# Extraction of Inflation Expectation from bond yields

In my introductory monetary economics course we have learned that inflation expectations can be calculated by comparing yields on index-linked and conventional bonds of equal maturity and assuming a risk neutral investor. One simple example given is:

A risk-neutral investor is indifferent between 1-year conventional and index-linked gilts (issued at par value, i.e. p = F) if expected returns until maturity equal: $$(1+i) F = (1+r) (1+\pi) F$$ so knowing $$i$$ and $$r$$ (from financial data), we can calculate $$\pi$$, the inflation expectation.

Now this I am completely fine with, but then the lecture goes on to the following example:

Extracting inflation expectations from gilts (assuming risk neutrality) Use Tr 4.5pc ‘42: i = 1.71%, and IL 0.625pc ‘42: r = −1.66% [Tradeweb] $$(1 + 0.0171)^N = (1 − 0.0166)^N (1+\pi^e_N)^N$$ giving $$\pi_N^e \approx 3.43%$$ break-even inflation for a horizon of N = 23 Years

My question is: how can this calculation be valid when the coupon rates are different for the two gilts? What are the assumptions (eg issued at face value)?

My thinking is that to extract inflation expectations, we must equate the expected returns of the bonds until maturity, just as in the earlier simple example. The rate of return is however clearly tied to the coupon payments, which each need to be multiplied at the relevant accrued yield, leading to a much more complicated equation for the inflation expectation.