## What is a Zero Coupon Inflation Swap (ZCIS)?

A zero coupon inflation swap is a type of derivative 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 zero-coupon inflation swap is also known as a breakeven inflation swap.

### Key Takeaways

- In a zero-coupon inflation swap, which is a basic type of inflation derivative, an income stream that is tied to the rate of inflation is exchanged for an income stream with a fixed interest rate.
- With a zero-coupon inflation swap, both income streams are paid as a one lump-sum payment when the swap reaches maturity and the inflation level is known, instead of actually exchanging payments periodically.
- As inflation rises, the inflation buyer receives more from the inflation seller than what he paid, but if inflation falls, the inflation buyer receives less from the inflation seller than what he paid.

## Understanding a Zero Coupon Inflation Swap (ZCIS)

In a zero coupon inflation swap, which is a basic type of inflation derivative, an income stream tied to the rate of inflation is exchanged for an income stream with a fixed interest rate. A zero-coupon security does not make periodic interest payments during the life of the investment. Instead, a lump sum is paid on the maturity date to the holder of the security.

Likewise, with a zero coupon inflation swap, both income streams are paid as one lump-sum payment when the swap reaches maturity and the inflation level is known, instead of actually exchanging payments periodically. The payoff at maturity depends on the inflation rate realized over a given period of time, as measured by an inflation index. In effect, the zero coupon inflation swap is a bilateral contract used to provide a hedge against inflation.

Under a zero coupon inflation swap, 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.

The payments from both legs captures 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. As inflation rises, the buyer earns more; if inflation falls, the buyer earns less. 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.

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

Fixed Leg = A * [(1 + r)^{t} – 1]

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

Inflation Leg = A * [(I_{E }÷_{ }I_{S}) – 1]

**where:**

A = Reference notional of the swap

r = The fixed rate

t = The number of years

I_{E} = Inflation index at the end (maturity) date

I_{S} = Inflation index at the start date

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

For example, assuming two parties enter into a five-year zero coupon inflation swap with a notional amount of $100 million, 2.4% fixed rate, and the agreed upon inflation index, such as CPI, at 2.0% when the swap is agreed upon. At maturity, CPI is at 2.5%.

Fixed Leg = $100,000,000 * [(1.024)^{5} – 1)]

= $100,000,000 * [1.1258999 – 1]

= $12,589,990.68

Inflation Leg = $100,000,000 * [(0.025 ÷ 0.020) – 1]

= $100,000,000 * [1.25 – 1]

= $25,000,000.00

Since the compounded inflation rose above 2.4%, the inflation buyer profited, else the inflation seller would have profited.

The currency of the swap determines the price index that is used to calculate the rate of inflation. For example, a swap denominated in U.S. dollars would be based on the Consumer Price Index (CPI), a proxy for inflation that measures price changes in a basket of goods and services in the United States. A swap denominated in British pounds would typically be based on Great Britain's Retail Price Index (RPI).

Like every debt contract, a zero coupon inflation swap is subject to the risk of default from either party either because of temporary liquidity problems or more significant structural issues, such as insolvency. To mitigate this risk, both parties may agree to put up collateral for the amount due.

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), municipal and corporate inflation-linked securities, inflation-linked certificates of deposit, and inflation-linked savings bonds.