P1.T3 Ch.9 notes (FX Markets): Nominal Interest Rate Formula

[dtammerz]

On p.7 of Ch.9's notes (Foreign Exchange Markets) under the Learning Objective "Describe the relationship between nominal and real interest rates", I'm not clear which formula we should be using if given a question. What is the relationship between these two equations, and are they used for different situations?

Nominal interest rate ≅ real interest rate + (expected) inflation rate
Nominal interest rate = [(1+real interest rate)*(1+expected inflation)] - 1

 

[David Harper CFA FRM]

Hi @dtammerz The one approximates the other. That's all. It's called the Fisher equation, see https://en.wikipedia.org/wiki/Fisher_equation For example, let's say the real interest rate is 2.0% per annum with annual compound frequency and the expected inflation rate is 3.0%, then the nominal interest rate is given by (1 + rr)*(1+ri) = (1+2%)*(1+3%) -1 = 5.06%.

If we multiply these terms, we get (1 + rr)*(1+ri) = 1 + rr + ri + rr*ri; in this case, (1+2%)*(1+3%) = 1 + 2% + 3% + (2%*3%) = 1 + 5.060%. The final term, rr*ri = 5%*6% = 0.060%, is called a cross-product. The idea (the convention) is that when both values (ie, real rate and inflation) are small, their (cross) product must be (very) small, as is the case here. Consequently, the exact (1 + rr + ri + rr*ri) is approximated by (1 + rr + r1) which will understates by the cross-product. In this example, its convenient to approximate the nominal interest rate by simply adding inflation to the real rate: the nominal rate ≈ 3% + 2% = 5.0%. This ignores (underestimates by) the 3%*2% = 0.060% cross-product. I hope that's helpful,

 

[dtammerz]

Hi @dtammerz The one approximates the other. That's all. It's called the Fisher equation, see https://en.wikipedia.org/wiki/Fisher_equation For example, let's say the real interest rate is 2.0% per annum with annual compound frequency and the expected inflation rate is 3.0%, then the nominal interest rate is given by (1 + rr)*(1+ri) = (1+2%)*(1+3%) -1 = 5.06%.

If we multiply these terms, we get (1 + rr)*(1+ri) = 1 + rr + ri + rr*ri; in this case, (1+2%)*(1+3%) = 1 + 2% + 3% + (2%*3%) = 1 + 5.060%. The final term, rr*ri = 5%*6% = 0.060%, is called a cross-product. The idea (the convention) is that when both values (ie, real rate and inflation) are small, their (cross) product must be (very) small, as is the case here. Consequently, the exact (1 + rr + ri + rr*ri) is approximated by (1 + rr + r1) which will understates by the cross-product. In this example, its convenient to approximate the nominal interest rate by simply adding inflation to the real rate: the nominal rate ≈ 3% + 2% = 5.0%. This ignores (underestimates by) the 3%*2% = 0.060% cross-product. I hope that's helpful,

Thank you! This is helpful.