GF584 Unit 5 Put or Participating Forward Comparison Example

A Put or a Participating Forward for Sales Not Yet Made: A Unit 5 Option Strategy Comparison

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Purdue University Global

GF584: Treasury Management II

Unit 5 Option Strategy Comparison

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[Date]

The dryer maker, its forecast, the market inputs and every premium are composite and illustrative; the articles and textbook cited are real.

Why Options for a Forecast

The fourth-quarter receipts are forecast, not ordered. Dealers book most fourth-quarter orders after the Australian winter crop is assessed, so the 15.5 million could be 10 million in a poor season. A forward sized to the full amount would leave the company owing Australian dollars it might not receive. An option gives protection without an obligation, which suits an amount that may not appear.

Inputs, Stated Once

1. Spot: 0.6620 dollars per Australian dollar.

2. One-year forward: 0.6649.

3. Volatility: 10.5 percent.

4. Dollar interest rate: 4.05 percent; Australian rate: 3.60 percent.

5. Tenor: one year, to the end of the fourth quarter.

Pricing With the Foreign Rate Included

Currency options are priced with the Garman-Kohlhagen model, which adjusts the Black-Scholes approach for the interest earned on the foreign currency (Garman & Kohlhagen, 1983). A one-year Australian dollar put struck at 0.6500 costs about 0.0199 dollars per Australian dollar, about $308,700 on 15.5 million. Financed for a year at the dollar rate, the premium is about $321,200 by settlement, which makes the put's net floor about 0.6293.

Solving for a Zero-Premium Strike

The participating forward combines a bought put on the full 15.5 million with a sold call on half of it, 7.75 million, both at the same strike. The strike is found by solving for the level at which the put's premium equals half a call's premium, so no money changes hands. That level is 0.6459. Below it, the company sells all 15.5 million at 0.6459. Above it, half is sold at 0.6459 through the exercised call and half at the market rate.

Seven Rates, Three Columns

Dollar proceeds at settlement, in millions, unhedged first, then the put net of financed premium, then the participating forward:

1. At 0.58: 8.990; 9.754; 10.011.

2. At 0.61: 9.455; 9.754; 10.011.

3. At 0.64: 9.920; 9.754; 10.011.

4. At 0.67: 10.385; 10.064; 10.198.

5. At 0.70: 10.850; 10.529; 10.431.

6. At 0.73: 11.315; 10.994; 10.663.

7. At 0.76: 11.780; 11.459; 10.896.

What Each Position Buys and Surrenders

The put buys a floor at about 0.6293 net and keeps every gain above the strike, minus the premium. It surrenders $321,200 of financed premium up front, which makes it the worst choice when the rate ends near today's level.

The participating forward buys a floor at 0.6459, higher than the put's net floor, at no premium. It surrenders half of any rise: above 0.6459, only 7.75 million benefits. At 0.76 it trails the put by about $563,000.

The participating forward looks free, but its price is an obligation: the sold call binds on 7.75 million Australian dollars whether or not the dealer orders arrive, so in a poor season the company could owe currency it never earned.

Where the Lines Cross

The two structures give equal proceeds at about 0.6873. Below that rate, the participating forward wins because its floor is higher and it carries no premium. Above it, the put wins because it keeps all of the rise on the full amount. With the one-year forward at 0.6649, the market's central case sits below the crossover, which favors the participating forward on rate grounds alone.

Volume Decides

The comparison so far assumes 15.5 million arrives. If fourth-quarter orders come in at 10.0 million and the rate rises to 0.73, the put is simply left unused on the missing 5.5 million. The participating forward is different: the bank exercises its call on 7.75 million, and the company must deliver that amount from receipts of 10.0 million, leaving only 2.25 million at the market rate. If orders fell below 7.75 million, the company would have to buy Australian dollars at 0.73 to deliver at 0.6459.

Research on optimal hedging finds that when quantities are uncertain, firms should favor instruments whose payoffs fall away as volumes fall, which is the case for options over forwards (Brown & Toft, 2002).

A Middle Choice Considered

A put struck lower, at 0.6300, would cost about two thirds as much, roughly 0.0126 per Australian dollar, but set a net floor near 0.6170, below the budget rate the sales plan uses. A put spread, buying the 0.6500 put and selling a 0.6000 put, would cut the premium further but leave the company exposed again below 0.60, the very fall the hedge is meant to cover. Both were rejected because they lower the cost by giving back protection in the scenario that matters most.

Checks

The put premium was recomputed from the inputs above. Each payoff row was checked by hand at two rates, and the crossover was solved directly from the two proceeds formulas.

Recommendation

Buy the put. The participating forward is cheaper on today's rate view, but it carries a volume obligation the company cannot be sure of meeting. The $308,700 premium is the price of protection that does not depend on dealers placing orders. If, by midyear, fourth-quarter orders are booked above 12 million, the company could add a forward on the booked amount and keep the put for the rest (Eiteman et al., 2016).

References

Brown, G. W., & Toft, K. B. (2002). How firms should hedge. The Review of Financial Studies, 15(4), 1283-1324. https://doi.org/10.1093/rfs/15.4.1283

Eiteman, D. K., Stonehill, A. I., & Moffett, M. H. (2016). Multinational business finance (14th ed.). Pearson.

Garman, M. B., & Kohlhagen, S. W. (1983). Foreign currency option values. Journal of International Money and Finance, 2(3), 231-237. https://doi.org/10.1016/S0261-5606(83)80001-1