Case 060Hedging with futuresCore

An Indian wire maker will buy 500 tonnes of copper in three months, priced in dollars. It hedges copper at USD 9,000 and dollars at 83.80. At delivery copper is 9,600 and USD/INR 85.10. Work the rupee cost hedged and unhedged, and split the difference.

The situation

Tamirabarani Wires buys copper cathode priced in dollars a tonne and sells wire in rupees. It has a firm order that needs 500 tonnes in three months. Today copper futures for that month trade at USD 9,000 a tonne and the three-month USD/INR forward is 83.80. The treasurer buys 500 tonnes of copper futures and buys USD 4.5 million forward at 83.80.

Three months later copper is USD 9,600 a tonne and spot USD/INR is 85.10. The company takes delivery at the market price and closes both hedges.

Your task

Compute the rupee cost of the copper with and without the two hedges, split the saving into a copper part and a currency part, and show what happens if only one of the two risks is hedged.

Quick check

Before working it: the company hedges copper but leaves the dollar open. Its rupee cost is:

Worked solution

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

30-second answerThe answer to give first

Hedged, the copper costs Rs 37.71 crore; unhedged it would have cost Rs 40.85 crore, a difference of Rs 3.14 crore. Of that, Rs 2.55 crore is the copper price rising from 9,000 to 9,600, valued at the delivery rate, and Rs 0.58 crore is the rupee weakening from 83.80 to 85.10 on USD 4.5 million. Hedging only copper leaves the bill at Rs 38.30 crore; hedging only the dollar leaves it at Rs 40.22 crore.

Step 1Why are there two risks in one purchase?

A family booking a foreign holiday carries two prices: the hotel's rate in its own currency, and what that currency costs in rupees on the day they pay. Either can move, and fixing one does nothing for the other. Tamirabarani's copper bill is tonnes times the dollar price times the rupee rate, so two of the three factors are market prices, and each needs its own hedge. The copper futures fix the dollars per tonne; the forward fixes the rupees per dollar; and only the pair together fix the rupees per tonne.

The relationship

\text{hedged} = 500 \times 9{,}000 \times 83.80 = \text{Rs } 37.71 \text{ crore} \qquad \text{unhedged} = 500 \times 9{,}600 \times 85.10 = \text{Rs } 40.85 \text{ crore}

500	tonnes to be bought
9,000 and 9,600	the hedged and the delivery-day copper price, USD a tonne
83.80 and 85.10	the forward rate bought and the spot rate on delivery day

What it says in wordsThe rupee cost is tonnes times dollars a tonne times rupees a dollar, once at the hedged prices and once at the delivery-day prices.

Step 2How do you split the Rs 3.14 crore into copper and currency?

Change one factor at a time and say which order you used, because the split depends on it. Hold the rate at 85.10 and move copper: 600 dollars a tonne times 500 tonnes is USD 300,000, which at 85.10 is Rs 2.55 crore. Then move the rate on the hedged dollar amount: USD 4.5 million times 1.30 rupees is Rs 0.58 crore. The two parts sum to Rs 3.14 crore exactly, with the copper move carrying 81% of the saving and the currency move 19%. Done in the other order, copper at 83.80 is Rs 2.51 crore and currency on USD 4.8 million is Rs 0.62 crore; the total is the same, the split moves by the cross term.

The copper futures remove Rs 2.55 crore and the dollar forward Rs 0.58 crore from the Rs 40.85 crore unhedged bill, reaching Rs 37.71 crore; hedging copper alone leaves Rs 38.30 crore and the dollar alone Rs 40.22 crore.

Step 3What happens if only one risk is hedged?

With copper hedged and the dollar open, the company has USD 4.5 million to buy at 85.10: Rs 38.30 crore, which is Rs 0.58 crore worse than fully hedged. With the dollar hedged and copper open, it buys USD 4.8 million of copper but has forwards for only USD 4.5 million at 83.80; the remaining USD 300,000 is bought at spot, so the bill is Rs 40.22 crore. An Indian buyer of a dollar-priced commodity carries two risks, and a hedge on one of them leaves the other fully open, which is why the treasury policy has to name both.

Hedge in place	Dollar price fixed?	Rupee rate fixed?	Rupee cost, crore	Against fully hedged
None	no	no	40.85	+3.14
Copper futures only	yes	no	38.30	+0.58
Dollar forward only	no	mostly	40.22	+2.51
Both	yes	yes	37.71	0

Rupee cost of 500 tonnes under each hedging choice. The dollar-only hedge covers USD 4.5 million, so the extra USD 300,000 the copper rise requires is bought at spot.

Say the limitations as a treasurer would. The copper futures contract is for a standard grade at an exchange warehouse; the cathode the company buys will carry a premium that moves on its own, which is basis risk. The hedge is sized on 500 tonnes and USD 4.5 million; if copper rises, the dollars needed rise too, so a tidy hedge is slightly under-hedged on currency by construction. And in the mirror case, copper at 8,400 and the rupee at 82.50, both hedges show losses of the same size, and the board must be ready to read those as the price of certainty rather than as mistakes.

Where candidates lose it

Candidates compute the saving as 500 times 600 times 83.80 plus 4.5 million times 1.30 and get Rs 3.10 crore, missing the cross term of Rs 0.04 crore. State the order you changed the factors in, and the split then reconciles exactly.

The second miss is calling the copper hedge a complete hedge. It fixes dollars a tonne and leaves USD 4.5 million of currency risk, which here cost Rs 0.59 crore.

What the interviewer asks next

Copper falls to USD 8,400 and the rupee strengthens to 82.50. Recompute, and draft the one-line explanation of the hedge losses for the board.
Why might the company hedge the currency for less than USD 4.5 million, and for more?
Could the company hedge both risks in one instrument, and what would it give up?

Company names and figures are illustrative.

1The situation

2Your task