# Zero-Coupon Inflation Swap (ZCIS): Formula, Examples and Benefits

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## What Is a Zero-Coupon Inflation Swap (ZCIS)?

A zero-coupon inflation swap (ZCIS) is a type of [derivative](https://www.investopedia.com/terms/d/derivative.asp) in which a fixed-rate payment on a notional amount is exchanged for a payment at the rate of inflation. It is an exchange of cash flows that allows investors to either reduce or increase their exposure to the changes in the purchasing power of money.

A ZCIS is sometimes known as a breakeven inflation swap.

### Key Takeaways

*   A zero-coupon inflation swap (ZCIS) is a type of inflation derivative where an income stream tied to the inflation rate is exchanged for an income stream with a fixed interest rate.
*   A ZCIS pays both income streams as a single lump sum when the swap reaches maturity, and the inflation level is known instead of exchanging periodic payments.
*   As inflation rises, the inflation buyer receives more from the inflation seller than what they paid.
*   Conversely, if inflation falls, the inflation buyer receives less from the inflation seller than what they paid.

## Understanding a Zero-Coupon Inflation Swap (ZCIS)

An [inflation swap](https://www.investopedia.com/terms/i/inflation-swap.asp) is a contract that transfers inflation risk from one party to another through an exchange of fixed cash flows. A ZCIS is a basic type of inflation derivative, where an income stream tied to the inflation rate is exchanged for an income stream with a fixed interest rate. A [zero-coupon](https://www.investopedia.com/terms/z/zero-couponbond.asp) security does not make periodic interest payments during the life of the investment. Instead, a lump sum is paid on the [maturity date](https://www.investopedia.com/terms/m/maturitydate.asp) to the security holder.

Likewise, with a ZCIS, both income streams are paid as one lump-sum payment when the swap reaches maturity and the inflation level is known. The payoff at maturity depends on the [inflation rate](https://www.investopedia.com/terms/i/inflation.asp) realized over a given period, as measured by an inflation index. In effect, the ZCIS is a bilateral contract used to provide a [hedge](https://www.investopedia.com/terms/h/hedge.asp) against inflation.

> **Important**
>
> While payment is typically exchanged at the end of the swap term, a buyer may choose to sell the swap on the over-the-counter (OTC) market prior to maturity.

Under a ZCIS, the inflation receiver, or buyer, pays a predetermined fixed rate and, in return, receives an inflation-linked payment from the inflation payer or seller. The side of the contract that pays a fixed rate is referred to as the fixed leg, while the other end of the derivatives contract is the inflation leg. The fixed rate is called the breakeven swap rate, even though the two parties may not actually end up with even payouts.

The payments from both legs capture the difference between expected and actual inflation. If actual inflation exceeds expected inflation, the resulting positive return to the buyer is considered a [capital gain](https://www.investopedia.com/terms/c/capitalgain.asp). As inflation rises, the buyer earns more; if inflation falls, the buyer earns less.

## Computing the Price of a Zero-Coupon Inflation Swap (ZCIS)

The inflation buyer pays a fixed amount, known as the fixed leg. This is:

> $\begin{aligned}\text{Fixed Leg}=A\times[(1+r)^t-1]\end{aligned}$

The inflation seller pays an amount given by the change in the inflation index, known as the inflation leg. This is:

$\begin{aligned}&\text{Inflation Leg}=A\times[(\text{I}_{\text{E}}\div \text{I}_{\text{S}})-1]\\&\textbf{where:}\\&A=\text{Reference notional of the swap}\\&r=\text{The fixed rate}\\&t=\text{The number of years}\\&\text{I}_{\text{E}}=\text{Inflation index at the end (maturity) date}\\&\text{I}_{\text{S}}=\text{Inflation index at the start date}\end{aligned}$

## Example of a Zero-Coupon Inflation Swap (ZCIS)

Assume that two parties enter into a five-year ZCIS with a notional amount of $100 million, a 2.4% fixed rate, and the agreed-upon inflation index, such as the [Consumer Price Index (CPI)](https://www.investopedia.com/terms/c/consumerpriceindex.asp), at 2.0% when the swap is agreed upon. At maturity, the inflation index is at 2.5%.

