# Inflation rate expectations and exchange rates

Inflation affects the future purchasing power of any currency. If you have inflation in the Eurozone then €1 today will buy more than €1 in the future. In other words the currency becomes less valuable.

If two currencies experience different levels of inflation then their purchasing powers will deviate over time, because one currency loses its value faster than the other. If you apply the law of one price then logically this will have an effect on forward exchanges rates of the two currencies.

Before we see how to apply we need to consider that the rate of return on an investment can be measured in NOMINAL terms (e.g. the interest rate the bank advertises) and in REAL terms (the rate after inflation has done its nasty work on your investment).

Nominal rate = Real rate + the effect of inflation

(1 + nominal rate)^{n} = (1+ real rate)^{n} x (1+ inflation rate)^{n}

n= number of years

In the following example we are going to calculate the market expectations of inflation for two different currencies. The market’s **expectations of inflation **in the two currencies will be reflected in the forward exchange rates.

Assume that the Eurozone and USA have real interest rates of 4%. Nominal interest rates are 8.94% for the Euro and 6.5% for the dollar.

Expected inflation for the Euro

(1.0894)^{1/2}/(1.04)^{1/2} = (1 + Eurozone expected inflation)^{1/2}

1.04374/1.0198 = (1 + Eurozone expected inflation)^{1/2}

(1 + Eurozone expected inflation)^{1/2} = 1.0234852

(1 + Eurozone expected inflation) = ^{1/2}√1.0234852

^{1/2}√x = x^{2}

(1 + Eurozone expected inflation) = 1.0234852^{2}

= 1.0475

Expected Eurozone inflation = 4.75%

Expected inflation for the dollar

(1.065)^{1/2}/(1.04)^{1/2} = (1 + expected dollar inflation)^{1/2}

1.0320/1.0198 = (1 + expected dollar inflation)^{1/2}

(1 + expected dollar inflation) = 1.0119631^{2}

= 1.0240

Expected dollar inflation= 2.4%

The ratio of the difference in inflation should be reflected in the ratio between spot and forward exchange rates between the currencies.

Inflation difference ratio

(1.0475)^{1/2}/(1.0240)^{1/2} = 1.02348/1.0119

Ratio = 1.01144

To find the 180 day forward rate based on inflation expectations we must multiply the spot rate by the inflation difference ratio.

1.01144 x 0.6266 = 0.6337

(You may get a slightly different result, (0.63377), this is because in the original calculation I did not reduce the number of decimal places to four).

Note.

We have calculated the market’s expectations of inflation NOT how they arrive at their expectations. Many factors may influence expectations of inflation including government policy, the economic cycle, free trade agreements, war, natural disasters and new technology to name but a few.

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