21.Consider a fund that aims to replicate an equity index using a strategy based on forward contracts. Assume the fund holds short-term forward contracts for this purpose with a notional amount of 100 that are cleared through a qualifying central counterparty. Further, assume that the fund’s financial position can be represented by the following T-account balance sheet:

Finally, assume that the bank’s equity investment in the fund comprises 20% of the shares of the fund, and therefore is 20% × 95 = 19.

Using the LTA, the fund’s balance sheet exposures of 100 are risk weighted according to the risk weights that would be applied to these assets by the bank. For cash, the risk weight is 0%; for the government bonds, the risk weight is also 0%. The margin receivable is an exposure to a qualifying CCP, which has 2% risk weight. The underlying risk weight for equity exposures (100%) is applied to the notional amount of the forward contracts.

Assume that the bank is able to determine that the amount of the CCR exposure to the CCP is 10, which then receives the 2% risk weight for exposures to a qualifying CCP. Note that there is no CVA charge because the forward contracts are cleared through the qualifying CCP.

The total RWA for the fund is:

20×0% + 30×0% + 50×2% + 100×100% + 10×2% = 101.2
 

Given the total assets of the fund of 100, the average risk-weight for the fund is:

Avg RW_fund = 101.2 / 100 = 101.2%
 

With fund assets of 100 and fund equity of 95, leverage is calculated as the assets-to-equity ratio, or 100/95≈1.05. Therefore, the risk-weight for the bank’s equity investment in the fund is:

Risk Weight = 101.2% × (100/95) = 106.5%
 

Applying this risk weight to the bank’s equity investment in the fund of 19, the bank’s RWA on the position for the purpose of calculating minimum required capital is 106.5% × 19 = 20.24.

22.Consider a fund with current balance-sheet assets of 100, and assume that the bank is unable to apply the LTA due to a lack of adequate information. Suppose that the fund’s mandate states that the fund’s investment objective is to replicate an equity index. In addition to being permitted to invest in equities directly as assets and to hold cash balances, the mandate allows the fund to take long positions in equity index futures up to a maximum notional amount equivalent to 80% of the fund’s balance sheet. Since this means that with 100 in assets the fund could have futures with a notional value of 80, the total on-balance-sheet and off-balance-sheet exposures of the fund could reach 180.

Suppose that the fund’s mandate also places a restriction on leverage, allowing the fund to issue debt up to a maximum of 10% of the total value of the fund’s assets. This debt constraint implies that with 100 in assets, the fund’s maximum financial leverage would be at a mixture of 10 debt and 90 equity, for a maximum assets-to-equity ratio of 100/90≈1.11.

Finally, assume that the value of the bank’s investment in the fund is 20.

For the computation of RWA, the on-balance-sheet assets are assumed to be invested to the maximum extent possible in the riskiest type of asset permitted under the mandate. The mandate allows either cash (which has a zero risk weight) or equities, so the full 100 is assumed to be in equities, with a 100% risk weight.

Next, the fund is assumed to enter into derivatives contracts to the maximum extent allowable under its mandate – stated as 80% of total assets – implying a maximum derivatives notional of 80. This amount receives the risk weight associated with the underlying of the derivatives position, which in this example is 100% for publicly traded equity holdings.

The calculation of RWA must include an amount for the counterparty credit risk associated with derivatives. If the bank cannot determine the replacement cost associated with the futures contracts, then the replacement cost must be approximated by the maximum notional amount of 80. If the PFE is similarly indeterminate, an additional 15% of the notional amount must be added for PFE. Thus, the CCR exposure is 1.4 x (80×1.15) = 129. Assuming the futures contracts clear through a qualifying CCP, a risk weight of 2% applies to the CCR exposure, and no CVA charge is assessed for the CCP.

The total RWA for the fund is the sum of the components for on-balance-sheet assets, off-balance-sheet exposures, and CCR:

100×100% + 80×100% + 129×2% = 182.58
 

Given the total assets of the fund of 100, the average risk-weight for the fund is:

Avg RW_fund = 182.58 / 100 = 182.58%
 

As noted above, the fund’s maximum leverage is approximately 1.11 at an assets-to-equity ratio of 100/90. Therefore, the risk-weight for the bank’s equity investment in the fund is:

Risk Weight = 182.58% × (100/90) = 202.87%
 

Applying this risk weight of 202.87% to the bank’s equity investment in the fund of 20, the bank’s RWA on the position for the purpose of calculating minimum required capital is 202.87% × 20 = 40.57.