I just don't get the backwardation...Roll return doesn't seem intuitive.

So i understand what backwardation is…ever lower forward prices, and I understand that people earn a positive roll return.

And I see the book definition , somewhat paraphrased is “a positive return will be earned from a simple buy and hold strategy. The positive return is earned because as the futures contract moves closer to maturity, its price must converge to spot”

How is this structured? If you are long the contract, you are obligated to buy the commodity in the future. What happens then? You buy it and then sell it spot for a higher price, then reinvest in a lower contract and sell it at spot in the future, then repeat?

Intuitively, to me, it seems that since there are lower futures contract prices, it would converge to spot, ever lower so one would continue to have lower valued futures and spot prices losing money. In other words I buy at a dollar today and its worth .98 in the future, repeat…it doesn’t seem like a moeny maker.

I know this is a fairly basic topic, but I just can’t make intuitive sense of it and Im missing something, I know. Its seems like I knew this at level 2 and just forgot.

U should actually understand structure of backwardation.

Backwardation: Sp > Fp.

And the future price appraoching the spot price when time pass…

Reason is convenience benifit for physically holding decrease…other kept unchange.

example: spot price today (May) 90$, Future price (Oct) 80$. The future price will approaching 90 when time pass because benifit from holding underlying decreasing when time pass (convenience benifit going down). That means Future price (Oct delivery) on June will be 82, July be 84…assum 1 month convenience benifit is 2$

So you just buy the future contract to day at 80 and hold until Oct to take profit of 10$.

If there is no market volatility, it can be said that: (I fixed Fp for 1 month delivery)

  • Today spot price 10$, Fp (1 month delivery - June) 8$

  • spot price on June 10$ and one month Fp (Jul delivery) 8$ and so on…

OP, you got it backward (actually bad of wording there). You got it the other way around.

In backwardation, the Futures will increase to the Spot, not go down like you said. So, thus you have a positive roll return

backwardation - futures prices less than spot. most often occurs when suppliers of commodity want a guranteed price to sell their commodity in the future, they are willing to accept lower price in order to sell commdity at guranteed price.

contango - futures price greater than spot price. most often occurs when buyers of commodity want guaranteed price for commodity and are willing to pay higher price in order to secure guranteed price for commodity they are buying and using.

Again, I get the definition. My Question is the delta/profit.

Can someone give me a simple example with a couple of steps?


Period 1, spot 90 Forward 80

Period 2, spot 85, forward 75

As Period 1 ends, the 80 dollar forward converges to 85.00 spot, we buy at 80 and deliver at 85 making a $5 delta, and then get into the $75 forward…

Is that how it works? I figured the forward, lets say 80, was the implicit future spot price. In order to profit, period 2’s spot had to be higher than period 1’s forward expiration, does it not?

Consider for portfolio diversification purposes you need to hold a commodity in your portfolio, let’s say 100 ounce gold. Buying it physically is undesirable due to costs, so you would use futures. Let’s say sport price is $2000 per ounce. Say, you have one year gold future available in market for $2010. You need $2000*100 to be invested in gold to gain the desired exposure. You go long on future. You put full collateral, $2010*100, in debt instrument to earn the collateral yield at the end. At maturity let’s say gold spot is $2015. You have, $2015-$2010 = $5, spot return on futures maturity. After this your portfolio still needs a 100 ounce of gold exposure and you need to go long on a new gold future (roll over). Say, you have one year gold future available in market today at $2013 (backwardation, future price is less than spot, $2015). The roll return comes from the fact that you now need less collateral $2013 - $2010 = -$2. This $2 is your roll return; take it out from your collateral in debt instrument as profit, you now have the same exposure of 100 ounce of gold in your portfolio back again.

I thought in backwardation you’d see consistently lower futures prices, in your example futures prices is 2010 then 2013…if you saw list of futures prices that said





Thats a contango term structure is it not?

Forget about old future price $2010. If spot price ($2015) > futures price ($2013) it is backwardation and vice-versa for contango.

When market is in contango, your roll return will be -ve. You need to addin additional collateral.

I e. page 173 Book 5, “If forward prices more distant in time are higher we say the market is in Contango” you imply backwardation is forward lower than spot, when according to text, backwardation is that forward curve is downward sloping, not a forward/spot relationship. In your illustration the term structure is upward sloping.

So again if forward prices are downward sloping, the spot curve, I assume, would be too, so where is the postiive roll return?

To reiterate, I understand what backwardation and contango is, I understand backwardation produces roll return, and I understand its because the futures converge to spot. What I don’t understand is HOW. What is the mechanics mathematically.

I was confused by that too. I don’t get how declining forward curve implies backwardation. I thought backwardation was simply a relationship between spot price and forward price.

Roll return happens only when you roll, meaning you held position in the past with appropriate collateral invested in bonds. And when you roll, if future price is below spot, you need less collateral.

@ Nashwbe…it seems to me that is implied…correct me if im wrong, but in order for forward prices to be lower in the future then spot MUST be lower as well becaue of the convergence. You arent going to have spot goign one way and forward another, so yeah forward will be lower than spot but forward will be lower than forward also.

Ugh, I was hoping you wouldn’t say that. I’m admittedly really weak on understanding the concepts behind commodity spot-forward prices. I figure that with all the convenience yields, storage costs and lease rates/dividend yields, there is no clear-cut relationship between future spot price and future forward price. Maybe in period 2, the spot price has a huge rise, but the dividend yield plummets, pushing the forward price down on a net basis.

I could easily be wrong…

I probably just need to do a lot more cash and carry and other commodity math and this would all come clear.

Ignore the my example above. Got it wrong.

Below from old discussion makes sense.

Change in futures = (changes in futues - change in spot price) + change in spot price = roll return + spot return

If future prices and spot prices changed consistently, there is no roll return. However, if they did not then you have a roll return.

So then the spot HAS to be greater than the futures price at expiration and you buy at your locked in futures price and sell at spot?

Enter into contract at T0 but commodity at T1 sell spot at T1? Re enter futures contract at T1?

I was thinking cash and carry would make this clear, but cash and carry is arbitrage not roll return.

I guess at the end of the day, maybe I don’t need to understand “why”, just learn the formulas, know the definitions and be done…

a declining forward curve implies backwardation because the more distant Forward prices are lower than the more proximate forward prices.