F=S*(1+rDC)^t/(1+rFC)^t … derivatives, t in year(s) or F=S*(1+rDC*t/360)/(1+rFC*t/360) … econ in notes, t in day(s). Which one to use?
Both will give you the same answer isn’t it?
Yea, the results are almost the same, although not exactly. It shall be OK to use either of them in the exam. For 1.5 year forward contract and some higher rates(soon?), (1+0.15)^1.5 = 1.233 (1+0.15*540/360) = 1.225
First, these two formula are different. I think, if we have Libor (add-on rates) in the question, we will use the formula below, F=S*(1+rDC*t/360)/(1+rFC*t/360) If any effective interest rate in the question, then this one will be the choice. F=S*(1+rDC)^t/(1+rFC)^t … derivatives, t in year(s) I also confused on this one. Let us discuss more!!!
I’m fairly certain that the calculations diverge for time periods greater than one year. For one year or less, the two methods come out the same. I don’t feel like working out the math though…
They will definitely diverge. If you put t in the exponent, you assume compounding, otherwise you don’t. (1+r)^t, t in years assumes yearly compounding. (1+r*t/360) deannualizes the interest rate and doesn’t compound. You should be fine with this formula for anything t < 360, assuming there’s no compounding during the year. Since most forward/spot rate questions have a “t” in the order of 90 or 180 days or so, you should be fine with the second formula.