LO 58.2: Explain the calculation of risk-weighted assets and the capital

LO 58.2: Explain the calculation of risk-weighted assets and the capital requirement per the original Basel I guidelines.
Basel I put forth two capital requirements: 1. The banks total assets to capital ratio had to be less than 20 (i.e., capital to total
assets had to be greater than 1/20 or 5%). This capital requirement was similar to the requirements in many countries prior to 1988.
2. The banks on- and off-balance sheet items had to be used to calculate risk-weighted
assets (RWA). RWA is intended to measure a banks total credit exposure. The ratio of capital to risk-adj usted assets is called the Cooke ratio, after Peter Cooke from the Bank of England. Basel I stipulated that the Cooke ratio must exceed 8%.
Most banks met the first requirement. However, the risk-based capital requirement (i.e., the second requirement) was the key change to capital regulation. The process for calculating risk-weighted assets includes assigning a risk weight that reflects the banks credit risk exposure, to each of the on- and off-balance sheet items. A sample of some of the risk weights assigned to various asset categories is shown in Figure 1.
Figure 1: Risk Weights for On-Balance Sheet Items
Risk Weight (%)
Asset Category
50% 100%
Cash, gold, claims on Organisation of Economic Co-operation and Development (OECD) countries such as U.S. Treasury bonds and insured residential mortgages Claims on OECD banks and government agencies like U.S. agency securities or municipal bonds Uninsured residential mortgages Loans to corporations, corporate bonds, claims on non-OECD banks
Example: Risk-weighted assets
The assets of Blue Star Bank consist of $20 million in U.S. Treasury bills, $20 million in insured mortgages, $50 million in uninsured mortgages, and $150 million in corporate loans. Using the risk weights from Figure 1, calculate the banks risk-weighted assets.
(0.0 x $20) + (0.0 x $20) + (0.5 x $50) + (1.0 x $150) = $175 million
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Topic 58 Cross Reference to GARP Assigned Reading – Hull, Chapter 15
Off-balance sheet items are expressed as a credit equivalent amount. The credit equivalent amount is, in essence, the loan principal that is considered to have the same credit risk. This means the bank converts off-balance sheet items into on-balance sheet equivalents for the purpose of calculating risk-based capital. The weight is then multiplied by the principal amount (i.e., the credit equivalent amount) of the item to arrive at a risk-weighted value. A conversion factor is applied to the principal amount of the instrument for non-derivatives. Off-balance sheet items that are similar, from a credit perspective, to loans (e.g., bankers acceptances), have a conversion factor of 100%. Other off-balance sheet items, such as note issuance facilities, have lower conversion factors.
For interest rates swaps and other over-the-counter (OTC) derivatives, the credit equivalent amount is calculated as:
max(V, 0) + a x L
where: V = current value of the derivative to the bank a = add-on factor L = principal amount
The first term in the equation [max(V, 0)] reflects the banks current exposure. If the counterparty defaults and V, the current value of the derivative, is positive, the bank will lose V If the counterparty defaults and Vis negative, the exposure is 0 (i.e., no gain or loss to the bank). The add-on amount (a x L) allows for the possibility that the banks exposure may increase in the future. Add-on factors are higher for higher risk derivatives (e.g., longer maturities, riskier underlying assets). A sample of add-on factors is shown in Figure 2.
Figure 2: Add-on Factors as a Percent of Principal for Derivatives
Remaining Maturity
in Years
Interest Rate
Exchange Rate
and Gold year 15 years < 1 year 1 to 5 years > 5 years
0.0 0.5 1.5
1.0 5.0 7.5
6.0 8.0 10.0
10.0 12.0 15.0
Flxample: Credit equivalent amounts for off-balance sheet items
Blue Star Bank has entered a $175 million interest rate swap with a remaining maturity of three years. The current value of the swap is $2.5 million. Using the add-on factors in Figure 2, calculate the swaps credit equivalent amount.
The add-on factor is 0.5% of the interest rate swap principal.
credit equivalent amount = $2.5 + (0.005 x $175) = $3,375 million
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Topic 58 Cross Reference to GARP Assigned Reading – Hull, Chapter 15
The credit equivalent amount is multiplied by the risk weight for the counterparty to calculate risk-weighted assets. Risk weights are similar to those shown in Figure 1 with the exception of corporate counterparties. If the counterparty is a corporation, the risk weight is 50%. If the counterparty is an OECD bank, the risk weight is 20%.
Example: Calculating risk-weighted assets for an off-balance sheet item
In the previous example, Blue Star Bank entered an interest rate swap that had a credit equivalent amount of $3,375,000. Calculate the risk-weighted assets assuming (1) the counterparty is an OECD bank and (2) the counterparty is a corporation.
RWA assuming counterparty is an OECD bank: $3,375,000 x 0.2 = $675,000
RWA assuming counterparty is a corporation: $3,375,000 x 0.5 = $1,687,500
The total RWAs of the bank are calculated by summing the on- and off-balance sheet risk- weighted items as follows:
M N E wiLi + E wic i i=i
j= i
where: w- = the risk weight of the counterparty of the zth on-balance sheet item Lj = principal of the zth on-balance sheet item w. = the risk weight of the counterparty of theyth off-balance sheet item C. = credit equivalent amount of theyth off-balance sheet item The bank must maintain at least 8% capital to risk-weighted assets.
Example: Calculating risk-based capital
Using the information from the previous three examples, calculate Blue Star Banks required capital, assuming the swap counterparty is a corporation.
($175 million + $1.6875 million) x 0.08 = $14,135 million
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Topic 58 Cross Reference to GARP Assigned Reading – Hull, Chapter 15
According to Basel I, capital has two components, Tier 1 capital and Tier 2 capital.
Tier 1 capital (or core capital) consists of items such as: Equity (subtract goodwill from equity). Non-cumulative perpetual preferred stock. Tier 2 capital (or supplementary capital) consists of items such as: Cumulative perpetual preferred stock. Certain types of 99-year debentures.
Subordinated debt with an original maturity greater than five years (where the subordination is to depositors).
Equity capital (i.e., Tier 1) absorbs losses. Supplementary capital (i.e., Tier 2) is subordinate to depositors and thus protects depositors in the event of a bank failure. At least 50% of capital must be Tier 1. This means there is a 4% Tier 1 capital to risk-weighted assets requirement (i.e., 8% x 0.5). Half of the Tier 1 requirement has to be met with common equity. Under Basel I, some countries required banks to have more capital than required by The Accord.
Professors Note: Basel I had a number o f shortcomings that were rem edied over the com ing years with new capital accords. For example, Basel I treats all corporate loans the same in terms o f capital requirements. The creditworthiness o f the borrower is ignored. Also, Basel 1 did not include a m odel o f default correlation.
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