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Cash flow at risk, expected liquidity, funding cost risk, liquidity generation capacity and liquidity risk itself each need to be understood and then used in practical analysis.

FRM® Part II · Liquidity and Treasury Risk Measurement and Management · Monitoring Liquidity · FRM2.LTR.7.c

The idea

Five ideas describe a bank's liquidity analytically. Expected liquidity is the expected cumulative net cash flow over a horizon. Cash flow at risk is the shortfall of net cash flow below its expected value that is not exceeded at a stated confidence level. For normal flows, z is the standard normal value for that confidence level and σ is the standard deviation of net cash flow. In that normal case, the cash flow at risk over the stated horizon is approximately CFaR = z × σ. Liquidity generation capacity is the cash the bank can raise by selling or pledging assets, after haircuts and excluding assets already encumbered. Funding cost risk is the risk that refinancing costs rise, for example a spread widening applied to the amount that rolls over, for the time remaining after the roll. Liquidity risk is the possibility that outflows beyond expectation exceed capacity, so that cash is lacking. Compare the stressed cash flow with capacity, not just expected flow with capacity.

Formulas

Cash flow at risk of normal net cash flows

CFaR = z × σ

z
the one-sided standard normal quantile, 2.326 at 99%
σ
the standard deviation of net cash flow over the horizon

Measured from the expected value. The worst-case outflow is the expected outflow plus CFaR, and that is what to compare with liquidity generation capacity.

Increase in funding cost after a spread widening

Extra cost = A × Δs × τ

A
the amount of funding that rolls over
Δs
the widening in the bank's funding spread
τ
the fraction of the year remaining after the roll

Only funding that actually reprices bears the wider spread, and only after the roll.

A practice question

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

Which description best fits cash flow at risk in liquidity analysis?

  1. The expected net cash flow over the horizonWhy not: Describes expected liquidity, not the shortfall around it.
  2. The extra interest cost of replacing funds that cannot be rolledWhy not: Describes funding cost risk, not a cash flow shortfall.
  3. The volume of cash that can be raised by selling or pledging assetsWhy not: Describes liquidity generation capacity, not a cash flow loss measure.
  4. The largest shortfall of net cash flow below its expected value over a horizon at a stated confidence level - correct

Cash flow at risk is a percentile of the cash flow distribution measured against its expected value, like VaR for cash flows.

A harder one

A bank expects a net cash flow of -120 (USD million) over the next 30 days. The standard deviation of net cash flow is 80 and the distribution is approximately normal. Cash flow at risk is defined as the shortfall below the expected net cash flow at 99% one-sided confidence (z = 2.326). It is closest to:

  1. USD 132 millionWhy not: Uses the 95% multiplier 1.645 instead of 2.326 for 99% confidence.
  2. USD 306 millionWhy not: Adds the expected outflow of 120 to the shortfall, reporting the worst-case level rather than the deviation from expected.
  3. USD 186 million - correct
  4. USD 206 millionWhy not: Uses the two-sided 99% multiplier 2.576 instead of the one-sided 2.326.

CFaR = 2.326 x 80 = 186. The worst-case net cash flow would be -120 - 186 = -306, but CFaR as defined is the deviation from expected.

The hardest tier

A bank's expected cumulative net cash outflow over the next month is USD 150 million. Its 99% cash flow at risk, measured relative to the expected value, is USD 120 million, and its liquidity generation capacity is USD 200 million. Which statement is correct?

  1. No shortfall: capacity of 200 exceeds the expected outflow of 150Why not: Compares capacity with expected flow only and ignores the tail of the distribution.
  2. Shortfall of USD 120 millionWhy not: Takes cash flow at risk alone as the shortfall and ignores the expected outflow and capacity.
  3. Shortfall of USD 270 millionWhy not: Adds expected outflow and cash flow at risk but does not deduct the generation capacity.
  4. Shortfall of USD 70 million at the 99% level - correct

The worst case outflow at 99% is 150 + 120 = 270. Subtracting capacity of 200 leaves a shortfall of 70. Liquidity risk compares stressed outflow with capacity, not expected outflow with capacity.

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