# What is the difference between Cost of Currency Hedging and the Price of a Currency Pair Forward?

I am looking at Reuters Datastream and all they seem to provide is the settlement price of the CME EURGBP contract (which more or less equals current spot).

But what does it actually cost me to currency hedge? Is the "cost of hedging" and the price of a forward the same thing?

There seem to be varying formulas floating online.

For cost of hedging: $$\text{cost} = \frac{1 + \text{interest rate of base currency}}{1+ \text{interest rate of reference currency}} - 1$$

For price of a forward: $$P(t) = N_{b} \cdot D_{b}(t,T) \cdot S(t) - N_{r} \cdot D_{r}(t,T)$$ where $$D_{b}$$ and $$D_{r}$$ are discounts for base and reference currencies (kind of related to previous formula via rates), $$S(t)$$ is current spot rate. Not really sure where to get notional principals $$N_{b}$$ and $$N_{r}$$; tried looking on Bloomberg; is one of $$N$$s (pressumably $$N_{b}$$) not always equal to 1?

Would be excellent to get some concrete numbers as well to get a sense of scale.

The concept of covered interest rate parity (CIP) dictates that the forward price should equal the spot price multiplied by the ratio between domestic and foreign interest rates: $$\ F = S*(1+i_d)/(1+i_f) \\$$

In practice CIP means that the outcome of buying an FX forward should be equal to borrowing money in domestic currency (at the domestic interest rate), buying the foreign currency at spot and then lending the foreign currency (at the foreign interest rate). For various reasons this relation has not completely held up in the latest years, but it's mostly still close enough.

The formula you had for the cost of hedging is accurate given that CIP holds, as this would be equal the premium of the forward price over spot price, i.e. rearranging the CIP equation we first get: $$\ F/S = (1+i_d)/(1+i_f) \\$$. With the premium of forward over spot being $$\ F/S-1 \\$$, we get $$\ F/S -1 = (1+i_d)/(1+i_f) -1 \\$$.

However, the actual cost is of course given by the ratio between the market forward and spot price. At the time of writing the 12 month forward points for EURGBP equal to 114.52 (Bloomberg ticker EURGBP12M CURNCY) and the spot rate equals to 0.89968. This would make the 12 month forward price of EURGBP $$\ 0.89968 + 114.52/10000 = 0.911132 \\$$.

So the cost of hedging (GBP to EUR) would be $$\ F/S-1 = 0.911132/0.89968-1 = 0.0127 \\$$.

edit: the correct multiplier for forward points was 10000 not 100000.

• So just to confirm: $$\text{price of a single FX forward contract} = \text{cost of hedging} = \frac{F}{S}-1$$ (assuming a hypothetical lot size of 1; whereas in real world it seems more like 100,000 so would need to additionally multiply by that)? – A.L. Verminburger Oct 10 '19 at 13:21
• <-- (1). 2) Also, is $\text{forward price} = \text{settlement price}$? – A.L. Verminburger Oct 10 '19 at 13:40
• 3) Assuming (1),(2) are correct the price it gives is the "Fair Value". I.e. say I am a bank issuing an FX forward and my customer wants settlement at F-0.1. That means I would price the contract at $\text{fair value} + 0.1 = \frac{1+i_{b}}{1+i_{r}} - 1 + 0.1$? – A.L. Verminburger Oct 10 '19 at 13:43
• 1) Basically any FX trade is a forward contract, just the market price quoting convention is at t+2 (days) settlement. So if you wanted a settlement t+1 or t+0, that would basically be a "reverse" forward trade. So basically any forward is just the spot (t+2) price plus the forward points. In this decomposition the forward points is indeed the premium you are paying (or receiving) for doing the FX as forward (instead of spot). But instead of speaking of price, the convention is to speak of the forward points or the forward or outright rate (spot+forward points). – MGL Oct 11 '19 at 11:57
• 2) Yes, forward price = settlement price – MGL Oct 11 '19 at 11:58