Charta is on Google Play: practise on the go. Get the app
Charta

Describe how nominal interest rates relate to real interest rates.

FRM® Part I · Financial Markets and Products · Foreign Exchange Markets · FRM1.FM.9.j

The idea

The nominal interest rate is the stated rate. The real interest rate is the nominal rate adjusted for inflation, so it measures the growth in purchasing power. The Fisher relationship links the two through growth factors: Nominal growth factor = (1 + real rate) × (1 + expected inflation). The nominal growth factor is 1 plus the nominal rate. In approximate form, nominal rate = real rate + expected inflation. The exact form, rearranged for the real rate, is Real rate = (1 + nominal rate) ÷ (1 + inflation) − 1. At low inflation the approximation is close, but at high rates it overstates the real rate. With a nominal rate of 30% and expected inflation of 20%, the real rate is 1.30 ÷ 1.20 − 1 = 8.33%, not 10%. Lenders set nominal rates from the real return they require plus expected inflation, so differences in nominal rates between countries often reflect differences in expected inflation rather than real returns. Ex ante real rates use expected inflation, and ex post real rates use realised inflation.

Formulas

Real interest rate from the exact Fisher relationship

real rate = (1 + nominal rate) ÷ (1 + inflation) − 1

nominal rate
the stated interest rate
inflation
expected inflation for an ex ante rate, realised inflation for an ex post one

The approximation, nominal less inflation, overstates the real rate when rates are high: 30% nominal with 20% inflation is 8.33% real, not 10%.

A practice question

From the question bank, with the reason each wrong option is wrong.

According to the Fisher relationship in its approximate form, if the required real interest rate is 2.5% and expected inflation is 3.0%, the nominal interest rate is approximately:

  1. -0.5%Why not: Subtracts expected inflation from the real rate; the nominal rate is the real rate plus expected inflation.
  2. 5.5% - correct
  3. 7.5%Why not: Multiplies the two rates in percent (2.5 x 3.0) instead of adding.
  4. 3.0%Why not: Sets the nominal rate equal to expected inflation, omitting the real return the lender requires.

Nominal rate is approximately real rate plus expected inflation: 2.5% + 3.0% = 5.5%. The exact form is (1 + nominal) = (1 + real)(1 + inflation).

A harder one

A one-year nominal interest rate is 30% and expected inflation is 20%. Using the exact Fisher relationship, the expected real interest rate is closest to:

  1. 10.00%Why not: Uses the approximation (30% - 20%), which overstates the real rate at high inflation.
  2. 56.0%Why not: Multiplies the growth factors instead of dividing nominal by inflation.
  3. -7.69%Why not: Inverts the ratio, giving a negative real rate.
  4. 8.33% - correct

(1 + real) = (1 + nominal)/(1 + inflation) = 1.30/1.20 = 1.0833, so the real rate is 8.33%. The simple difference of 10% is only an approximation that overstates the real rate when inflation is high.

The hardest tier

A one-year nominal government bond yields 12% and a one-year inflation-linked bond has a real yield of 4.0%. Using the exact Fisher relationship, the market's implied expected (breakeven) inflation is closest to:

  1. 8.00%Why not: Subtracts the real yield from the nominal yield, which is the approximation and overstates the exact breakeven.
  2. 7.69% - correct
  3. 16.48%Why not: Multiplies the factors instead of dividing nominal by real.
  4. -7.14%Why not: Inverts the ratio, giving a negative inflation rate.

(1 + inflation) = (1 + nominal)/(1 + real) = 1.12/1.04 = 1.0769, so breakeven inflation is 7.69%. The simple 12% - 4% = 8% is only the approximation.

In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.

Start free →

More in Foreign Exchange Markets