Valuation of Currency Forwards

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Galli

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Really struggling to understand the formula for valuing a curreny forward at any point in time. I’m only having difficulties figuring out why the Spot rate at time t is discounted by the Rf of the foriegn currency by a factor of T-t.
For example:
90-day forward
Spot rate at t = 0 = $.60
Spot rate at t = 30 = $.61
Why do I take the PV of the S1 by the foreign Rf to arrive at the forwards valuation at t=1? I get we have to take the PV of the forward to arrive at its value at t=1 since its valuation is based on t=3. But aren’t we trying to dervive the value of the anticipated forward rate at T=1 versus the given spot at t=1? I think it would make sense if the questions asked what the value of the forward contract is right now if the spot rate in 30 days was .61…
S2000, read your blog that breaks the formula down… It helped but is still not fully clicking.
 
I think I made sense of this….From the example above
60 / 1 = spot rate t = 0
61 / 1 = spot rate t = 1
Where 1 = a unit of Foreign currency.
in reality, we should increase the 1 unit of foreign currency by the expected return over the holding period. So we aren’t necessarily discounting the domestic currency, we’re inflating the “unit” of foreign currency by the expected interest earned by holding that denomination of currency over the respective period… Is that a correct statement? I sure hope so, I am beyond ready to move passed this subject!!!
 
Galli wrote:
I think I made sense of this….From the example above
.60 / 1 = spot rate t = 0
.61 / 1 = spot rate t = 1
Where 1 = a unit of Foreign currency.
in reality, we should increase the 1 unit of foreign currency by the expected return over the holding period. So we aren’t necessarily discounting the domestic currency, we’re inflating the “unit” of foreign currency by the expected interest earned by holding that denomination of currency over the respective period… Is that a correct statement? I sure hope so, I am beyond ready to move passed this subject!!!
Click to expand...
 
If Spot rate is specified as DC/FC and so is the forward Rate F (DC/FC)
F = S * (1+rdc) / (1+rfc) – formula for Forward Price in terms of Spot Price
This can be rewritten as
S/(1+rfc) - F/(1+rdc) = 0
This is what the formula for the currency forward is also doing.
In Short, mnemonic SFFD = San Francisco Fire Department.
Spot discounted at Foreign Risk free - Forward discounted at the Domestic Risk Free Rate.
 
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