Hedging future USD cost using different IR and forwards

Question

I am facing a problem where I suppose an expense in 6 months from now of 2,500USD. My home currency shall be EUR, and I am trying to hedge given the following information.

Spot exchange rate: (USD/EUR) 1.3195
6m forward rate: 1.3000
Euro 6m IR: 2.8%
U.S. 6m IR: 1.5%

First, does the euro trade at a premium against the dollar? - I think it trades at a discount, as we have the arbitrage opportunity to borrow EUR, invest in Europe and swap back to USD in 6m from now. - but how exactly do I calculate and quantify the "premium"?

Next, "calculate the future cost of 2,500USD if you hedge now using the forward contract". My idea is: $\frac{2,500}{1.3}$ to get the EUR cost in 6m. But will I still have to divide by 2.8% to get the current cost?

Then, construct a synthetic forward hedge. Calculate the future EUR cost of hedging now with the synthetic forward, and give the theoretical forward rate. Unfortunately, I have no idea on this. The synthetic forward works close with the put-call-parity, but I see no way to construct put or call option from the above data.

Finally, calculate the expected euro cost in 6m if you do not hedge anything. - This means I have to calculate the expected future spot rate. Am I correct with using

$x=1.3195 \cdot \frac{1+0.015}{1+0.028}$

to keep the IRP up? (Can we assume IRP?)

Also, would we refer to the uncertainty in the value of future cash flows due to exchange rate fluctuations, as above, as exchange (rate) risk, or broadly transaction risk? Is there a generally accepted definition of transaction risk?

Best, Marie.

Answer 1

My 10 cents: Yes, the EUR is trading at a discount to USD. Think 100 - 2.8 = 97.2 for EUR, whereas 100 - 1.5 = 98.5 for USD so EUR is at a discount to USD.

The calculation of premium and discount is in the forward pips. In your case it's

spot - pips = forward  
1.3195 - 0.0195 = 1.3000

So yes, the EUR cost in 6 months is $2500 / 1.3 = €1923.07 you agree today to pay €1923.07 in exchange for the $2500 in 6 months time.

Then, there is no data given by the interest rates on the expected future spot rate. All you know is those are the interest rates. The spot rate is independent of the interest rates so you can't predict it. It's random.

I think this then clears up the definition of the risks facing you. You remove spot risk by taking on the forward deal. Instead you're exposed to interest rate risks (less volatile than spot). I think transaction risk is more about credit i.e. will the counterparty actually pay in 6 months time?

I have some training on FX/MM here. The interest arbitrage example may interest you :)