A US investor has purchased Sterling Treasury bills and wishes to hedge against the falling value of Sterling. Buying the out-of-the-money put (strike price $1.8500) will protect against a fall below that figure. The sale of the out-of-the-money call at $1.8900 will mean that the investor will benefit from any rise in Sterling to $1.8900 but not above that figure. The cost of buying the put is off-set by the revenue from writing the call, resulting in this instance in a zero cost strategy.

The reader will note that if Sterling rises above $1.8900, the written call position will make a loss. This is off-set by the rising value in dollar terms of the underlying Sterling investment. Conversely, if Sterling falls below $1.8850, the puts make a profit which off-sets the currency losses on the investment in the Sterling Treasury bills.

This strategy, although a zero cost one, does have limited benefits and should not be considered as a free lunch. The investor is able to benefit from a small rise in Sterling, up to 1.8900, but at the cost of incomplete protection from a fall. This is because the put strike price of $1.8500 is below the current spot price of $1.8750.

It is possible to develop cylinder options with greater potential for gains, but a brief consideration of the principles involved in the above example will indicate that this potential can only be attained at the cost of greater premium or less downside protection.

As traded currency options use the US dollar as the base currency, a Sterling-based investor wishing to hedge, say US Treasury bills would buy a call on Sterling (a put on the dollar) and sell a put on Sterling (a call on the dollar) in order to create a similar hedge against a fall in the dollar. Thus, if the dollar fell against Sterling, the investor would exercise the call using the investment proceeds to acquire Sterling at the exercise price which would be below the then spot price. If, on the other hand, the dollar rose against Sterling (i.e. Sterling fell), the investment manager will have the put on Sterling exercised against him, but the loss would be off-set by the higher Sterling proceeds of the dollar Treasury bills.

Forward participation agreements

A strategy that has been developed in the OTC market is the forward participation agreement. This gives the buyer of the agreement the benefits of an outright forward contract — i.e. a guaranteed floor level and no up-front fee — while avoiding the main drawback of the outright forward, which is the symmetrical pay-off.

We have already seen that the outright forward exchange agreement is costless to establish because the buyer pays for the protection against any unfavourable movement in exchange rates by foregoing any potential favourable movement. The forward participation agreement enables the buyer to participate in the favourable movement albeit at a reduced rate, while ensuring a guaranteed floor rate, although this will be below the current forward rate.

An hypothetical example of a forward participation purchase agreement to purchase dollars for Sterling will illustrate this. Assume that the Sterling/dollar spot rate is 1.7500 and the three-month forward rate is 1.7000, and the buyer agrees the floor exchange rate of, say, 1.6500. This is the rate that will apply at expiry. In effect, the investor has purchased an out-of-the-money put with an exercise price at this level.

As the investor has chosen the floor rate, the investment bank specifies the participation rate. Assume that the chosen participation rate is 75%. The investor will participate in 75% of any favourable movement in the exchange rate.

If Sterling falls below 1.6500, he will benefit from the guaranteed floor rate of 1.6500. If, on the other hand, Sterling rises to 1.8000, he will benefit from 75% of any movement in the rate above 1.6500 — i.e. 75% of 15 cents or 11.25 for an exchange rate of 1.7625.

The analytical problem in valuing these contracts is to determine the participation rate that compensates for the non-payment of an up-front premium and the asymmetry of the pay-off. Remembering that this strategy is a zero cost strategy, and the investor has bought a put option, then he must have to sell an option in order to earn the off-setting revenue. He effectively sells a call on a proportion of the rise in the exchange rate above the exercise price of the purchased put.

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