How do you compute the breakeven on a zero-coupon inflation swap?

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AcadiFi · Accepted Answer

A zero-coupon inflation swap has a single settlement at maturity. The inflation receiver pays (1 + K)^N - 1 × notional where K is the fixed breakeven rate; the inflation payer pays (CPI_T / CPI_0) - 1 × notional. K is the quoted ZC rate and equals the market's expected compounded inflation over N years, adjusted for inflation risk premium and seasonality.

Let's say Windmill Endowment buys a 7-year ZC inflation swap at K = 2.55% on $40M notional. CPI_0 = 312.45. If CPI_T = 372.10 at maturity, realized factor = 372.10/312.45 = 1.1909, so compounded realized inflation = 19.09%. Fixed leg = (1.0255)^7 - 1 = 19.31%. Net = (0.1909 - 0.1931) × $40M = -$88,000 to the inflation receiver. Very close to zero because market's expectation was nearly correct.

The ZC swap rate is the cleanest market measure of breakeven inflation. Compared to TIPS-derived breakevens, ZC swaps are free of liquidity premia differences between nominal and TIPS markets, but they reflect dealer credit and inflation risk premium (typically 15-40 bp).

Compared to YoY swaps, ZC is computationally cleaner — no convexity adjustment needed — but leaves all cash flow concentrated at maturity. Pension funds hedging deferred liabilities often prefer ZC because a lump sum at retirement date aligns naturally.

How do you compute the breakeven on a zero-coupon inflation swap?

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