Real exchange rate and quote structure

Suppose the exchange rate is quoted as FC:DC (same as DC/FC).

Then the equation for the real exchange rate

Real S(DC/FC) = S(DC/FC) * ( P(FC) / P(DC) )

That is to say, in other circumstances you follow the DC/FC convention for putting the rates into the formula, but here it is inverted, the FC on top and the DC in the denominator.

Why is it inverted? I don’t get it.

Because they don’t use inflation rate or interest rate but Purchasing power index, therefore it goes that way. You gotta be careful in this formula

OK; it’s something you memorize by heart. I get it.

Why not think about it like the following?

NOM$/Y = REAL$/Y * (1+P$)/(1+PY)

You agree with that? The nominal rate is always real * inflation. Notice that $ on top and Yen on bottom throughout.

What’s the real rate?

REAL$/Y = NOM$/Y / (1+P$)/(1+PY)

… = NOM$/Y * (1+Py)/(1+P$)