 months

Long position in interest rate government bond future: Contract size AED 50mn.

The treatment of interest rate future positions assume a bank is exposed to a long position in a 6-month interest rate future bought today and settled in two months' time. The long position in interest rates needs to be slotted into the 6-12 months’ time band because the maturity of the long position is considered to be eight months. This is because the position is taken on today and will be settled in two months with a maturity of six months.

Delivery date after 6 months & remaining maturity of the CTD government security 3.5 years.

Cheapest to deliver CTD refers to the underlying instrument that result in the greatest profit or the least loss when delivered in satisfaction of futures contracts.

Calculating the general market risk capital charge comprises two main steps and a number of sub-steps.

Step 1: Map each interest rate position

We are using the maturity method to map the positions. None of the bank’s positions have a coupon of less than 3%, so we will use a ladder of 13 time bands. Each position is mapped to the appropriate time band according to its residual maturity.

Step 2: calculate the total capital charge

Overall net open position

The net open position is the sum of all the positions across all the time bands. The net open position is AED 3m short, which leads to a capital charge at 100% of AED 3,000,000.

Calculation:

+75*0.2%=+0.15

-50*0.4%=-0.2

+150*0.7%=+1.05

+50*2.25%=+1.125

-150*3.75%=-5.625

+13.33*3.75%=+0.5

Vertical disallowance

The long position of AED 0.5m is offset against the short position of AED 5.625m as per the marked area. The matched position is AED 0.5m and the net open position is AED -5.125m.

This leads to a capital charge of 10% of AED 0.5m, or AED 50,000

Calculation

Matched position = 0.5

Net open position = -5.625+0.5= -5.125

Horizontal disallowance

The third part of the capital charge is a charge for the horizontal disallowance. There are three rounds of horizontal offsetting.

In round 1, the horizontal disallowance within each zone is calculated. In this example, charge applies to zone 1 only because it is the only zone with a long and a short position. (With more than one position). The short position, -0.2 is offset against the total long position, +1.2. The matched position is 0.2 and the net open position is +1.

The capital charge for the horizontal disallowance within zone 1 is 40% of AED 0.2m, or AED 80,000

In round 2, calculate the horizontal disallowance between adjacent zones, i.e., between:

Zone 1 and zone 2

Zone 2 and zone 3

In this example, zone 1 and zone 2 both contain long positions, so there is no matched position and therefore no offsetting between these zones. The long position of 1.125 in zone 2 is offset against the short position of -5.125 in zone 3. The matched position is 1.125 and the net open position is -4. The capital charge for the horizontal disallowance between zones 2 and 3 is 40% of AED 1.125m= AED 450,000.

In round 3, we calculate the horizontal disallowance between zones 1 and 3.

In this example, the long position of 1 in zone 1 is offset against the short position of -4 in zone 3. The matched position is 1 and the net open position is -3. The capital charge for the horizontal disallowance between zones 1 and 3 is 100% of AED 1m = AED 1m.

After the three rounds of horizontal offsetting, the total charge for the horizontal disallowance is AED 80,000 + AED 450,000 + AED 1,000,000 = AED 1,530,000

Having completed the horizontal and vertical offsetting, the remaining overall net open position is AED 3m, which is equivalent to the overall net open position we calculated across all time bands when we calculated the first part of the capital charge.

We have now calculated the total capital charge for general market risk for this example.

   2.Specific Market Risk – Example

Relate to the same example as above.

Given that, the government bonds are AAA-rated and that the qualifying bond is BBB-rated.

The interest rate swap does not incur a specific risk charge. The AAA-rate government bonds incur a 0% specific risk charge. The qualifying bond has a residual maturity of 8 years and is BBB-rated, so if has a specific risk charge of 1.6%

The capital charge is 1.6% of AED 13.33m, or AED 213,280.

Bank XYZ has the following positions in its equity portfolio for a particular national market.

To calculate the general market risk charge, we must first determine the overall net open position. The sum of the net long positions is AED 650,000 and the sum of the net short positions is AED 870,000. The overall net open position is short AED 220,000.

The capital charge for general market risk is 8% of AED 220,000, or AED 17,600.

Next, we must work out the specific risk charge.

The capital charge for specific risk is 8% of AED 1,520,000 or AED 121,600.

That lead to, overall capital charge for this portfolio is AED 17,600 + AED 121,000, or AED 139,200.

Below is an example of calculating the capital charge for FX risk.

A bank has the following positions that have been converted at spot rates into its reporting currency, United Arab dirhams (AED).

The higher of the sum of the net long and net short currency positions is AED 300m.

The capital charge is therefore calculated as 8% of AED 300m, plus the net position in gold (AED 35m):

Capital charge = 8% of AED 335m = AED 26.8m

Another example;

A bank has the following positions that have been converted at spot rates into its reporting currency (AED)

The sum of the net long positions is AED 225m and the sum of the net short positions is -AED 145m. The capital charge is calculated as 8% of the higher of these two positions, so the charge is 8% of AED 225m, or AED 18m.

