Liability Matching: Compare Dates Before Comparing Duration

Describe the liability before choosing an asset measure

A liability schedule should state amount, currency, due date and whether each item is fixed or contingent. An estimated expense is not equivalent to an unconditional contractual payment. Inflation linkage, optional timing and uncertain quantities introduce different dependencies. Combining all of them into a single present value may be useful for some purposes, but it does not remove the need to understand the payments represented by that total.

CFA Institute's liability-driven framework begins with the timing and certainty of obligations. An educational adaptation is to keep confirmed amounts separate from scenario amounts, and to retain the underlying dates even when reporting annual totals. The relevant question is not whether assets and liabilities occupy the same calendar bucket, but whether the asset receipts are actually available before the corresponding payment must be made.

Distinguish payment matching from value matching

Cash-flow matching compares receipts and uses directly. Duration matching compares their sensitivity to a specified interest-rate movement. CFA Institute's portfolio overview treats these as distinct approaches to liability-based mandates. Equal present values alone do not establish either a date-by-date match or an adequate sensitivity match. A long-dated asset may have sufficient present value while delivering none of the cash required for an earlier obligation.

This distinction determines what evidence a calculation should retain. A cash-flow exercise needs a dated ledger. A sensitivity exercise needs asset and liability valuation bases, rate conventions and the chosen shock definition. Combining the labels without those records creates false reassurance: a statement that duration matches does not prove that a payment can be funded without selling, and a payment match does not imply stable interim accounting values.

Solve a small match backward from the last obligation

Assume fixed hypothetical obligations of USD 5,400 at the end of year one and USD 5,200 at the end of year two. Available teaching instruments are one-year and two-year noncallable bullet bonds, both paying 4% annually, with exact receipt-date alignment. Assume no default, fees, taxes or reinvestment. Work backward: the second-year payment requires two-year face amount 5,200 / 1.04 = USD 5,000.

That two-year bond also pays USD 200 in year one. The remaining first-year need is therefore 5,400 - 200 = USD 5,200, supplied by one-year face amount 5,200 / 1.04 = USD 5,000. Checking forward, year one receives USD 5,200 from the maturing bond plus USD 200 from the other, while year two receives USD 5,200. Both obligations match exactly under the assumptions.

Separate face amounts from the cost of the match

The example determines hypothetical face amounts from payment requirements. It does not establish how much those bonds cost to acquire, because no purchase yields or prices were supplied. Total face of USD 10,000 is not necessarily the required cash budget. An affordability calculation would need consistent purchase values and transaction assumptions, while an implementation review would need evidence that the chosen amounts and instruments are actually available.

The backward calculation also relies on exact maturity and coupon alignment. If a receipt arrives after an obligation, the apparent match fails even if both are in the same year. If a receipt arrives earlier, its retention must be specified, including whether any interest is assumed. A useful ledger records residual cash through time, not merely a zero grand total after all assets and liabilities have been added together.

Use duration matching as a conditional sensitivity statement

Duration-based matching can be useful when exact cash-flow replication is unavailable, but it addresses a narrower question about changes in value. For unequal asset and liability values, comparing only duration in years can be misleading. Currency sensitivity depends on both duration and value. The relevant comparison may therefore be dollar duration or basis-point value, with compatible discount curves and conventions on both sides of the balance sheet.

A first-order match still leaves curvature and nonparallel curve movements to examine. A portfolio whose short and long exposures offset in aggregate can respond differently from a liability concentrated at one intermediate date. Key rate sensitivities can make that difference visible. None of these measures removes the need to identify how an actual payment will be made, particularly if doing so requires selling an asset before its maturity.

List the risks that a nominal match cannot remove

A promised receipt fails to fund an obligation if the payer defaults or pays late. A nominal receipt can also fail to match an obligation that changes with inflation or another index. Currency differences introduce another mismatch. These are not minor rounding errors around an otherwise complete hedge; they are different ways that the asset and liability cash flows can diverge from the schedule used to establish the match.

A sale-dependent plan additionally needs liquidity and transaction-cost assumptions. A sensitivity-based plan needs review as time passes and exposures change. Document what event would invalidate the current comparison: an altered obligation, a changed payment date, a revised index rule or an instrument feature previously omitted. Monitoring should follow the assumptions that support the match, rather than treating a favorable initial calculation as a permanent certification of funding adequacy.

Report the match and its unresolved dependencies

A concise result can state which dated payments match, which depend on retained cash and which depend on a sale or an uncertain receipt. Keep the hypothetical payment ledger distinct from any personal funding recommendation. This guide does not select securities, set reserve levels or assess a real entity's obligations. Its arithmetic shows how to avoid counting a coupon twice or confusing sufficient total value with correctly timed cash.

The site's narrow tools value regular fixed-coupon bullet bonds at coupon dates with integer maturities and annual, semiannual or quarterly payments. They do not optimize portfolios, simulate defaults or calls, or resolve actual settlement calendars. An exact match in the educational table therefore remains conditional on its deliberately aligned dates and promised payments. Its strength is transparency about those conditions, not an assertion that broader liability risks have disappeared.

Primary references

1. CFA Institute: Liability-Driven and Index-Based Strategies
2. CFA Institute: Overview of Fixed-Income Portfolio Management