Question

 YOU are the financial officer at an Austrian company that wants to BUY USD 1.000.000 of solar equipment from a U.S. producer. You need to pay for the equipment in 90 days.

You have the following information available:

Spot rate $1.125 / €  90-Day forward rate $1.09 (actual spot rate expected based on historical distribution: $1.05 - $1.12)

Interest rates: US $ 4% EUR 2%

FX options available:

Contract size $125.000

CALLS : June (3 months ahead), strike price $1.10/€, Premium € 2000 per contract

PUTS : June (3 months ahead), strike price $1.00/€

Premium €1000 per contract

Futures contracts available:

Contract size $250.000

June contract, FX rate $1.11

Margin to maintain 10%

Describe your foreign exchange exposure

Describe how you would use the following instruments to hedge, i.e. how would each instrument work? (more important to describe than to calculate): Forward Contract , Options Contract

Would you recommend that the company hedge this transaction? Which instrument (any of the instruments, not just the two above) would you recommend?

Answer 1

The values given are

1 € = $1.125 (Spot)

Interest rates: US = 4% (per year and for 90 days it will be 4/4 = 1%)

EUR = 2% (per year and for 90 days it will be 2/4 = 0.5%)

Now if the company paid the USD 1.000.000 today, the amount paid by the company in Euro will be

1000000/1.125 = 888889 €

Now for no arbitrage opportunity to exist the forward rate will be

Spot * (1+Interest Rate(USD)/1+Interest Rate(Euro)) = 1.125*((1+0.01)/(1+0.005)) = 1.1305

Now if the spot rate after 90 days is 1.09 then the company will end paying

1000000/1.09 = 917431 €

Hence company should short the forward to lock the amount paid. Hence if the rate decreases company will benefit from short position and will account for the loss in the payment of equipment and if the rate increases the company will have a loss in forward but will pay less amount for the equipment

Now if the company goes short on the forward the forward will not give any gains till 1.09, hence company has to bear the cost for the fall of spot from 1.125 to 1.09 which will be

1000000/1.09 - 1000000/1.125 = 91743 - 888889 = 28542 €

Above 1.125 the company will gain on the amount paid for the equipment which will compensate for the loss on forward and below 1.09 the company will pay more on the amount paid for the equipment but the forward will gain

For Options

Now since company gains on the rate increase and lose on the rate decrease the company should buy puts to protect the loss

Since the strike given for Put is 1.00 the loss of the rate decrease from 1.125 to 1.00 will; be

(1.125-1.00)*1000000 = 125000 €

Now since the contract size is 125000, the total number of contracts require will be 1000000/125000 = 8

Hence the total premium will be 8 * 1000 € = 8000 €

Hence premium paid will be only 8000 € but the fact the put protection will come only below $1.00/€ the risk involved is quite high

Above 1.125 there will be no further loss on option as such and in fact the amount paid on equipment ill decrease but the upside looks limited as per the historical distribution: $1.05 - $1.12

Futures contracts:

Now the futures are quoted at $1.11 and again the company need to Short the futures to lock the price but the futures will gain only below 1.11 and hence the loss borne by company in that case will be

1000000/1.11 - 1000000/1.125 = 900900 - 888889 = 12012 €

And above 1.125 the futures will lose but the amount paid on equipment will be less

Number of contracts require will be 1000000/250000 = 4

The Margin paid will be = 250000 * 4 * 1.11 * 10% = 111000 €

Conclusion:

As per the above explanation the Euro should appreciate as per the arbitrage theory and should move up to  1.1305 hence in that case there is no need to hedge the transaction as company will end paying less for the equipment after 90 days but if company wants to hedge to avoid any sudden changes in the rates then the best would have been the Put options of 1.125 strike itself if they are available as that would have provided the instant protection below the current spot. However still premium of that strike would have clearly stated which one is best suited hedge.

But since that data is not given the company would be better off with the Future as the expected loss is less as compare to other options available and futures are better regulated as compare to forwards.

And as far as margin is concerned that is just an initial deposit for safety purpose.