Q about the currency exchange rate

[kbh5220]

EX)
The spot ABE/DUB exchange rate is 4.5671, the 90-day riskless ABE rate is 5%, and the 90-day riskless DUB rate is 3%. What is the 90-day forward exchange rate that will prevent arbitrage profits?
In the books calculation, 4.5671{(1+(0.05/4))/(1+(0.03/4))}
I wonder why is the riskless rate divided by four.
Does “90-day riskless rate” mean that it’s already considerd to the quartile of a year?

 

[S666]

No the risk less rate is an annual rate, so 360 days in effect.
As you want only the 90 day forward, you divide the annual 360 day rate by (360/90) = 4
Or of course the analogous calculation is to multiply by 90/360 = 0.25.
The point is, you have to convert the 360 day riskless rate into a 90 day rate.

 

[S2000magician]

First, remember that interest rates are always – always! – quoted as annual rates.
If they apply to a period of time other than one year (as here), you have to adjust the rate to match the required time period.
Second, note that the rates here are nominal rates; that’s the reason that you multiply the rate by a fraction. If they were effective rates, you would get the appropriate time-period rate by compounding.
I wrote an article about this that may be of some help: http://financialexamhelp123.com/covered-interest-rate-parity-irp-pricing...

 

[kbh5220]

Thanks for all of whom replied to this question.^^.

 

[S2000magician]

My pleasure.