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Chapter 5: Currency

A

Ayushi Arora

Member
Hi,
There is an example given under Covered Interest Parity formula to calculate Spot rate. I am not sure if the forward rate and Spot rate in formula should be foreign per unit domestic currency or domestic per unit foreign currency.
Based on the example, I think it is foreign per unit of domestic currency.
Let me know if my understanding is right or there are other ways to approach such questions?

Thanks
 
Hi,

The spot rate and forward rate can be expressed in either terms (one is the reciprocal of the other) but to be consistent with the Core Reading formula the spot rate should be the cost of one unit of the foreign currency in terms of domestic currency.

Joe
 
Hi,

A question related to the same section, in this section the relationship between forward and spot currency rate is given as:

Forward Rate = Spot Rate * ((1+interest rate in domestic market i.e., UK in the example)/(1+interest rate in foreign market))

Whereas, in example 2 on Page Number 4 of Chapter 3: Derivatives (2), the one year forward rate is calculated as:

Spot rate * ((1+spot interest rate in foreign market)/(1+spot interest rate in domestic market))

Also, if I back solve for forward rate, using spot rate of 1.5704$ per Euro in the first formula gives a forward rate of 1.51485$ per Euro which I believe is not the right answer as the forward rate 1.5$ per euro (rounded up from 1.499$ per euro). But. if I use the second formula to calculate the forward rate, I get the forward rate as 1.49998$ per Euro.

Can you please confirm if I am missing something or these two are different things?

Regards,
Chirag
 
Hi Chirag,

You can use either formula provided that you are using the correct spot rate. £/$ spot rate will have pound interest rate on numerator and dollar interest rate on denominator. $/£ interest rate will be the opposite. If it helps, I like to think about forwards as a deferral of a purchase. Let's take example 2 from page 4 of chapter 3:

Ignoring the actual full value of the forward here and just focusing on exchange rates: Instead of buying $1 for £0.667 today, I am deferring the purchase for 2 months. This means I get to invest my £0.667 in the pound market and earn 7% pa interest, but I am giving up 4% interest in the $ market (that I would earn if I converted immediately). Hence I can multiply my £0.667 by 1.07/1.04. Hence the forward exchange rate £/$ = 0.685897 and by taking the reciprocal of that I get the $/£ exchange rate of 1.4579.

Alternatively, I could get to this directly. Instead of buying £1 for $1.50, I can invest my $1.50 in the $ market and earn 4% interest but I give up 7% interest in the UK market. Hence the forward exchange rate $/£ is 1.5 * 1.04/1.07 = 1.4579.

1.5$ per euro = $/euro spot rate * exp(dollar spot rate * 90/365) / exp(euro spot rate * 90/365). So if we take LHS and multiply by reciprocal of fraction on RHS we get $/euro spot rate = 1.5074 as shown.

Hope this helps.
Joe
 
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