Q4.17 in notes incorrect? (covered interest parity)

[person]

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.

 

[andy orodo]

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.

 

[person]

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.