_$\begin{aligned}\text{Fixed Leg}&=\$100,000,000\times[(1.024)^5-1)]\\&=\$100,000,000\times[1.1258999-1]\\&=\$12,589,990.68\\\text{Inflation Leg}&=\$100,000,000\times[(0.025\div0.020)-1]\\&=\$100,000,000\times[1.25-1]\\&=\$25,000,000.00 \end{aligned}$_

The fixed leg counterparty received a lump sum payment of 12.59M at expiration but had to pay out 25.0M, resulting in a net loss. Since the compounded inflation rate rose above 2.4%, the inflation buyer profited; the inflation seller would have profited if the inflation index dropped below 2.25% because, at that rate, they would have broken even.

## Special Considerations

The currency of the swap determines the price index used to calculate the inflation rate. For example, a swap denominated in U.S. dollars would be based on the CPI, a proxy for inflation that measures price changes in a basket of goods and services in the United States. Meanwhile, a swap denominated in British pounds would typically be based on Great Britain's [Retail Price Index (RPI)](https://www.investopedia.com/terms/r/rpi.asp).

Like every debt contract, a ZCIS is subject to the [risk of default](https://www.investopedia.com/terms/d/defaultrisk.asp) from either party, either because of temporary liquidity problems or more significant structural issues, such as insolvency. Both parties may agree to put up [collateral](https://www.investopedia.com/terms/c/collateral.asp) for the amount due to mitigate this risk.

Other financial instruments that can be used to hedge against inflation risk are real yield inflation swaps, price index inflation swaps, [Treasury Inflation-Protected Securities (TIPS)](https://www.investopedia.com/terms/t/tips.asp), municipal and corporate [inflation-linked securities](https://www.investopedia.com/terms/i/inflation-indexedsecurity.asp), inflation-linked certificates of deposit, and inflation-linked savings bonds.

## Benefits of Inflation Swaps

The advantage of an inflation swap is that it provides an analyst with a reasonably accurate estimation of what the market considers to be the "break even" inflation rate. Conceptually, it is very similar to how a market sets the price for any commodity, namely the agreement between a buyer and a seller (between demand and supply) to transact at a specified rate. In this case, the specified rate is the expected rate of inflation.

Simply put, the two parties to the swap agree based on their respective takes on what the inflation rate is likely to be for the period in question. As with [interest rate swaps](https://www.investopedia.com/terms/i/interestrateswap.asp), the parties exchange cash flows based on a notional principal amount (this amount is not actually exchanged), but instead of hedging against or speculating on [interest rate risk](https://www.investopedia.com/terms/i/interestraterisk.asp), their focus is solely on the inflation rate.

## What Is a Zero-Cost Inflation Swap?

This hedge against inflation is called a zero-coupon inflation swap because the instrument has no coupon (interest payment) until maturity. It is sold to another investor with payment due at maturity for the inflation rate at that time.

## What Is a Zero Coupon Swap?

A [zero-coupon swap](https://www.investopedia.com/terms/z/zero-coupon-swap.asp) is a contract where one party makes fixed interest payments to another, and the other makes floating payments based on the agreed-upon interest rate index.

## How Does an Inflation Swap Work?

An inflation swap is a contract where one party agrees to pay a fixed rate, and the other pays a floating rate based on an inflation index.

## The Bottom Line

A zero coupon inflation swap is where a debt instrument with an inflation-adjusting interest payment is sold to another investor for a fixed amount, delivered at maturity. Investors use it as a way to hedge against inflation.  

_Correction—Aug. 23, 2023:_ A previous version of this article did not specify the point at which two investors engaged in a zero-coupon inflation swap would break even. Content was added to reduce any confusion and address the inflation rate at which a breakeven would occur.