Hi, The CIP formula is: F = S (1+rd)/(1+rf) But I believe this form relies on S and F representing a 'Domestic per foreign' exchange rate. If F and S are 'Foreign per domestic', does the formula need to be ... (1+rf)/(1+rd)? Q4.17 in the notes seems to use the former equation, but with a foreign per domestic exchange rate, which I don't think is right. Any help appreciated.
Usually FX rates are quoted foreign/domestic. If the foreign interest rate is greater than that of the domestic then the foreign currency is expected to appreciate in value in the future. Suppose the spot rate is $2/£1 and the US rate is 5% p.a. and the UK 4% p.a. then the 1 year forward would be: Forward = ($2/ £1) * (1.04/1.05) = $1.98/£1 i.e. the US dollar has now appreciated against the pound since the interest rates were higher. Hence the formula: F = S * (1+rd) / (1+rf) where the S and F is quoted foreign/domestic.
Thanks for the reply. Can I contrast your response with Q2 in the sept 2011 paper? In this, the exchange rate is 1.15 A per B (A/B). A has a lower interest rate, so would expect A to depreciate against B. But the formula used is: Forward rate = Spot rate × (1 + rA)2 / (1 + rB)2 = 1.15 × (1.02)2 / (1.03)2 = 1.1278 (taken from answers). So A has in fact appreciated against B, as the A/B exchange rate has fallen. An alternative explanation is to consider the following 2 scenarios: Have an amount Xa (X units of A)... 1. Convert to B's currency at spot rate S, and then invest at B's rate (assume 1 yr for now): Xa(1+Rb)/S 2. Invest at Ra, then convert in the future at the future rate F: Xa(1+Ra)/F The 2 approaches should equal for no arbitrage, rearrange these to get the same formula as the notes use. Applying this same argument to your USD/GBP argument above gives the opposite formula to the one you use.
