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Explain how Basel I's original guidelines arrive at risk-weighted assets and at the capital a bank must hold.

FRM® Part II · Operational Risk and Resilience · Capital Regulation Before the Global Financial Crisis · FRM2.ORR.21.b

The idea

Basel I (1988) is a historical framework, since superseded, that measures credit risk with risk-weighted assets. RWA = sum of exposure × risk weight. On the balance sheet the historical Basel I weights are 0 percent for cash and OECD government securities, 20 percent for claims on OECD banks, 50 percent for residential mortgages and 100 percent for corporate loans, and they should not be generalised to current Basel frameworks. Off-balance-sheet items are first turned into a credit equivalent amount. Guarantees and standby letters of credit count at 100 percent, undrawn commitments over one year at 50 percent, and derivatives at current replacement cost (if positive) plus an add-on from notional and maturity. That amount is then multiplied by the counterparty weight. Required capital is at least 8 percent of RWA. Tier 1 must be at least 4 percent of RWA, and eligible Tier 2 cannot exceed Tier 1. A common mistake is applying 8 percent to total assets rather than to RWA.

Formulas

Basel I risk-weighted assets

RWA = Σ E × w

E
each exposure, or credit equivalent amount for off-balance-sheet items
w
the risk weight of the counterparty or asset

Minimum total capital is 8 percent of RWA. Applying 8 percent to total assets is the usual error.

Credit equivalent of a derivative under Basel I

CE = max(V, 0) + a × L

V
the current replacement cost of the contract
a
the add-on factor for the contract type and remaining maturity
L
the notional principal

The credit equivalent is then multiplied by the counterparty's risk weight, 20 percent for an OECD bank.

A practice question

From the question bank, with the reason each wrong option is wrong.

Under Basel I, what is the minimum total capital that a bank must hold, expressed as a fraction of risk-weighted assets?

  1. 4 percent, all of it Tier 1 capitalWhy not: 4 percent is the Tier 1 minimum, not the total capital minimum.
  2. 8 percent, with at least half of it as Tier 1 capital - correct
  3. 10 percent, all of it Tier 1 capitalWhy not: Confuses Basel I with later, higher requirements; the 1988 Accord set 8 percent.
  4. 12.5 percent, with at least half of it as Tier 1 capitalWhy not: 12.5 is the reciprocal of 8 percent used to convert capital charges into RWA, not a capital ratio.

Basel I (the Cooke ratio) requires total capital (Tier 1 plus Tier 2) of at least 8 percent of RWA, with Tier 1 of at least 4 percent. The factor 12.5 = 1/0.08 is used only to convert other capital charges into RWA.

A harder one

A bank has: cash USD 10 million, OECD government bonds USD 30 million, loans to OECD banks USD 60 million, residential mortgages USD 100 million and corporate loans USD 200 million. Under Basel I, its minimum total capital is closest to:

  1. USD 32.00 millionWhy not: Applies 8 percent to total assets of USD 400 million instead of to risk-weighted assets.
  2. USD 10.48 millionWhy not: Uses the 4 percent Tier 1 minimum instead of the 8 percent total capital minimum.
  3. USD 20.96 million - correct
  4. USD 24.96 millionWhy not: Gives the mortgages a 100 percent weight; Basel I assigns 50 percent to residential mortgages.

RWA = 10x0 + 30x0 + 60x0.20 + 100x0.50 + 200x1.00 = 262. Capital = 8% x 262 = 20.96.

The hardest tier

A bank has a four-year interest rate swap with an OECD bank counterparty. The swap has a positive replacement cost of USD 3.0 million and a notional of USD 100 million. The Basel I add-on factor for an interest rate contract with remaining maturity of one to five years is 0.5 percent. Minimum capital against this swap is closest to:

  1. USD 48 thousandWhy not: Omits the add-on for potential future exposure and uses only current replacement cost.
  2. USD 56 thousand - correct
  3. USD 72 thousandWhy not: Uses a 1.5 percent add-on, the factor for contracts over five years, instead of 0.5 percent.
  4. USD 280 thousandWhy not: Applies a 100 percent weight; the counterparty is an OECD bank, so the weight is 20 percent.

Credit equivalent = 3.0 + 0.5% x 100 = 3.5. RWA = 3.5 x 20% = 0.7. Capital = 8% x 0.7 = 56 thousand.

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