Mark to Market Forwards

So an important concept in econ is marking to market forwards on currency. Also in derivatives is valuing currency forwards.

So in the econ section,

Vt = (Ft-F0) / (1+r)

the value is the difference in the new forward and the original forward discounted back by the domestic rate. Makes sense…

In the derivatives section,

Vt = S0/(1+rf) - F0/(1+r)

the value is the difference in the spot rate discounted by the foreign rate and the forward rate discounted by the domestic rate. Also makes sense.

So a question from Schweser gives the following

current USD/EUR spot = 1.3110 - 14

30-day forward = +3.18/+3.38

30-day USD rate = 0.21%

30-day EUR rate = 0.90%

Original forward all-in rate = 1.3912 USD/EUR

The two methods listed above give slightly different answers and this question wants the reader to use the first. Is there a rhyme/reason to which one to use when valuing a forward? Shouldn’t both yield the same values? In questions in the past, they have but not this one. Is this question just poorly constructed? (i.e. is there an arbitrage? Is seems like the forward rate violates covered interest parity…)

The reason that they give slightly different answers is that the formula in Econ assumes that the interest rates given are nominal, while the formula in Derivatives assumes that the interest rates given are effective. I wrote an article reconciling these formulae:

If you get a question on this in Econ, use nominal rates; if you get a question in Derivatives, use effective rates.