   1.Simplified approach

XYZ bank is exposed to a number of positions in the same commodity. The bank’s reporting currency is AED. The following positions are held in EUR:

Firstly, calculate the current value for these positons in the reporting currency.

The following is the current situation:

Further calculation to the position after conversion to local reporting bank’s currency

640*4.25=2,720
-800*4.25=-3,400
480*4.25=2,040
-480*4.25=-2,040

Calculate the capital charge, first a capital charge of 15% of the overall net open position in the commodity is required.

The overall net position is the sum of the long and short positions:
AED 2,720 – AED 3,400 + AED 2,040 – AED 2,040 = - AED 680
The overall net positon is short AED 680. This leads to a capital charge of AED 102 (680 * 15%) Next, a capital charge of 3% of the bank’s gross positon in the commodity is required.
The gross position is the sum of the absolute values of the long and short positions:
AED 2,720 + AED 3,400 + AED 2,040 + AED 2,040 = AED 10,200

XYZ bank’s gross position is AED 10,200. This leads to a capital charge of AED 306 (10,200 * 3%).
Now, sum the charges to find the total capital charge for this commodity. The charge for the overall net open position is AED 102, and the charge for the bank’s gross position in the commodity is AED 306.
Therefore, XYZ bank’s total market risk capital charge for positions held in this commodity is AED 102 + AED 306, or AED 408.

   2.Maturity ladder approach

Recall that XYZ bank is exposed to a number of positions in the same commodity. The bank’s reporting currency is AED. The following positions are held in EUR:

Step 1:

First express each commodity position in terms of the standard unit of measurement, and value in the reporting currency at the current spot price.

The following is the current situation:

This is done the same way as for the simplified approach.

Step 2:

Slot each position into a time band in the maturity ladder according to its remaining maturity. Physical stocks should be allocated to the first time band.

Step 3:

Apply a capital charge: of 1.5% to the sum of the matched long and short positions in each time band to capture spread risk.

*start with the 3-6 months’ time band.
Multiply the sum of the ling and short matched positions by the spread rate 1.5%, to calculate the capital charge: (AED 2,720 + AED 2,720) * 1.5% = AED 81.6

Step 4:

Apply a capital charge of 0.6% to the residual net position carried forward to the next relevant time band, multiplied by the number of time bands it is carried forward.

The maturity ladder approach allows for netting between unmatched long and short positions across time bands. The residual net position in a time band can be carried forward to the next relevant time band, thus offsetting exposures in time bands further out. Because this is imprecise, resulting in an “imperfect hedge”; a capital charge is required.

The residual net position in the 3-6 months’ band is short AED 680. This net position is carried forward two time bands to offset exposures in the next relevant time band, the 1-2 years’ band.

*The capital charge is calculated as follows: AED 680 * 2 * 0.6% = AED 8.16

Step 5:

Repeat step 3 and step 4 for each time band.

When determining the matched position in each time band, take into account the residual net position carried forward.

*(680+680)*1.5% = AED 20.4
**(1,360*2*0.6%) = AED 16.32
***(1,360+1360) *1.5% = AED 40.8

Step 6:

Apply a capital charge of 15% to the overall long or short net open position.

The net position in the final time band is subject to a capital charge of 15% as to say 680 * 15% = AED 102

Step 7:

Derive the total capital charge by summing the charges for spread risk, for positions carried forward and for the overall net open position.

In this example, the capital charge calculated using the maturity ladder approach; AED 269.28 is significantly lower than that calculated using the simplified approach, AED 408.

   Simplified approach

A bank holds 100 shares currently valued at USD 10, and also holds an equivalent number of put options with a strike price of USD 11 (each option entitles the bank to sell one share).
Since these are equity options, they are subject to the capital charges for general market risk and specific risk according to the standardised framework for equity risk. The capital charge is levied at 8% for general market risk and 8% for specific risk, giving a summed charge of 16%.

Market value of 100 shares = USD 1,000

First, multiply the market value by the sum of general market risk and specific risk charges.
USD 1,000 x 16% = USD 160
Then, calculate the amount the option is in-the-money.

(USD 11 - USD 10) x 100 = USD 100

The capital charge is the general market risk and specific risk charge less the amount the option is in-the-money.
USD 160 - USD 100 = USD 60

A similar methodology applies for options whose underlying is a foreign currency, an interest rate related instrument or a commodity.

Another example for simplified approach
A bank holds 500 shares currently valued at USD 25.50 and holds an equivalent number of put options with a strike price of USD 26.25 (each option entitles the bank to sell one share).

The capital charge is calculated as follows:
Market value of 500 shares = USD 12,750
USD 12,750 x 16% (that is, 8% specific plus 8% general market risk) = USD 2,040

The amount the option is in-the-money = (USD 26.25 - USD 25.50) x 500 = USD 375.
This gives a capital charge of USD 2,040 - USD 375 = USD 1,665