How to Isolate F(f/d) - S(f/d) in FX

CFA Level II
#1

I find the intuition relatively simple for the Forward currency equation

(1+DomesticIntRate**)** = SPOT foreignperdomestic (1 + ForeignIntRate) ( 1/ F ORWORD foriegnperdomestic)

Under Libor the Interest rates are multiplied by Actual/360 … Okay got it.

I can manipulate the equation so that

FORWARD foriegndomestic = SPOT foreigndomestic * ( 1 + ForeignIntRate) / (1+ DomesticIntRate)

How do you manipulate the equation to be the forward - Spot differential … ??

i.e. to this ------>

Forward foreignDomestic - SPOT fforeignDmomestic = SPOT foreignDomestic * (i foreign- i domest )* (1/1+i domest )

I understand that this is an algebra question… I could just memorize each equation but I prefer to remember one!

so if anyone can show me the steps I would greatly appreciate it!

~Josh

#2

Start with

FORWARD foriegndomestic = SPOT foreigndomestic * ( 1 + ForeignIntRate) / (1+ DomesticIntRate)

Subtract SPOTforeigndomestic from both sides

FORWARD foriegndomestic - SPOT foreigndomestic = SPOT foreigndomestic * ( 1 + ForeignIntRate) / (1+ DomesticIntRate) - SPOT foreigndomestic

= SPOT foreigndomestic * [( 1 + ForeignIntRate) / (1+ DomesticIntRate) - 1]

= SPOT foreigndomestic * [( 1 + ForeignIntRate) / (1+ DomesticIntRate) - (1+ DomesticIntRate) / (1+ DomesticIntRate)]

= SPOT foreigndomestic * [( 1 + ForeignIntRate - 1 - DomesticIntRate) / (1+ DomesticIntRate)]

= SPOT foreigndomestic * [( ForeignIntRate - DomesticIntRate) / (1+ DomesticIntRate)]

#3

Thanks! That helped a lot!