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Saturday, December 5, 2009

Difference between spot interest and forward rate

The easy way to understand the difference:

Let's say you take a trip to your local bank to get a loan for a house. When establishing such a loan you get the choice between
A) Having a floating interest, or
B) Having a fixed interest

The floating interest rate will now change each year, and each years interest can be understood as a forward rate, example:
Year 1: 5,3%
Year 2: 4,88%

The fixed interest is based on what the bank think will happen in the future. So let's say the bank offers you a fixed rate for two years at 5,09%.

Now, is there a relation between these numbers? Yes there is!

It's pretty easy, the relation is:
(1+spotrate)² = (1 + FW1) * (1 + FW2)
spotrate = 2 year fixed interest, or 2 year spot rate.
FW1 = Year 1s interest rate, or forward rate for year 1.
FW2 = Year 2s interest rate, or forward rate for year 2.

1,0509² = 1,053 * 1,0488
!!! I rounded off the secon years interest to 4,88%. It's supposed to be: 4,8804188%

To sum up:
A spot rate can be a rate for 1 or more years set at the CURRENT time.
A forward rate can be looked as the floating interest.

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