Real interest rate confusing definition

Question

I'm currently reading "Financial Markets and Institutions" by Cornett and Saunders.

On the section on interest rates, the real interest rate is defined as:

A real interest rate is the interest rate that would exist on a security if no inflation were expected over the holding period (e.g., a year) of a security".

What does this mean? Isnt the real interest rate simply the nominal rate minus inflation? Why is it defined as quoted above? What am I missing?

Thanks in advance for helping me understand this wording better.

Answer 1

What matters for pricing in terms of inflation are expectations of inflation, because inflation is not known at the time of pricing. So, you get the (expected) real rate of the security if you remove these inflation expectations, or, rephrasing your statement, if inflation was expected to be zero.

More generally, the there are at least two definitions of the real rate, depending on the context. In the above example, because inflation is unknown, the expected, or ex-ante, inflation rate is subtracted from the nominal rate. If inflation is known, then actual inflation is subtracted, which then gives the effective, or ex post, real rate.

To summarize:

Real rate (expected or actual) = Nominal rate (expected or actual) - Inflation(expected or actual).

Answer 2

The real interest rate $r$ is not observable. However, we can observe the nominal interest rate $i$ and the inflation rate $\pi$. This gives us the Fisher equation:

$$ r \approx i - \pi .$$

Thus, when $\pi = 0$ (that is, the when there is no inflation), $r \approx i$ (the real interest rate is the nominal interest rate advertised).