## Break-even Inflation Rate

The break-even inflation rate (BEI) is a market-based measure of expected inflation. It is the difference between the yield of a nominal bond and an inflation-linked bond of the same maturity.

BEI is comprised of two elements: expected inflation ($latex \pi$) and risk premium for uncertainty in inflation ($latex \theta$).

The fundamental difference between the pricing formula as applied to, for example, a three-month T-bill and its application to, for example, a default-free zero-coupon bond relates to their investment horizons. The relative certainty about the real payoff from a three month T-Bill and thus the relative certainty about the amount of consumption that the investor will be able to undertake with the payoff means that the investment in the T-Bill will be a good hedge against possible bad consumption outcomes. In other words, the payoff, in real terms, from a three month T-Bill is highly unlikely to fall if the investor loses his or her job during the T-Bill’s three month investment horizon. The low, probably zero, correlation between the T-Bill’s payoff with bad consumption outcomes will mean that the risk premium needed to tempt an investor to invest in the T-Bill will be close to zero.

However, it is unlikely that the same level of certainty would apply, for example, to a 20-year default-free conventional government bond. For such a bond, it would seem reasonable to assume that the risk premium would be higher than that related to a one- or three-month T-Bill. Note that the cash flow in Equation 10 is still certain, but only in nominal terms. Because investors will naturally have less confidence in their ability to form views about future inflation over 20 years relative to their abilities to form those views over three months, the greater uncertainty about the real value of the bond’s payoff will cause investors to demand a premium in compensation for this uncertainty, represented by πt,s.

The difference between the yield on, for example, a zero-coupon default-free nominal bond and on a zero-coupon default-free real bond of the same maturity is known as the break-even inflation (BEI) rate. It should be clear from the discussion earlier that this break-even inflation rate will incorporate the inflation expectations of investors over the investment horizon of the two bonds, θt,s, plus a risk premium that will be required by investors to compensate them predominantly for uncertainty about future inflation, πt,s. Although the evolution of real zero-coupon default-free yields over time should be driven mainly by the inter-temporal rate of substitution, the evolution of their nominal equivalents will, in addition, be driven by changing expectations about inflation and changing perceptions about the uncertainty of the future inflation environment. We can see this evolution by plotting the constant maturity zero-coupon break-even inflation rates over time.