Trying to get my head around calculating real exchange rates (see CFAI Volume 6, page 489, under International Asset Pricing).

Let’s assume the spot exchange rate is (using THB and AUD) ฿30 to $1.

Using the equation on page 489, S_{real} = S (P_{FC}/ P_{DC}), where the rates are direct quotes from an Australian perspective and AUD is the domestic currency (so the THB:AUD = $0.0333), then the equation reads:

S_{real }= 0.0333 x (0.66667/5) = $0.00444 (or $1 buys ฿225 in real terms). I don’t believe this result is correct, and that I’m missing something, probably related to the way my rates are presented (direct or indirect).

My thinking has always been like this: If a consumption basket in Thailand costs ฿20, and the consumption basket in Australia costs $5, then the real exchange rate between the two countries is ฿4 per $1 (or $0.25 as a direct quote from an Australian perspective).

Which means in order to make the above equation equal ฿4 is to use indirect quotes (from an AUD perspective) instead of direct quotes, so that

S_{real }= 30 x (0.66667/5) = 4

What am I missing here? Should indirect quotes be used instead of direct quotes (from an AUD perspective)? (Alternatively, should the foreign currency direct quote be used?)

The text says “direct quote FC:DC”, which means “1 FC buys x DC”. This is a direct quote for a domestic currency (p489)