Computation of long-term real rates

Hi!

I’m working on a model at monthly frequency. In the model, I have the 1-month inflation rate (pi) and the 1-month interest rate (i).

The 1-month real rate is computed as:
r = i - pi(+1)

What’s the correct way to compute, say, the 1-year real rate?

Without more context it is hard to tell. Do you mean the annualized real rate?

Thanks for the reply.

I’m referring to the model counterpart of the real rate computed in the data as the government bond at 1-year maturity minus breakeven inflation at the same maturity. I’m wondering how to compute correctly these objects in the model when it is calibrated at a different frequency (monthly).

It seems to me that it should be different from e.g. r = i - pi(+12). I could for example define additional model objects with parameters calibrated annually, but perhaps there is a smarter solution.

The problem is the one-year interest rate. Does your model have a one-year bond? The relevant inflation rate would be

pi_ann=p(+12)-p;

No, I don’t have the 1-year bond so far. Perhaps it would make sense to take a weighted average of monthly rates?

i_ann = ( i + i(+1) + i(+2) + … )/12.

It depends on what you are trying to achieve. If you buy a one-year bond, it’s return will be known at time t and not depend on future expected short term rates (unless the expectation hypothesis holds).

Thanks!