Using Futures & Options to Hedge Hedging is the creation of one risk to offset another risk. We will first look at the risk of being long in a currency; i.e., owning the currency, either outright or by means of the future receipt of a currency through such claims as an account receivable or a loan that we have made in a foreign currency.

Using Futures & Options to Hedge First we will look at being long in a currency through the outright purchase of 125,000 euros on the spot market. The foreign exchange risk that we will be exposed to is a result of the fact that the value of the euros will change on a daily basis.

Using Futures & Options to Hedge Let’s assume that we purchase 125,000 euros on the spot market at an exchange rate of USD 1.23 per euro. The following slide contains the basic data that we will continue to use throughout this presentation with respect to futures contracts, call options and put options.

Buy Euros on the Spot Market

We will purchase 125,000 euros on the spot market for USD 1.23 per euro or a total of 125,000 euros * USD 1.23 per euro = USD 153,750 Next, we will look at the profit/loss at different market values, or exchange rates, of the euro

Buy Euros on the Spot Market

If we plot the profit/loss that we realize versus the market rate of exchange at different levels, we will obtain the following graph:

Buy Euros on the Spot Market

Sell Euros with a Futures Contract Now let’s create a short position; that is, a position where we owe, or have a potential obligation, to deliver a currency. In this case, we will contract to sell euros at some point in the future at the set price of USD per euro and have to buy them at the market rate of exchange. For the time being, forget about the long position we just went through.

Sell Euros with a Futures Contract

Buying Spot and Selling with a Futures Contract Notice that when we bought euros in the spot market and were long, we made money if the euro appreciated. When we sold euros in the futures market, we lost money if the euro appreciated. Thus, a long position and a short position have opposite risks.

Buying Spot and Selling with a Futures Contract Now let’s combine the two positions: the long position of buying euros in the spot market, and the short position of selling euros in the futures market. In this view, we do not need to buy any euros in order to fulfill the futures contract since we already own them from our previous purchase in the spot market.

Buying Spot and Selling with a Futures Contract

Alternatively, we can view the two transactions as a single transaction, where we have locked in the sale price of the euros in the futures market at USD per euro, or a total of USD 153,625 and we purchased them in the spot market at USD 1.23 per euro, or a total of USD 153,750 and we have locked in a (loss) of USD 125.

Buying Spot and Selling with a Futures Contract

If we combine the two graphs of positions, we obtain the following graph with both positions depicted. As you can see, the profits (losses) from the long spot market purchase of euros position exactly offsets the losses (profits) from the short futures sale of euros position.

Buying Spot and Selling with a Futures Contract

Drawing the graph from our calculation of the combined positions yields the following graph. As you can see, the profit/loss is the same at all rates of exchange. The USD 125 net loss is a result of the futures rate (USD per euro) being slightly less than the current spot rate (USD 1.23 per euro).

Buying Spot and Selling with a Futures Contract

The reason that the futures rate is slightly less than the spot rate is due to the fact that U.S. interest rates are just slightly lower than european interest rates as indicated by the Interest Rate Parity equation. Interest Rate Parity must hold or else Covered Interest Arbitrage would occur (homework #2) and force the spot rate and futures rate to be consistent with Interest Rate Parity.

Buying a Call Option A Call option gives the owner of the call (the person who bought it) the right to purchase a set amount of foreign currency (125,000 euros in this case) at a set price (the “strike price” or “exercise” price) during a set period of time (the maturity date).

Buying a Call Option Let’s look at what would happen if we bought a call option with a Strike Price of USD 1.23 at a price of USD per euro. The price of a call option on 125,000 euros would thus be 125,000 euros * USD per euro = USD 2,287.50

Buying a Call Option Having bought the option, we would be long one option on euros. Whether we make money or lose money depends upon whether the exchange rate for euros increases or decreases by the maturity date. If we choose to exercise the option, we will purchase the euros at the exercise price and sell them at the spot (market) rate of exchange.

Buying a Call Option We will only choose to exercise the option if the market rate of exchange is higher than the strike price of the call option. Let’s look at the profit/loss that will result at different market rates of exchange from buying a call option with a strike price of USD 1.23 if we pay USD per euro for the option. Note that the price we pay for the option is a sunk cost that we have to pay up-front for the right to decide whether or not to exercise the option.

Buying a Call Option

Note that since the market price of the euro is less than the strike price, we would prefer to purchase any euros that we want on the open market, at USD 1.20 per euro, rather than at the exercise price of USD 1.23 per euro. Thus, we would let the option expire, but we would still be out the USD 2, that we paid for the option to begin with.

Buying a Call Option

Note that when the exchange rate at maturity is only USD 1.24 per euro, we will still exercise the option. Even though our net profit is a loss, we will be able to recover USD 1,250 from the exercise of the option to help offset our initial cost of USD 2, that we paid for the option.

Buying a Call Option

As you can see from the calculations and the graph, if you buy a call option, the most you can lose is what you paid for the option. On the upside, however, you gain as much as the currency appreciates with unlimited potential after covering the initial cost of the option.

Selling a Call Option The opposite of buying a call option is selling or “writing” a call option. The following example assumes that we sold a call option to someone else. Remember that whoever we sold the option to will only exercise it if it is in their best interest. It will then cost us money since, in order to sell the currency, we will first have to go buy it in the open market at the spot rate.

