A jeweller needs 100 kg of gold in six months. Spot is Rs 72,000 per 10 g, the six-month future Rs 74,500, storage 0.4% a year and the rate 7%. Buy now and store, or buy the future, and what is the market saying?

Buy the future. Buying now and storing costs about Rs 74,714 per 10 g at full carry, against Rs 74,500 for the future, a saving of about Rs 21.4 lakh on 100 kg. The future sits below full carry, which means holders of gold are being paid something to hold it: the gap is an implied lease or convenience yield of about 0.57% a year. That is a statement about the leasing market for gold, not a forecast of its price.

Buying a wedding sari a year early does not save the price of the sari; it ties up money that could have earned interest and it needs a cupboard. Gold bought today costs the spot price plus the interest on that money for six months plus storage and insurance: 72,000 grown at 7.4% a year for half a year is 74,714 per 10 g, of which 2,565 is interest and 149 is storage. That number is the full carryThe price at which a future would trade if it exactly covered the cost of financing and storing the asset until delivery, with no benefit from holding it. price, the most a rational buyer would pay for a future, because above it you would simply buy spot and store.

On 100 kg, which is 10,000 units of 10 g, the saving is 214 times 10,000, about Rs 21.4 lakh. Buying the future also keeps Rs 7.2 crore of cash in the business for six months and avoids the vault, so it is cheaper on the arithmetic and lighter on the balance sheet. Both routes lock the price today, so neither is a view on gold. The costs of the futures route that the question told you to ignore are the ones to name: initial margin, daily variation margin that must be funded if gold falls, and the need to take or roll delivery when the contract expires.

Turn the carry equation round and solve for the yield that makes 74,500 fair: r plus u less the log of F over S divided by T, which is 7.4% less about 6.83%, roughly 0.57% a year. A future below full carry means holders of gold are earning something from holding it, here a lease rate: central banks and bullion banks lend gold to jewellers and refiners, and that income offsets part of the carry. A larger gap would say gold is scarce to borrow or that physical holders value having it in hand, a convenience yield. Say the limit: the implied yield is only as good as the 7% and 0.4% you put in, and a firm that could borrow at 8% would compute a different gap and might reach a different decision.