Outline how contingent liquidity risk is priced and work out what that risk costs.

FRM® Part II · Liquidity and Treasury Risk Measurement and Management · Liquidity Transfer Pricing: A Guide to Better Practice · FRM2.LTR.14.d

The idea

Contingent liquidity risk is the risk that off-balance-sheet items such as undrawn credit lines, guarantees and margin calls are used in stress, so the bank must fund unexpectedly. Because an undrawn commitment is not on the balance sheet it escapes ordinary transfer pricing, and unpriced commitments look free, so businesses write too many. Practice is to charge the issuing unit for the cost of covering them. The bank estimates the stressed drawdown, holds a liquid asset buffer against it, and costs that buffer at its negative carry. The negative carry is the funding cost less the yield on the liquid assets held in the buffer. An alternative is expected cost, which weights the line by the draw, written Cost. Cost = Prob × Draw × Line × Premium. Prob is the probability of stress, Draw the drawdown fraction, Line the commitment size and Premium the stressed liquidity premium. The usual mistake is applying the rate to the full line or to the drawn amount rather than the expected stressed draw. The exam point: size the buffer from stressed drawdown on the undrawn part and cost it at the carry.

Formulas

Expected cost of contingent liquidity on a committed line

Cost = Prob × Draw × Line × Premium

Prob: the probability of the stress event
Draw: the fraction of the line drawn in stress
Line: the size of the commitment
Premium: the stressed liquidity premium on drawn funds

All four terms are needed. Applying the premium to the full line, or forgetting the probability, overstates the cost.

Annual cost of a buffer held against a committed line

Buffer cost = Draw × Undrawn × (Funding − Yield)

Draw: the stressed drawdown, as a fraction of the undrawn amount
Undrawn: the undrawn part of the line
Funding: the cost of funding the buffer
Yield: the yield on the buffer's liquid assets

The base is the undrawn part, since the drawn part is priced as an asset. Cost the buffer at its negative carry, not at the full funding rate.

A practice question

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

What is contingent liquidity risk?

The risk that off-balance-sheet commitments, such as undrawn lines, are drawn in stress and force unexpected funding. - correct
The risk that on-balance-sheet term deposits mature as scheduled and must be refinanced at a higher cost than expected.Why not: Describes ordinary contractual rollover risk, which is known in advance rather than contingent.
The risk that the market value of the liquid assets held as a buffer falls below the cost of holding them.Why not: Describes market price risk on the asset buffer, not contingent demands for funding.
The risk that a borrower fails to repay a drawn loan in full when it falls due under the contract.Why not: Describes credit risk, not the risk of unexpected funding needs.

Contingent liquidity risk arises from items whose cash flows depend on events, such as drawdowns on committed lines, guarantees and margin calls, which may need funding when markets are stressed.

A harder one

A bank grants a USD 500 million undrawn committed line. Treasury expects a stressed drawdown of 20% and holds a buffer against it in liquid assets yielding 1.0%, funded at 3.0%. What is the annual cost of the buffer?

USD 10.0 millionWhy not: Applies the 2.0% negative carry to the full USD 500 million line instead of the USD 100 million buffer.
USD 2.0 million - correct
USD 3.0 millionWhy not: Applies the full 3.0% funding cost to the buffer and ignores the 1.0% yield earned on the liquid assets.
USD 1.0 millionWhy not: Applies only the 1.0% asset yield to the buffer instead of the negative carry between funding and yield.

Buffer = 20% x 500 = USD 100 million. Negative carry = 3.0% - 1.0% = 2.0%. Cost = 100 x 2.0% = USD 2.0 million per year.

The hardest tier

A bank grants a USD 1,000 million committed line. Treasury requires a buffer of 25% of the undrawn amount, held in liquid assets yielding 1.5% and funded at 3.5%. What annual commitment fee on the undrawn amount just covers the cost of the buffer?

2.00%Why not: Uses the 2.0% negative carry without scaling for the fact that only 25% of the line is held as buffer.
0.88%Why not: Applies the 3.5% funding cost to the 25% buffer and ignores the 1.5% yield earned on the liquid assets.
0.50% - correct
0.38%Why not: Applies only the 1.5% asset yield to the 25% buffer instead of the negative carry between funding and yield.

Buffer = 25% x 1,000 = USD 250 million. Carry = 3.5% - 1.5% = 2.0%, so cost = 250 x 2.0% = USD 5.0 million. Fee needed = 5.0 / 1,000 = 0.50% of the undrawn amount.

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