Effective price

A hedger has two positions running at once. He converts currency in the spot market, and he squares off a derivative. Neither number on its own tells him how he did.

The effective price is the single rate that combines them. It is what the hedge actually delivered.

The workbook builds it as a sum: the effect of the change in the currency price on the underlying trade transaction, plus the effect of the change in the futures price on the futures contract.

One rule decides everything, and it is a rule about signs.

If you are receiving foreign currency — an exporter — a higher rupee rate helps you, so a gain on the hedge is added.

If you are paying foreign currency — an importer — a lower rupee rate helps you, so a gain on the hedge is subtracted from the rate you paid.

Get the sign right and the arithmetic is trivial. Get it wrong and every hedging question in the paper comes out wrong.

The workbook's own construction (Chapter 5, section 5.2.1). The effective price is the summation of the effect of change in USDINR price on the underlying trade transaction and the effect of change in future price on the currency futures contract.

Step by step for a receiver.

Step by step for a payer (section 5.2.2). The workbook is explicit about why this differs: since it is an import payment, a lower USDINR exchange rate would be beneficial for the importer, therefore a positive inflow from the futures contract is reduced from the remittance price.

What the number is for. It answers one question: was the hedger better or worse off than if he had not hedged? The workbook makes the comparison directly in section 5.2.1 — the futures contract locked in 81.70 whether the rupee depreciated to 83 or appreciated to 80, whereas not using currency futures would have resulted in an effective rate of 83 in the first case and 80 in the second.

Why the answer is the same on both sides. In the export case the workbook shows that a rupee depreciation gives +2.00 on the trade and -1.30 on the futures, while an appreciation gives -1.00 on the trade and +1.70 on the futures. Both net to +0.70. That symmetry is the definition of a hedge — and it is also why a candidate should be suspicious of an answer where the two scenarios differ.

Options change the arithmetic, not the idea. Chapter 5, section 5.3.7.1, works an unwound put position: premium received on unwinding minus premium paid is added to the rate the bank gave, because the exporter is a receiver.

For a receiver (exporter), working from the budgeted rate:

Effective price = Budgeted rate + (Spot change on the trade) + (Futures payoff)

Equivalently, working from the realised spot:

Effective price = Spot rate realised + Futures payoff

For a payer (importer):

Effective price = Remittance rate paid - Futures payoff

When only part of the exposure is covered:

Effective price = (Unhedged fraction x Spot rate) + (Hedged fraction x Hedged effective rate)

1. The exporter (the workbook's figures). A garment exporter budgets at spot 81, sells four-month futures at 81.75, converts at spot 83.00 and squares the futures at 83.05.

The workbook gives the shortcut too: 83.00 - 1.30 = 81.70.

Now flip the market. Spot at conversion is 80.00, futures squared at 80.05.

Same answer. On the full order of 10,000 shirts at USD 100 each — USD 1,000,000 — the hedge delivered Rs 8,17,00,000 either way, against Rs 8,30,00,000 unhedged in the first case and Rs 8,00,00,000 in the second.

2. The importer (the workbook's figures). A pulses importer buys 1,000 tonnes of chickpea at USD 1,600 a tonne — USD 1.6 million. Spot on the contract date is 81. He hedges half with two-month futures at 81.50. At payment, spot is 82.00 and futures 82.05.

Note that the importer wanted the lowest number. Full cover won because the rupee moved against him. Had the rupee strengthened instead, the ranking would have reversed — which is precisely what "the hedge removes the upside too" means in rupees.

3. Watch the sign. If a candidate had added the importer's 0.55 instead of subtracting it, the hedged half would read 82.55 and the effective price 82.275 — worse than doing nothing, which is a nonsense answer for a hedge that made money.

Chapter 5, section 5.2.1 (Combined position of futures and underlying export trade remittance), and section 5.2.2 (the import case, worked as a partial hedge), are where this is taught and computed. Section 5.3.7.1 applies the same logic to an unwound option position. This is the most reliably examined computation in the paper: the question hands you a budgeted rate, a contracted futures rate, a final spot rate and a squaring-off rate, and asks for the effective price. The Chapter 5 numbers — 81, 81.75, 83.00, 83.05 giving 81.70, and 81, 81.50, 82.00, 82.05 with half cover giving 81.725 — are worth knowing as worked answers.

• Added for a receiver, subtracted for a payer. An exporter adds the hedge gain to the realised rate; an importer subtracts it from the remittance rate. This one rule causes more wrong answers than anything else in Chapter 5.
• A lower effective price is good for an importer and bad for an exporter. The same number is a win or a loss depending on which side you are.
• Both scenarios must give the same effective price in a full hedge. If your two answers differ, a sign is wrong.
• A loss on the futures leg does not mean the hedge failed. In the workbook's export case the futures lost 1.30 and the hedge still worked, because the spot leg gained 2.00.
• Work from the budgeted rate or from the realised spot, not both. 81.00 + 0.70 and 83.00 - 1.30 are the same calculation; mixing them double-counts.
• For a partial hedge, weight the two rates, do not average them blindly — the weights are the hedged and unhedged fractions.
• Effective price is not the futures price. It is the rate the hedger ends up with after both legs, and it will rarely equal either the spot or the futures rate.