**Inflation breakevens**

*Introduction*

The Fisher equation is a way of decomposing a nominal yield into three components:

- Real yields
- Inflation expectations
- Inflation risk premium

It is expressed as:

(1 + nominal rate) = (1 + real rate) (1+ inflation expectations) (1+ inflation risk premium)

It is common for practitioners to combine the last two elements into one component and refer to it as the ‘inflation breakeven’. This is often casually (and incorrectly) interpreted as expectations of future inflation.

It is also quite common for the market to use a shorthand version of the equation which is expressed as:

Nominal yield = real yield + inflation breakevens.

However, it is useful to distinguish between the ‘Fisher breakeven’ which is the value derived when using the “1+” format and the ‘breakeven spread’ when using the shorthand version.

*Example*

If nominal yields are 5% and real yields 3%, ignoring the inflation risk premium this returns values of:

*Fisher breakeven*: (1.05) = (1.03) (1 + inflation breakeven) => Inflation breakeven is 1.94%

*Breakeven spread*: 5% = 3% + inflation breakeven => 2.00%

*Trading application*

So why have two values? One popular strategy is to trade inflation-linked bonds against a nominal Treasury. One way to look at this strategy is that you are trading a yield spread: real yields on the linkers against nominal yields on the Treasury. It is analogous to trading credit spreads using corporate bonds and Treasuries. In this instance it is easier to think in terms of the breakeven spread.

*Investment application*

The Fisher breakeven can be to decide whether to invest in a Treasury or a linker. The following example may help. Suppose we have a 1 year nominal bond trading at par, so its coupon and yield are 5%. Coupons are paid annually. So at maturity the bond will pay a cash flow of 105.

Suppose there is a one year linker, also trading at par with a real coupon and real yield of 3%. This bond will pay out a cash flow equal to the real yield uplifted by the change in inflation since some base dates. In this example since the bond has a maturity of one year the payout will be based on the change in an inflation index over the previous 12 months.

If we say that the initial inflation index level is 100 and 101.94 at maturity, the linker will also pay a cash flow of 105. This consists of two components:

Coupon: 3 x 101.94 / 100 = 3.06

Principal: 100 x 101.94 / 100 = 101.94.

Notice that the final inflation index value of 101.94 implies a realised inflation value of 1.94%, which was equal to the initial Fisher breakeven.

As an aside this also shows that the inflation protection comes mostly from the uplifted principal amount at maturity.

Since an investor would pick the instrument that generates the highest at maturity payoff, the Fisher breakeven provides us with a way of assessing a linker against a nominal bond. If you think that realised inflation will be greater than the breakeven, then buy the linker. If you think that realised inflation will be less than the breakeven then buy the nominal bond.

I would like to acknowledge that Troy Bowler provided a useful insight into the post.