# Backwardation/roll return

I’m having trouble visualizing and making sense of the issue of backwardation. How and why does it occur? Can someone please help to logically link the following statements: 1. Downward-sloping term structure of futures prices is backwardation. 2. When the futures markets are in backwardation, a positive return will be earned from a simple buy-and-hold strategy. 3. All else being equal, and increase in a commodity’s convenience yield should lead to futures market conditions offering higher roll returns; the converse holds for a decline in convenience yields. 4. A monthly roll return is computed as the change in the futures contract price over the moth minus the change in the spot price over the month. i kind of get it… kind of… but can someone explain this as if i were a 3-year old, especially to the point #4, why is it calculated as it is, considering that the total return on futures is roll return + spot return + collateral return

Let’s say you were a supplier of a commodity, then you have more invested in the commodity’s price than, say, and end user of the commodity whereby the end-user might only have a vested interest in the price of the commodity for one part of their operation. Then the supplier might push the forward price down in order to entice a speculator (or end-user) to take the forward trade to “lock in” a forward price and eliminate price risk. This is called “normal backwardation” and implies that it is “normal” for suppliers to have more interest in locking in a price than end-users or speculators so they push the forward price down so the end result is the forward curve is negatively sloped over time (positive convenience yield). Since the futures price will converge to the spot price at expiration, if you buy the commodity forward at a price less than spot, in general, you will earn a positive return as you converge towards expiry. For example, let’s say that the spot price is \$50 and the forward price in three months is \$40. You purchase a forward contract at \$40. Now, if the spot price stays at \$50 over the next three months, then you will earn \$10 or the difference between spot and forward (S-F = \$10) over the next three months. This is because it is guaranteed that the forward price at expiration will be equal to the spot price. This is called positive roll return. Note that a lot of things could happen over those three months. The spot could go to \$35 so that you lose \$5 at expiration but in general, you will make money with a positive roll towards expiration (backwardation) and lose it with a negative roll towards expiration (contango).

thank you this really helps to understand the dynamics of the trade from the standpoint of supplier/end user

So a positive convenience yield is associated with a negatively sloped curve since producers would rather hold on to the spot for now thus spot is higher than forward?

only if the convenience yield is greater then the riskfree rate, then the slope will be negative (i.e. downward sloping) F=Se^(r-c)T just think if c>r then the exponent is negative which then makes e<1 and the F < S

I have very basic question on this statement: “This is because it is guaranteed that the forward price at expiration will be equal to the spot price.” what does “forward price at expiration” exactly mean? i.e. the old forward contract or new forward contract price?

The spot price and forward converge at expiration; if it didn’t you could make a ton of money arbitraging the relationship.