Can someone explain to me why we are dividing the domestic currency by the foreigh interest rate to value a forward contract? We are essentially “taking away the dividend” as the CFA books say but they don’t explain why we use the foreign interest rate rather than the domestic interest rate if the currency is domestic.
So normal assets have: FP = S0 (1+r)
That’s the same as the numerator of the currency forward equation (a normal forward transaction happens only in your currency so r = risk free rate of your domestic currency). The underlying is a dull, lifeless object but you are buying with money (which can be invested while you have it in your hands). The short side is forgoing interest by not selling today, so must be compensated for it in the FP.
The currency forward is similar except both the underlying asset, and the money you are buying it with, are investable. You need to compensate the short side for the interest lost in your currency (lost, because you are handing the money over later, not now), and also, you must discount the interest that you are losing in the foreign currency (losing, because you are getting the foreign currency later, not now)
I wrote an article on this that may be of some help: http://financialexamhelp123.com/valuing-a-currency-forward-whence-came-that-formula/
S200magician, I’ve read carefully your article and still cannot understand the logic behind the transition between first and second expression: (1) Value = Spot Rate - PV(Forward Rate) => (2) V(t) = PV(Spot Rate) - PV(Forward Rate) To my mind the second expression is not true - you can not go and discount any Spot rate - it is given in any point of time. you are not discounting value (as it is described in your article) - you are measuring it at time t. Technically (1) and (2) are the same expressions just with subscript that we mesure value at time t with Value = V(t). PV(spot rate) = spot rate. We value the contract TODAY (at the moment t), and we discount FT to that moment t (you are absolutely correct), but SPOT price is already there in present moment t. What in general does discounting of SPOT price mean? Maybe it should not be spot? it looks like it should be some kind of forward rate (at time t, with maturity of T).
Why do you discount me by 90%?
We’re not discounting the spot rate per se; we’re discounting the amount of foreign currency to which the spot rate is being applied.
Suppose that you enter into a 180-day forward contract to purchase JPY1 billion for AUD. Sixty days later, the exchange rate is AUD/JPY 0.0106, and the 120-day JPY risk-free rate is 1.5%. If you settle the forward today, it won’t be for JPY1 billion; it’ll be for JPY995,024,876 = JPY1 billion ÷ 1.005. We can think of it as discounting the spot rate by 1.005, or as applying the undiscounted spot rate to the discounted amount of yen. It’s the same result either way.
Say you want to exchange for 1 foreign currency with some amount of domestic currency, there are two ways (value at time t). One is to exchange at time t and invest the foreign amount in foreign risk free rate till time T, the other is to hold the domestic currency, invest in domestic risk free rate till T and exchange it at currency forward rate. The difference is the forward value.
FTFY.
The key is that you’re exchanging for a fixed amount of the foreign currency _ in the future _, which is worth _ less than that fixed amount today _; the amount today is that future amount discounted by the foreign currency’s risk-free rate.