can the two interest rate parity formulas be used interchangeably

[goodyhi11]

Hi,

I am wondering if someone can shed some light on the difference of methods on computing interest rate.

Based on the 2 formulas on interest rate parity, it appears like the end results are similar, so I am wondering if these can be used interchangeably?

F = Spot * e^(R-Rf)*T

F = Spot * ((1+Rdc) / (1+Rfc))^T

thanks!

 

[David Harper CFA FRM]

Hi @goodyhi11 they are not conceptually different. The difference is merely compound frequency, which is a feature of the rate. So, for example, say: Spot = 5.00; T = 2.0 years; R = 3.0% and Rf = 1.0%. As stated, we don't have enough information actually because we aren't told if the rates are (eg) with continuous or annual compound frequency. If they are "with continuous compound frequency" (aka, continuously compounded) then we can use: F = Spot * e^(R-Rf)*T = 5.00*exp[(3.0%-1.0%)*2] = $5.2041.

Now, if we translates these rates into their annual analogs, then continuous 3.0% is equal to exp(3%)-1 = 3.045453% with annual compound frequency; and continuous 1.0% is equal to exp(1%)-1 = 1.005017%. Then F = Spot * ((1+Rdc) / (1+Rfc))^T = 5.00 * ((1+3.045453%) / (1+1.005017))^2 = 5.2041; i.e., exact same answer. No conceptual difference, just compound frequency. I hope that helps,