Different techniques to hedge transactions exposure are illustrated through comprehensive examples here:
I. Payables outstanding in foreign currency: With the payables, the corporation is concerned about a rising value of the foreign currency which would lead to higher dollar costs. Hedging these payables is done to minimize dollar outflow costs in the future.
ABC corporation has an outstanding DM 200,000 90-day payables. The following information is available:
Spot rate of the DM : $ 0.675 per DM 90-day Forward Rate : $0.685 per DM 90-day Interest rates are as follows:
US Germany 90-day deposit rate 5.0 % 5.0 % 90-day borrowing rate 6.0 % 6.0 %
A call option on the DM that expires in 90-days has an exercise price of $0.680 and has a premium of $0.02. A put option on DM that expires in 90-days has an exercise price of $0.660 and has a premium of $0.03.
The DM spot rate in 90-days is forecasted to be: Possible Rate Probability
$0.660 per DM 30 %
$0.690 per DM 70 %
1. A Forward Hedge 2. A Money Market Hedge 3. An Option Hedge and 4. Remaining Unhedged
You have been hired as a consultant to decide on the best possible hedge. Which one of the alternatives you will recommend, and why ?
Solution:
1. Forward Hedge: Purchase DM 90 days forward at the forward rate of $0.685 per DM, thereby locking-in the rate; regardless of what happens to the spot rate in the future, ABC will be able to get the DM at $0.685 per DM.
Cost = DM 200,000 * $0.685 per DM = $137,000
Note that ABC enters into a contract to purchase a DM at time 0 and the actual purchase and delivery occur 90-days later when the DM is needed to pay the payables.
2. Money Market Hedge
A money market hedge works on the general principle of creating an opposite sign currency cash flow for the same duration as that of the payables. For hedging payables, the steps include borrowing in dollars, converting to DM at the spot rate, investing DM in a German money market instrument at the German deposit rate, and repaying the dollar loan with interest at the US borrowing rate in 90 days. When the German investment matures in 90-days, the proceeds are used to pay the payables.
Steps:
1. Find amount of DM to be invested = Payables Amount /(1+Foreign Interest Rate) DM200,000 / (1+0.05) = DM190,476.19
Since foreign investment generates interest income, one needs to only invest the net amount which will grow into an amount equal to the payables amount.
2. Calculate amount of $ to be borrowed = DM190,476.19 * 0.675 = $128,571.43 3. Borrow $128,571.43 @ 6%
4. Convert $128,571.43 to DM at exchange rate of $0.675 per DM $ 128, 571.43 * 0.675 = DM190,476.19
5. Invest in Germany @ 5% = DM190,476.19 * 1.05 = DM200,000 6. Repay loan in 90 days plus interest
$128,571.43 * 1.06 = $136,285.72
When the German investment proceeds of DM200,000 are received in 90-days, the proceeds will be used to pay off the payables.
3. Option Hedge
The option hedge involves buying call option to hedge payables. Recall that the call option gives the right to buy the given currency at the strike price. Also remember that an option is just that, an option; if the rates are not favorable, one can walk away from that.
Expected Spot/
Probability Premium Exercise (Y or N) Total Price* Cost
$0.66 $0.02 NO $0.68 $136,000
(30% )
$0.69 $0.02 YES $0.70 $140,000
(70%)
* Total Price = Purchace Price + Premium Expected cost of call option
= $136,000 (0.3) +$140,000 (0.7) = $138,800
4. Remain Unhedged
Expected Spot Total Price Probability
$0.66 $132,000 30%
$0.69 $138,000 70%
Expected Cost of Remaining Unhedged = $132,000(0.3) + 138,000(0.7)
= $136,200
5) Which one of the alternatives should one choose?
In choosing among the hedging alternatives for payables, one has to choose a lower cost alternative; one also has to consider the risk among different alternatives and go for more certain outcome since
corporations do not like uncertainty.
While the expected cost of doing nothing, or remaining unhedged has the lowest cost of $136,200, there is a 70% chance that its cost might be as high as $138,000. The money market hedge has the lowest cost of $136,285.72, and it is 100% certain. Therefore, a money market hedge is recommended here.
However, the forward hedge is close behind with a $137,000 cost.
2. Receivables
Another US corporation (XYZ Corporation) is expecting an inflow of DM300,000 Receivables in 90-days. It is considering:
1. A Forward hedge 2. Money Market Hedge 3. An Option Hedge and 4. Remaining Unhedged
1. Forward Hedge
The forward hedge to hedge receivables involves selling the currency forward at the forward rate thereby locking-in the rate.
Sell DM300,000 @ the 90 days forward rate DM300,000 * $0.685 = $205,500
2. Money Market Hedge
As before,the Money Market Hedge is built on the principle of building an opposite currency flow for the same amount to the flow that is being hedged: in this case, since the receivables being hedged is an inflow of DM300,000 to be received 90-days from now, we need to create a DM300,00 outflow in 90-days. We can accomplish this by borrowing in DMs, converting to US dollars, investing those dollars in the US; when the proceeds from the receivables are received, the corporation will use those proceeds to pay off the DM loan.
Amount to be borrowed in DM
= Receivables/(1+Foreign Interest Rate) = DM 300,000/(1+0.06)
= DM 283,018.27
US dollars Received after converting to the DM at the Spot Rate = DM 283,018.27 * 0.675
= $ 191,037.74
Invest the US dollars in the US at the US deposit rate Amount accumulated after 180 days
= $ 191,037.74 *(1+0.05) = $ 200,589.62
3. Option Hedge
This technique to hedge receivables involves buying put option. Recall put options give the right to sell a currency at the strike price.
Expected Spot/
Probability Premium Exercise (Y or N) Total Price Cost
$0.66 $0.03 Indifferent $0.63 $189,000
(30%)
$0.69 $0.03 YES $0.66 $198,000
(70%)
Expected inflow from the put option= $189,000 * (0.3) + $198,000 * (0.7) = $195,300
Expected Spot Total Price Probability
$0.66 $198,000 30%
$0.69 $207,000 70%
Expected inflow from remaining unhedged= $198,000 * (0.3) + $207,000 * (0.7) = $204,300
5) Given the three alternatives above, the choice here is to choose the one that has the highest certain cash inflow. Here, the forward hedge, with a 100% certain inflow of $205,500 is the clear winner. Although remaining unhedged has an expected value of $204,300, a number very close to that of the forward hedge amount of $205,000, the unhedged amount is only an expected amount based on forecasted exchange rate. Since it is an uncertain outcome, we will go along with the certain forward hedge amount.