Calendar Spread Arbitrage: Near vs. Far Months

Far-near spread = the bill for storing inventory

Buying the near month, taking delivery and storing it until the far month means paying 6 months of interest and storage. So the far month should cost at most that much more than the near month; this is the full carry. When the spread exceeds it, buying near and selling far locks in a profit: a calendar spread arbitrage.

The upper limit is hard; the lower limit is soft

When the spread is too wide, anyone can borrow to take delivery and arbitrage it, so the upper limit is firm. When it's too narrow (or the far month is even cheaper), the reverse trade needs you to hand over the physical first, which only inventory holders can do. Holders of the physical value the convenience yield, so backwardation can persist for a long time.

Locked-in profit ≠ smooth sailing

Both legs are futures, so before expiry the spread may widen first and you'll have to top up margin. Actually taking delivery also means meeting delivery grade, warehouse receipt and locked-in financing rate requirements. The arbitrage profit is realized at the finish line, but you have to carry the cash flow all the way there.

Key takeaways

• Full carry spread = near-month price × interest rate × time between them + storage and insurance. It's the fair upper limit for the far month over the near month.
• If the far month is priced above full carry: buy near, sell far, take delivery on the near month and deliver on the far month. The profit doesn't depend on the gold price.
• When the spread is too low, only holders of physical goods can run the reverse arbitrage. Without inventory, betting on the spread recovering is just speculation.
• The spread can widen before expiry, so keep margin ready. Delivery grades, warehouse receipts and funding costs are all real-world frictions.

Try it yourself

You can do these exercises in this lesson's interactive simulation:

1. Click "Example: spread $70 · rate 5% · storage $4": what's the full carry spread? How much is locked in per ounce? How much for 1,000 ounces?
2. Drag "Spread at near-month expiry" from −$40 to +$100: how low does the green "Better of the two" line go? Why do you earn more the more the spread narrows?
3. Drag the far − near spread to $20: what does the explanation card say with "No gold in hand"? Switch to "Gold in inventory": how much can you lock in per ounce?
4. Go back to a $70 spread and drag the funding rate to 0%: what does the full carry spread become? What does the locked-in profit become?

Quiz and explanations

1. Near-month gold is $2,000, the funding rate is 5%, the far month is half a year later and storage plus insurance over the period is $4. What's the full carry spread?

Answer: $54.$2,000 × 5% × 0.5 + $4 = $54.

2. The far month is $70 above the near month and full carry is $54. Ignoring trading costs, if you buy near, sell far and go through delivery, how much do you lock in per ounce?

Answer: $16.$70 − $54 = $16, regardless of the gold price at expiry.

3. The far month is actually $20 cheaper than the near month (deep backwardation). Can a trader with no gold run a risk-free reverse arbitrage?

Answer: No: the near month requires delivering physical gold at expiry. Without inventory you can only close out, and the result depends on how the spread moves.A reverse calendar arbitrage starts by delivering physical goods. Without inventory, selling near and buying far is just speculation on the spread recovering.

Terms in this lesson

• backwardation (Backwardation): A market where futures (or later months) trade below spot (or nearer months).
• calendar spread arbitrage (Calendar Spread Arbitrage): Arbitrage between futures months of the same product: when the far month is too expensive versus the near month, buy near and sell far, take delivery on the near and redeliver on the far.
• convenience yield (Convenience Yield): The benefit of actually holding the goods (no shortages, ready to use); it makes holders reluctant to sell, so futures can stay below fair value for a long time and reverse arbitrage may not work.
• full carry (Full Carry): The most the far month should cost over the near month = near price × interest rate × time between + storage and insurance for that period; beyond it, a calendar cash-and-carry works.
• margin (Margin): The deposit set aside when you open a position = position value ÷ leverage.
• no-arbitrage band (No-Arbitrage Band): The price range set by trading costs: when a mispricing stays inside it, arbitrage isn't profitable after costs.