Case 017Hedging with futuresWarm up

A sugar mill sells futures at Rs 38,000 a tonne to hedge a sale in four months. At delivery spot is Rs 35,500 and the future Rs 36,300. What price does it effectively get, and what if the basis had widened to minus Rs 1,500 with the future unchanged?

The situation

Gomtiva Sugar will sell 50,000 tonnes of sugar from its mill in four months. Worried that a good cane harvest will push prices down, it sells sugar futures for that month today at Rs 38,000 a tonne on the full quantity. It will sell the physical sugar to local buyers at the spot price on the day and close the futures at the same time.

At the sale date the local spot price is Rs 35,500 a tonne and the futures price is Rs 36,300, a basis of minus Rs 800. A second case: suppose the futures price is the same Rs 36,300 but local spot is weaker, so the basis is minus Rs 1,500. Ignore margin interest and costs.

Your task

What price per tonne does the mill effectively receive in each case, how does that compare with not hedging, and what risk did the hedge leave with the mill?

Quick check

Before computing: the mill sold futures at Rs 38,000. What price has it actually locked in?

Worked solution

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

30-second answerThe answer to give first

The mill gets Rs 37,200 a tonne: it sells at Rs 35,500 and gains Rs 1,700 on the futures, which is the Rs 38,000 sold plus the minus Rs 800 basis. On 50,000 tonnes that is Rs 186.0 crore against Rs 177.50 crore unhedged. If the basis had been minus Rs 1,500, spot would be Rs 34,800 and the mill would get Rs 36,500, Rs 700 a tonne less. The hedge removed the price risk and left the basis risk.

Step 1What price does the mill actually get?

Suppose you agree a price for your harvest at the big market in the city, but you will sell at the village gate on the day. You know the city price; what you do not know is the gap between the village and the city on that day. The mill sells sugar at its local spot price of Rs 35,500 and buys back the futures it sold at 38,000 for 36,300, a gain of Rs 1,700, so it receives Rs 37,200 a tonne in all. That number has a simpler name: the futures price it sold, 38,000, plus the basisThe spot price of the commodity a hedger actually trades minus the price of the futures contract used to hedge it, on the same day. It reflects location, grade and timing differences. at delivery, minus 800.

The relationship
Peff=ST+(F0−FT)=F0+(ST−FT)=38,000+(−800)=37,200P_{eff} = S_T + (F_0 - F_T) = F_0 + (S_T - F_T) = 38{,}000 + (-800) = 37,200
S_Tthe spot price received at the sale date, Rs 35,500
F_0, F_Tthe futures price when the hedge was placed and when it was closed, 38,000 and 36,300
S_T - F_Tthe basis at the sale date, minus 800
What it says in wordsRearranging shows that what the hedger receives is the futures price it sold plus the basis on the day it closes. The futures level at delivery drops out entirely.
What the mill gets: the futures price it sold, plus the basis on the day it deliversRs per tonne (axis starts at 33,000)34,00035,00036,00037,00038,000Basis at delivery -800futures sold at 38,00035,500spot sale+1,700futures gain37,200effectivebasis -800Basis widens to -1,500futures sold at 38,00034,800spot sale+1,700futures gain36,500effectivebasis -1,500The futures gain is the same 1,700 in both panels; only the gap between the mill's spot price and the future changes.
In both cases the futures gain is Rs 1,700 a tonne, so the mill ends at the 38,000 futures price plus the basis: Rs 37,200 when the basis is minus 800 and Rs 36,500 when it widens to minus 1,500.
Step 2How does it compare with not hedging, and with a wider basis?
RsSpot per tonneFutures gain per tonneEffective per tonneOn 50,000 tonnes, Rs crore
Unhedged35,500035,500177.50
Hedged, basis -80035,500+1,70037,200186.00
Hedged, basis -1,50034,800+1,70036,500182.50
The hedge adds Rs 1,700 a tonne, Rs 8.5 crore on 50,000 tonnes, and turns Rs 177.50 crore of unhedged revenue into Rs 186.00 crore; a basis 700 wider costs Rs 3.5 crore of that back.

Prices fell Rs 2,500 a tonne at the mill gate between the hedge and the sale, and without the hedge the mill would have taken all of it. The futures gain of Rs 1,700 a tonne, Rs 8.5 crore on the whole crop, covers most of the fall; what it does not cover is the change in the basis, which the mill keeps one for one. In the second case the futures price ends at exactly the same 36,300, so the futures gain is the same, but the mill's own sugar sells Rs 700 lower, and the effective price falls Rs 700 to 36,500. Nothing in the futures position could have offset that, because the futures did not move.

Step 3Why does the basis move, and what can the mill do about it?

The basis is the price of the difference between the mill's sugar and the exchange's sugar. It moves with local supply, transport costs to the delivery centre, the grade of sugar and the time left on the contract, so a mill in a district with a bumper crop can see its local price fall further than the exchange price. The mill can narrow the risk three ways: choose the futures month that expires closest to the sale date, so less time value sits in the basis; deliver against the futures if its sugar and location qualify, which forces the basis to converge; and track its own historical basis by month, so the budget price is 38,000 plus the expected basis rather than 38,000. Say the limits of the working: the futures gain arrives as daily margin over four months, not on the last day, so a rally in between would have required cash; costs and interest are ignored; and the whole crop was hedged although the mill's own output was itself uncertain.

Where candidates lose it

Candidates say the hedge locked Rs 38,000 a tonne. It locked 38,000 plus the basis, and the interviewer asks the second question precisely to see whether the candidate knows the futures price can stay put while the mill's own price moves.

The second loss is to compute the effective price from the futures alone, adding the gain to 38,000 or subtracting it from the futures close. Work from the cash the mill actually receives: spot sale plus the futures gain.

What the interviewer asks next

  • The futures had instead risen to Rs 40,000 with the basis at minus 800. What does the mill get, and how did it pay for the hedge in the meantime?
  • The mill's historical basis in that month ranges from minus 400 to minus 1,600. What budget price would you give the board?
  • Why does the basis usually narrow as the futures contract approaches expiry?
  • If the mill is unsure of its output, what share of it would you hedge, and why?

Company names and figures are illustrative.