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Distinguish cash flows that are deterministic from those that are stochastic and give examples of both.

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

The idea

A cash flow is deterministic when both its amount and its timing are fixed by contract and do not depend on future events or on anyone's discretion. Examples are the coupons and redemption of a bond the bank holds or has issued, scheduled instalments on a fixed-rate loan, and the repayment of a term deposit on its stated maturity date. A cash flow is stochastic when amount, timing or both depend on random market variables or on the behaviour of customers. Examples are drawdowns on committed credit lines, withdrawals from non-maturity deposits, loan prepayments, and margin or collateral calls on derivatives. Deterministic flows can be placed directly on a maturity ladder. Stochastic flows need distributions, behavioural assumptions or scenarios, and a buffer sized for the uncertainty. The usual mistake is to treat a contractual schedule as certain when the counterparty holds an option that can change it.

A practice question

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

Which of the following is a deterministic cash flow for a bank?

  1. Cash drawn by a corporate client under an undrawn committed credit line agreed with the bankWhy not: Treats a client-controlled drawdown as certain; its timing and size depend on the client's decision, so it is stochastic.
  2. The contractual coupon the bank must pay on its own outstanding fixed-rate bond - correct
  3. Variation margin payable on the bank's interest rate swap portfolioWhy not: Ignores that margin flows depend on future market moves and are therefore stochastic.
  4. Withdrawals from instant-access savings accountsWhy not: Confuses behavioural outflows, which have no fixed amount or date, with contractual ones.

A coupon on the bank's own fixed-rate bond has contractually fixed amount and date, so it is deterministic. Drawdowns, margin calls and instant-access withdrawals depend on client behaviour or markets and are stochastic.

A harder one

A treasury desk lists the following expected flows for next month (USD million; drawdowns and prepayments are at the clients' discretion): coupons on fixed-rate bonds held +12; maturing term deposits issued by the bank -40; scheduled principal instalments on fixed-rate loans +25; drawdowns on undrawn committed credit lines -15; mortgage prepayments +8. What is the net deterministic cash flow?

  1. -3 - correct
  2. -10Why not: Adds all five items, so stochastic flows (drawdowns, prepayments) are included in the deterministic total.
  3. +37Why not: Counts only the deterministic inflows and leaves out the deterministic term deposit outflow of 40.
  4. -7Why not: Reports the net of the stochastic items (-15 + 8) instead of the deterministic ones.

Deterministic items: +12 - 40 + 25 = -3. Drawdowns and prepayments depend on client choice (-15 + 8 = -7) and are stochastic, so they are excluded.

The hardest tier

Consider four cash flows: (i) coupon on the bank's own fixed-rate bond, (ii) variation margin on the bank's swap portfolio, (iii) withdrawals from current accounts, (iv) repayment of a repo borrowing on its stated maturity date. Which are stochastic?

  1. (ii) and (iii) only - correct
  2. (i), (ii) and (iii)Why not: Classes a fixed contractual coupon as random merely because it is an outflow.
  3. (iii) and (iv)Why not: Misses the market-driven margin flow and calls the stated-date repo repayment random because it may be rolled.
  4. (ii), (iii) and (iv)Why not: Treats the contractual repo repayment amount and date as random, confusing refinancing risk with cash flow uncertainty.

The coupon and repo repayment have fixed amount and date (deterministic); whether the repo can be refinanced is a separate funding question. Margin follows market moves and current-account withdrawals follow customer behaviour, so those two are stochastic.

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