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048

Case 048Currency derivatives and corporate FX hedgingCore

Nagzira Machine Tools must pay USD 2 million in six months. The six-month forward is 84.40; a six-month dollar call struck at 84.50 costs 0.90 rupee per dollar. Compare the forward and the option if the rate ends at 82.00, 84.50 or 87.00.

1The situation

Nagzira Machine Tools has ordered a CNC machining centre from a German supplier, invoiced in dollars: USD 2 million, payable in six months on delivery. The project budget assumed a rate of 85.00 rupees to the dollar. Its bank offers two hedges.

The first is a six-month forward to buy dollars at 84.40. The second is a six-month dollar call, the right but not the obligation to buy dollars at 84.50, for a premium of 0.90 rupee per dollar, Rs 18 lakh paid today. The CFO wants the rupee cost of each hedge, and of doing nothing, if the rate in six months is 82.00, 84.50 or 87.00. Ignore the interest cost of paying the premium six months early.

2Your task

Compute the rupee cost under each choice and outcome, find the rate at which the forward and the option cost the same, and recommend one for a company that has a budget rate of 85.00.

Quick check

Below what final rate does the option end up cheaper than the forward?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

The forward costs Rs 16.88 crore in every outcome; the option costs Rs 16.58 crore at 82.00 and Rs 17.08 crore at 84.50 or above. The option is cheaper only if the rate ends below 83.50; above that the forward wins by up to Rs 20 lakh. Doing nothing costs Rs 17.40 crore at 87.00. With a budget of 85.00, both hedges protect it, and the forward does so for less unless Nagzira expects a meaningful rupee rally.

Step 1What does each choice cost in each outcome?

Work all three choices on one line per outcome. The forward fixes the cost at USD 2 million times 84.40, Rs 16.88 crore, whatever happens; the call costs the lower of the market rate and 84.50, plus the 0.90 premium, so Rs 16.58 crore at 82.00 and Rs 17.08 crore at 84.50 and at 87.00; staying open costs Rs 16.40, Rs 16.90 and Rs 17.40 crore. The premium is paid in every case, which is the detail that decides most comparisons of this kind.

Rate in six monthsForward, Rs croreCall option, Rs croreOpen, Rs croreCheapest
82.0016.8816.5816.40Open
84.5016.8817.0816.90Forward
87.0016.8817.0817.40Forward
Rupee cost of USD 2 million: the forward never moves, the option is capped at 85.40 a dollar, and staying open is cheapest only when the rupee strengthens.
Step 2Where do the forward and the option cost the same?

Above the strike the option is exercised and costs 85.40 a dollar, always 1.00 worse than the forward. Below the strike it is abandoned, so Nagzira buys in the market and the premium is a sunk cost. The option catches up with the forward only when the market rate plus 0.90 falls to 84.40, which means a final rate of 83.50, about 1.1% below the forward. So the option is a bet that the rupee strengthens by more than its premium, with protection if it does not.

Rupee cost of USD 2 million, Rs crore: forward, call option, or open16.416.817.217.68182838485868788Rupees per dollar in six monthscross at 83.50forward: 16.88 alwayscall: capped at 17.08open82.00: call 16.58
The forward is flat at Rs 16.88 crore, the call costs one for one with the rate below 84.50 plus its premium and is capped at Rs 17.08 crore above, and the two cross at 83.50, so the option is cheaper only if the rupee strengthens below that rate.
Step 3Which would you recommend, and why?

Think of a fixed-price contract with a builder against a contract with a ceiling and a fee: the fee buys the chance to pay less if material prices fall, and you pay it whether or not they do. Nagzira's budget is 85.00, and both hedges keep it inside: the forward at 84.40, the option at worst 85.40, but the forward is cheaper in every outcome above 83.50, so unless the CFO has a real reason to expect the rupee to strengthen more than about a rupee, the forward is the better hedge. The option earns its premium in two situations: when the payment itself is uncertain, for instance if the order could be cancelled, because an unused option simply lapses while an unused forward must be closed out at whatever it is worth; and when the company is competing against a rival that is unhedged and would gain if the rupee rallied.

State the limits. The premium is paid today and the comparison ignores its interest cost, about 0.03 rupee a dollar at 7% for six months, which moves the crossover slightly lower. The forward needs a credit line with the bank and may need margin if it moves against Nagzira; the bought option, once paid for, needs neither. Rules on which exposures can be hedged and with what documentation apply to both; confirm the current framework with the bank. And the outcomes are three points on a continuous range: the honest summary is the crossover rate, not a table of three cases.

Where candidates lose it

The common loss is comparing the strike, 84.50, with the forward, 84.40, and calling them nearly the same. The option's worst case is strike plus premium, 85.40, a full 1.00 rupee above the forward on USD 2 million, Rs 20 lakh.

The second is calling the option the safer choice because it has no obligation. Both hedges cap the cost; the option costs Rs 18 lakh more for the right to benefit from a rally, and the candidate has to say why Nagzira wants that right before recommending it.

What the interviewer asks next

  • The supplier may deliver late by up to two months. Which hedge copes better, and why?
  • How would a zero-cost collar, buying the 85.50 call and selling the 83.00 put, change the picture?
  • What happens to the option premium if rupee volatility rises before Nagzira trades?
  • The rupee is at 83.00 after three months. Should Nagzira do anything with either hedge?
← Case 047Painganga Capital sold a one-month at-the-money straddle on Torna Logistics at 22% implied volatility, vega Rs 2 lakh per vol point, delta hedged daily. Realised volatility was 18%. Estimate the P&L, and describe a path that would have made the trade lose even so.Case 049 →At 10 am on expiry day, Baitarani Capital is short 200 lots (lot 50) of the Satpura 50 22,000 straddle, sold for 60 points, with the index at 22,000. What is the P&L at settlement if the index ends at 21,900, 22,000 or 22,150, and how does gamma behave through the day?

Company names and figures are illustrative.

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