# A Brief Introduction to Roll Yields

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by: Hard Assets Investor

Tipping the mailbag over, this missive from John caught my eye:

I read your article, "Futures: The Three Sources of Return" with interest. I have a follow-up question regarding the calculation of roll yields.

If I own the two-month contract at \$100 and it converges up to the one-month price of \$101 in 30 days' time, is the roll yield simply 1% per month, or 12% annualized?

First things first, John. We have to make sure we're talking the same language first. "Rolling" refers to the simultaneous sale and purchase of futures contracts on the same commodity, but of different delivery months. A long position in April gold, for example, could be swapped for the June gold delivery.

Rolling serves to extend an open long or short position into the next available contract month, making a roll the rough analogue to a "buy-and-hold" position in a stock portfolio.

Most often there's a price differential between the delivery month being exited and the delivery month acquired. As I write this, for example, April COMEX gold is trading for \$931.80 an ounce, while the June delivery last changed hands at \$935.00 an ounce.

The difference between the two deliveries reflects a supply of gold that can be effectively stored between April and June for a cost of \$3.20 an ounce. That cost reflects storage, insurance and financing charges.

Because June trades higher than April - evidence of a normal, or contango market - there'd be a cost of \$3.20 an ounce, or \$320 per contract, to roll a gold futures position forward now. That's an annualized roll yield of -2.06%, to wit:

[Roll cost (\$3.20)/Near-month price (\$931.80)] x [12 months/delivery spread (2 months)]

Note how contango thus works to lower the return on a long-only futures portfolio or index.

From your example, John, I'm not sure if you're actually contemplating a roll. You cite the price of a distant futures rising to converge with the price of a nearby delivery over a month's time. Convergence of futures prices to the spot or cash price is the necessary link that keeps futures on track with physicals. At delivery, the expiring futures price MUST equal spot.

If you bought the two-month contract a month ago, you now own a one-month contract. It ought to, therefore, be trading at the one-month price. After all, you've used up a month of carrying costs. In another month, the value of your futures contract should converge to the spot price, representing the further diminution of carrying charges.

Now, if your point of reference is your purchase date - that is, your two-month contract rises to the level that a one-month contract traded at on your purchase date - we've got a different kettle of fish.

If a two-month contract is trading at \$100 when a one-month delivery is being sold for \$101, the market's not in contango; it's inverted. Here, the economic incentive is not to store the commodity, but to sell it NOW. In an inverted, or backwardated market, roll yields are positive. There's a dollar (\$101-\$100) to be made simply by rolling a long contract forward, to wit:

[Roll benefit (\$1)/Near-month price (\$100)] x [12 months/delivery spread (1 month)]

And that works out to be 12%.

You can see what makes futures attractive for some traders. When competing investment yields are low, the returns available inside the futures term structure can seem mighty attractive. Keep in mind the inherent risk, however. Futures can - and do - flip from inversion to normalcy rapidly.

You can't sleep at this switch.