spreads

Say you have a beginning nominal exchange rate of $2.00 / pound. Also, say the US price level is 2 and a UK price level is 1 and UK inflation is projected to be 1% and US inflation is projected to be 5%.

The expected nominal exchange rate can be found with the formula... E(S)=S * (Inflation counter / Inflation base)^T

So the expected nominal rate would be... 2.00 * (1.05/1.01) = $2.08 / pound. Notice that since the US had higher expected inflation, the $ depreciated relative to the pound.

Whereas, say instead that the nominal rate actually turned out to be $2.10 / pound, the real rate is given by... real S = S end * (price level begin * inflation foreign / price level begin * inflation domestic).

So the expected real rate would be... 2.1 * ([1*1.01]/[2*1.05]) = $1.01 / pound. Notice in this case had we calculated the original real rate it would have been 2.00 * (1/2) = $1.00 / pound. Which means there was real movement of 1%, which is due to the actual nominal rate of $2.10 being higher than the expected nominal rate of $2.08.