The book says roll yield is the return from rolling the commodity futures forward, and
roll yield = change in futures price - change in spot price
Can someone please explain in plain English why is the formula so? I don’t see how change in forward price minus change in spot price represents the return from rolling forward the futures.
Thanks!
Contract rolling is required when the current contract expires. Expiry forces the futures price to the spot price. This “forcing” the futures price to spot price is the part of future price change not explained by the CHANGE in spot.
Change in futures = (changes in futues - change in spot price) + change in spot price = roll return + spot return
It’s kind of decomposition. Roll return is a return component that excludes the spot price change. In other words, roll return won’t be affected by the spot price change.
Check out an AM question on this topic.
There is no secret , the futures tracks the spot closely just prior to expiration .
The next contract out does not track it so closely because there is an element of mystery about forward prices and risks involved apart from time value of money in a forward sense.
If you exit a front and enter a back , you collect or pay on the difference i.e. between spot and the forward and they call it “rolling” . In continuously held contracts someone is gaining and someone is losing in this operation of rolling , which is referred to as roll yield. The roll yield is available at any point in the life of the futures contract but typically one is always close to expiration , hence the term spot is used interchangeably with the front contract which is being exited.
I actually disagree with that formula in a general sense. For instance, let’s say the forward curve steepens but spot is constant. Even if no time has passed, a long position has increased in value. That has nothing to do with the “roll”, which is the gain or loss that you experienced when your position converges in time to zero.
Anyway, what they are trying to say is if the forward curve looks like this:
Time| 0, 1, 2, 3, 4, 5
Fwd | 1, 0.9, 0.8, 0.7, 0.6, 0.5
Let’s say you hold the T=5 forward contract at T=0. At T=1, *assuming spot price and forward curves do not change*, the forward price for your contract will have moved from 0.5 to 0.6. Thus, you earn that 0.1 difference through “roll” yield alone.
Again, note that this is only true if the forward curve does not change shape.
T=0 Forward price = 0.5
T=1 Forward Price = 0.6
Change in Forward = 0.6 - 0.5 = 0.1
Change in Spot = 0 -> since you say Spot is constant
Roll Yield = 0.1 - 0 = 0.1 … which is what you have stated above
What I mean is, if the forward curve changes shape, you cannot attribute your gain or loss to just “roll”. If at T=0, the T=5 forward price spikes from 0.5 to 0.55, you made 0.05 profit. However, no “rolling” has occurred.
ohai , very confused by your words . How exactly would your position converge to zero? You purchased afutures contract at some existing price . When you as a speculator exit the position that same futures contract has a different price , usually not what you paid for it. So how does that become zero in a general case?
Here’s how a speculator would collect roll yield :
Buy a first nearby futures contract.
When a day or so is left to the expiry , sell the futures contract you bought 1 period ( say 1 month ) ago , and invest in the next contract out. In the process , if the gods are similing at you and imposing backwardation on the market , you collect the roll yield i.e. selling an appreciated futures contract very similar in price to the spot , and getting into an under-appreciated ( hence backwardated ) futures contract . Sell High Buy low. Collect this “roll yield”
Repeat next period( say month ). In time , if your bets on backwardation work out enough times , you’re rich , like John Arnold of Centaurus. Also works if enough times the contract is contango and you’re able to successfully short the futures at those times.
The maturity of your forward contract converges to zero. If you buy a 1y forward, after 1 year, it becomes a zero year forward.
Yes, I agree that roll yield exists. However, not all profit or losses from forward contracts is due to roll.
roll yield is only used with futures . don’t recall it used with forwards , I may be wrong though ( frequently am )
janakisri, “When a day or so is left to the expiry , sell the futures contract you bought 1 period ( say 1 month ) ago , and invest in the next contract out. In the process , if the gods are similing at you and imposing backwardation on the market , you collect the roll yield i.e. selling an appreciated futures contract very similar in price to the spot , and getting into an under-appreciated ( hence backwardated ) futures contract . Sell High Buy low. Collect this “roll yield”” I understand this part, but according to your (and the book’s) explanation, the profit from rolling over the contract should be S(T)-F(T), as you get proceeds from selling at spot price S(T) and at the same time spending F(T) to roll over the contract. Why should the formula be: change in F(T)-change in S(T)?
do the research after 25 days …
put it into short term for the time being, and go ahead with finishing up whatever else you have to…
now that you have had this discussion, is the WHY so important?
I think a little algebra helps here:
Roll yield = Δ futures price – Δ spot price
= (new futures price – old futures price) – (new spot price – old spot price)
= (new futures price – new spot price) – (old futures price – old spot price)
= profit on new contract – profit on old contract
Though algebraically the same, I think that this last formula better spells out what’s happening, and the source of positive or negative roll yield. For example:
Thus, the roll yield is $1.10 – $1.00 = $0.10: the profit on the new forward contract is 10¢ higher than the profit on the old forward contract; that’s the roll yield.
Helpful. Thanks.
Hi S2000, just with regard to your example above, so if collateral yield were to equal $0.50…
Spot (price) return = $1.40
Roll yield = $0.10
Collateral yield = $0.50
Total return = $1.40+$0.10+$0.50 = $2.00
Is that correct?
@S2000magician - thanks as always for your easy to understand ways of explaining things. Could you explain why this is violates uncovered interest rate parity? I am struggling to make the connection between this and interest rates.