Selling a Call Option Selling a call option without owning the currency is known as a “naked” call option since you don’t own the currency to “cover” your position if the option is exercised. Selling a call option is another “short” position since you, possibly, will have to come up with the currency to satisfy an obligation.

Selling a Call Option

The profit/loss of selling a naked call option is exactly the opposite that of someone who buys a call option. The graph of profits and losses at different market rates of exchange are mirror images of each other as may be seen in the following graph.

Selling a Call Option

Note that the break-even for both the long and short positions is just under USD 1.25 per euro. In fact, the break-even market rate of exchange is USD which is the strike price plus the premium paid for the option = USD USD = USD

Selling a Call Option Also notice that the buyer of a call option has a limited downside potential for loss (what was paid for the option) and an unlimited upside potential for profit. The seller of a call option has the opposite: a limited upside potential for gain (the proceeds of selling the call option) and an unlimited downside potential of loss.

Buying a Put Option A put option is very much like a call option with the exception that it gives the owner the right to sell a fixed number of units of a foreign currency at a fixed price during a fixed period of time. The following example utilizes a put option with a strike price of USD 1.23 per euro and a cost of USD per euro.

Buying a Put Option First, we’ll look at buying a put option with a strike price of USD 1.23 per option. The cost will be = 125,000 euros * USD per euro = USD 2,537.50

Buying a Put Option Since the put option gives us the right to sell at a fixed price, it will only be exercised if the market rate of exchange is less than the strike price. Thus, we will make a profit by buying the currency in the open market at a price that is lower than the strike price, and selling it at the higher strike price of the put.

Buying a Put Option Thus, we will be selling the euros at a strike price of USD 1.23 per euro, or a total of = 125,000 euros * USD 1.23 per euro = USD 153,750 If the market rate of exchange is USD 1.20 per euro, our cost to purchase the euros is = 125,000 euros * USD 1.20 per euro = USD 150,000

Buying a Put Option

Selling (Shorting) a Put Option As you might surmise by now, selling a put option is just the opposite of buy a put option. The buyer of the put option will only exercise the option when it is in their favor, and, hence detrimental to the interests of the seller of the option. Following is the results for the seller of the preceding put option at different market exchange rates.

Selling a Put Option

As the following graph shows, the position of buying a put option and that of selling a put option are mirror images. The break- even point in this case is the strike price minus the premium paid for the option. = USD 1.23 per euro – USD per euro = USD per euro

Selling a Put Option

Combining Positions Now let’s combine some of the positions that we’ve considered. First, let’s look at the position of selling a call and buying a put. If the exchange rate goes up, the person we sold the call to will exercise. If the exchange rate goes down, we will exercise out put option. Regardless, we will be buying at the market rate and selling at the strike price.

Combining Positions Following is the results of each of the two positions from the preceding analyses. The gains/losses at different market rates of exchange from selling a call option and the gains/losses at different rates of exchange from buying a put option.

Selling a Call/Buying a Put

Notice that, regardless of the market rate of exchange, we will be buying the currency at the market rate and selling it at the strike price. This is the same as if we had agreed to selling euros with a futures contract.

Selling a Call/Buying a Put If you recall that scenario (see slide 20), we would realize a gain when the market rate per euro went down, but realize a loss when the market rate of exchange for the euro went up. Most of the difference between the results of the futures contract, and the selling of a call and the buying of a put, is due to the fact that I cheated.

Selling a Call/Buying a Put

The actual price of a put option was USD , not USD I changed the price in order to make the profits/losses from buying and selling a put option result in the amounts that they did for presentation purposes. The actual difference between the futures contract results and the selling a call/buying a put would have been $125.

Selling a Call/Buying a Put $125 dollars is about 1/10 of 1% and is due to the fact that the futures prices and the option prices are not at the same time or from the same markets. In theory, they should be the same since selling a call and buying a put is the equivalent of selling euros with a futures contract. The $1, difference is the same as 1 cent per euro.

Buying the Euro/Buying a Put Now let’s consider what would happen if we bought 125,000 euros today at the spot rate and bought a put option on the euros. By purchasing a put option, we have put a floor on the value of the euros. We have guaranteed that we can sell them for USD 1.23 per euro, the strike price of the put option.

Buying the Euro/Buying a Put One solution to what the payoff of this position will be at different market rates of exchange is to simply add the profits/losses of buying the euro to the profits/losses of buying a put, both of which were previously discussed:

Buying the Euro/Buying a Put

An alternative way of looking at this position is to simply consider what we would do if we bought the currency at the spot rate of exchange and simultaneously bought a put option. If the spot rate of exchange falls below the strike price, we will exercise the put. Otherwise, we will simply sell the euros at the market rate.

Buying the Euro/Buying a Put

If you compare the graph of owning the euro and buying a put option, you’ll notice that it is the same shape as buying a call option. We have essentially “created” a call option using the currency and a put option. In general, we can duplicate any position with the following relationship Currency – Call + Put = 0 (no risk)

Buying the Euro/Buying a Put Rearranging to solve for a call, we get Currency + Put = Call We could have created a “synthetic” put as follows: Currency – Call = Put

Buying the Euro/Buying a Put Why is being Long in the Currency, Short a Call option and Long a Put option risk-free? Simply because if the currency appreciates, the call that we sold will be exercised and we must sell at the strike price. If the currency depreciates, we will exercise out put option and sell at the strike price. Thus, no matter what happens, we will sell the currency at the strike price. This is exactly as if we had simply agree to sell the currency with a futures contract.