Case 007Hedging with futuresHard

A beverage maker expects to buy 10,000 tonnes of sugar but could need 7,000 to 12,000 depending on the weather. Compare hedging 10,000 tonnes against 8,000 in a hot summer and a cool one.

The situation

Bhimtal Beverages plans to buy 10,000 tonnes of sugar for the summer season, but its sales follow the weather: a hot summer means 12,000 tonnes and a cool one 7,000. Sugar futures for the season trade at Rs 40,000 a tonne. The treasurer's two candidate outcomes are a hot summer, in which the firm needs 12,000 tonnes and spot sugar is Rs 46,000, and a cool summer, in which it needs 7,000 tonnes and spot is Rs 35,000. Treat the two as equally likely.

The board has asked for a comparison of buying futures on the full 10,000 tonnes against 8,000 tonnes, and a view on which is safer.

Your task

Compute the total sugar cost and the cost per tonne under each hedge size in each summer, say which hedge is safer and on what measure, and explain why a smaller hedge can beat a full one here.

Quick check

Before the table: in the cool summer, what does the 10,000 tonne hedge do that the 8,000 tonne hedge does not?

Worked solution

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

30-second answerThe answer to give first

On cost per tonne, the 8,000 tonne hedge is safer: its worst case is Rs 42,000 a tonne in the hot summer, against Rs 42,143 for the full hedge in the cool one. The full hedge sells 3,000 tonnes of futures the firm never needs in a cool summer, losing Rs 1.5 crore when sales are weakest. Because volume and price move together here, the hedge that equalises cost per tonne across the two summers is about 9,059 tonnes, below the 10,000 tonne plan. On total rupees the full hedge looks tighter, so name the measure first.

Step 1What does each hedge cost in each summer?

Lay out the four cells before judging anything. Total cost is tonnes needed times spot, less the futures gain of tonnes hedged times spot less 40,000; cost per tonne divides that by the tonnes needed. In the hot summer the futures gain Rs 6,000 a tonne; in the cool one they lose Rs 5,000. A household that pre-pays for ten months of a tutor and then needs only seven has paid for three months of nothing, and that is what the over-hedge is.

HedgeHot: total, Rs croreHot: per tonneCool: total, Rs croreCool: per tonne
No hedge55.2046,00024.5035,000
8,000 t50.4042,00028.5040,714
10,000 t49.2041,00029.5042,143
The full hedge gives Rs 49.20 crore and Rs 29.50 crore, which is Rs 41,000 and Rs 42,143 a tonne; the 8,000 tonne hedge gives Rs 50.40 crore and Rs 28.50 crore, Rs 42,000 and Rs 40,714 a tonne; unhedged is Rs 46,000 and Rs 35,000.
Total cost and cost per tonne under each hedge size and each summerHedge sizeHot: 12,000 t at 46,000Cool: 7,000 t at 35,000Over-hedge, coolNo hedgeRs 55.20 crore total46,000 per tonneRs 24.50 crore total35,000 per tonnenoneHedge 8,000 tRs 50.40 crore total42,000 per tonneRs 28.50 crore total40,714 per tonne1,000 t sold, no sugarloses Rs 0.5 croreHedge 10,000 tRs 49.20 crore total41,000 per tonneRs 29.50 crore total42,143 per tonne3,000 t sold, no sugarloses Rs 1.5 croreRed per-tonne figure: the worst case of that hedge. Red cell: futures sold against sugar the firm never needed, a loss with nothing behind it.Full hedge worst case 42,143 per tonne in the cool summer; 8,000 t hedge worst case 42,000 in the hot summer.Total cost in crore rewards the full hedge; cost per tonne, which sets the margin per bottle, does not.
In the cool summer the full hedge carries 3,000 tonnes of futures with no sugar behind them, a Rs 1.5 crore loss that lifts cost per tonne to Rs 42,143, the worst per-tonne outcome of either hedge, while the 8,000 tonne hedge's worst case is Rs 42,000 in the hot summer.
Step 2Why does the measure decide the answer?

Look at the two ranges. In total rupees the full hedge spans Rs 29.5 crore to Rs 49.2 crore, a gap of Rs 19.7 crore; the 8,000 tonne hedge spans Rs 28.5 crore to Rs 50.4 crore, Rs 21.9 crore. By that measure the full hedge is tighter. But Bhimtal sells more bottles in a hot summer, so what sets its margin is the cost per tonne, and on that measure the full hedge has the single worst outcome, Rs 42,143, and it lands in the cool summer when revenue is weakest and the Rs 1.5 crore futures loss is a cash call. The 8,000 tonne hedge's bad case, Rs 42,000, lands in the hot summer when the firm is selling everything it makes. A hedge that hurts when the business is already hurting is the one to avoid.

Cost per tonne against hedge size: the two summers cross below 10,000 t36,00040,00044,00004,0008,00010,00012,000tonnes hedged with futures at 40,000hot summer: 12,000 t at 46,000cool summer: 7,000 t at 35,0009,059 t8,000 t hedge10,000 t hedgePer tonne, Rs8,000 t hedgehot 42,000 cool 40,71410,000 t hedgehot 41,000 cool 42,143worst case: 42,000 v 42,143lines cross at about9,059 t, 41,471/tbelow the 10,000 t plan
As the hedge grows, cost per tonne in the hot summer falls and in the cool summer rises; the two lines cross at about 9,059 tonnes, around Rs 41,471 a tonne, so a hedge of 10,000 tonnes is past the point where it stops reducing the firm's per-tonne risk.
Step 3What is the general rule, and what would you actually do?

When the quantity you need rises with the price, part of your exposure hedges itself on a per-unit basis: a hot summer costs more per tonne but spreads fixed costs and futures gains over more tonnes. The hedge that equalises cost per tonne across the two summers is about 9,059 tonnes, and any hedge above it starts adding risk back. The honest gap between the two sizes on the table is small, 143 a tonne, so the stronger answer reshapes the hedge rather than picking a number: lock the 7,000 tonnes the firm needs in any weather with futures, and cover the uncertain 3,000 to 5,000 tonnes with call options, which cost a premium but cannot lose Rs 5,000 a tonne on sugar that is never bought. Say the limit: two equally likely scenarios is a sketch, and a real treasurer would run a range of weather and price outcomes and would check how closely the futures track the sugar the firm actually buys.

Where candidates lose it

Candidates hedge the planning number because it is the number on the page, and never ask whether the volume is certain. A 10,000 tonne hedge is a bet that the summer will be average, and the question was built so that it is not.

The second loss is to compare only total rupee cost, declare the full hedge tighter, and stop. The interviewer wants you to say that per-tonne cost is what sets the margin for a firm whose sales move with the weather, and then to notice that the full hedge's worst case arrives in the weakest quarter.

What the interviewer asks next

  • Price the call options you would use for the uncertain layer: what strike, and how would you justify the premium to the board?
  • Suppose a cool summer came with high sugar prices because of a poor cane crop. How does that change the hedge?
  • The futures contract is for raw sugar and the firm buys refined. What risk does that add, and how would you size it?
  • Why might a seller of sugar, a mill, face the opposite problem?

Company names and figures are illustrative.