Roll yield confusion

As per Schweser Notes: “Roll yield is a return from the movement of the forward price over time toward the spot price of an asset. It can be thought of as the profit or loss on a forward or futures contract if the spot price is unchanged at contract expiration.”


In the professor’s Note is says: “Suppose the initial forward price of the base currency is above its initial spot price. If the currency is sold forward, F(T) and S(T) will converge at contract expiration and provide positive roll yield for the short position. The positive roll for the short position does not depend on whether the spot price increases or decreases. This is depicted in the figure below. To illustrate these concepts, suppose a manager sells the base currency forward when the initial forward price is above spot price F(0)>S(0) and the roll retrun will be positive. The positive roll does not depend on whether the underlying spot exchanger rate increases or decreases. The graphic illustrates that S(T) can end either above of below S(0)”

Question 1. What does F(T) represents here?

Question 2. First of all if the roll yield is assuming spot price remains unchange then how come above sentence in bold says spot price increases or decreases?

Question 2. Lets suppose the spot price increases above the forward price at inception. For example a investor enters into a 3 month forward contract at forward price of 15 and whereas the spot price is 10. At expiration the spot price goes up at 16, we took a short position at inception so we will have to buy the currency at spot rate of 16 and sell at 15(forward at inception) to close the contract. Then we enter a new contract. So isnt the roll yield is negative here? 15-16=-1? Is it necessary that when the currency is traded at forward premium, a short position will always give a positive roll yield?

Thanks in advance. Spent 1 hour on this but still confused

The idea is that the forward/futures price WILL converge towards the spot price at expiration. In your example you would be short the forward contract at 15, with the expectation that the forward price will decrease towards the spot price so that they are equal at expiration. The same principles are used in the commodities material and it may help you to work some examples there, where the markets are either in contango or backwardation. If the change in the contract price is greater than the change in the spot price over the period you earn a positive roll return (assuming you’re correctly long/short) and vice versa

We say the spot price remaings unchanged in a roll return? Right or wrong? If right then how come the above bold sentence says change in spot price over the period. But if wrong then why book says it remains unchanged?

Say in your example the spot price remained at 10, then the forward price moves from 15 to 10 so at expiration your roll return is 5. The book doesn’t say that the spot price doesn’t move, but your return is dependent on the movement in the contract price because that’s what you’re long/short

Bro you are telling what is written in the book. Can u give me example where the spot price is changing and the new spot price at the end of the initial contract is above the forward price(at inception not the new forward). How does a short position in the forward contract makes a positive roll yield here?

If you’re short the futures initially and spot goes up at expiration, it’s a negative to your existing position but can be a positive “roll” yield if the new contract is again at a forward premium since you’ll short the new contract higher. The roll depends on the closing of your existing contract vs the opening of the new one.

It’s funny how generic some of the answers are. I’m also confused about the concept of roll yield.

Let’s assume that an investors enters into a futures contract to buy X for 95$ in 3 months when the spot price of X is 100$. (Backwardation)

In 3 months, assuming that spot price remains UNCHANGED, in order to extend his position, the investor is required to close out the existing position and enter into a new one.

Here is where my questions begin:

  1. In order to close out the position, does the invesotor enter into an offsetting futures contract? (a couple of days before the expiration of the existing one lets say). so that would be entering into an offsetting contract to sell X for 99$ (assume futures price increased to 99$ as it converges towards spot price) in 2 days lets say effectivelt closing out the position and making 4$ in profit (i.e. positive roll yield) and then enternig into a new contract to buy X


Does the investor wait till the contract expiration and, assuming that the futures prices rolled up to the 100$ spot price, buy X for 95$ and sell for 100$ making a 5$ profit?

I think that as long as the spot price, in backwardation, does not drop so as to create contango, you will have a positive roll yield. so in the example above had the spot price dropped to 90$ for example (which means futres is in contango now) then i think (very uncertain) the offsetting futures position you would have to enter would have a price lower than your 95$ which means you lose money. i.e. negative roll yield.

I’m just thinking out loud here, anyone can confirim/refute and answer these questions?

@hadikadi- Second one is almost correct. The roll yield isn’t exactly right. You bought the initial futures @95. If your offsetting futures is done @90 at/near expiration ( futures=spot) it is a loss on your existing contract and not related to roll yield. But if the new 3mth futures you want to enter into (as part of your rolling) is > 90 then it’s a negative roll. If its <90 then it’s a positive roll since you’ll buy the new futures at a cheaper price vs spot/end value of initial futures. Contango =>negative roll yield Backwardation=>positive roll yield

The source of my confusion is the fact that roll yield is associated with “rolling into new contracts”, while it seems to me that roll yield, according to the literature, has nothing to do with the price of new contracts.

It seems that all we are doing is looking at whether or not the existing future price rolled up or down and determining whether its a positive or negative roll yield.

Returning to the example above, i am long X future @95 while spot is 100 (backwardation)

spot remains at 100 near expiration and my future price is near 100 now (convergance)

According to to the curriculum my roll yield is 5/100 = 5%

Where does the price of new contracts come into play? Why am i not determining my roll yield by comparing my old contract to new contracts? And finally, how does roll yield then differ from the yield from closing the position for good (i.e. not rolling into a new one)

The assumption is that new futures contract price also remains unchanged @95. The futures price for that tenor remains the same (5/100 is your yield).

Okay but for arguments sake lets just say the new futures price was not 95, lets say it was 97, what would my roll yield be?

I think the way you have to think about it is you need to roll into a new contract to maintain exposure to some asset. So you enter into a futures contract and at the expiration of that contract, to keep that exposure, you have to roll it forward again. To roll it forward again requires selling out or closing of the original contract and buying a new one. This is done at the spot rate because at expiration the futures price converges to the spot rate. This necessary closing out of the original contract and then entering into the new contract is the roll yield. So if you bought some futures @95 when the spot was 100 and the spot remains unchanged, then the roll yield, when you have to close out of this futures contract to enter into the next contract will be 5% since the spot remains unchanged. Hope I have that right.

This will help in understanding roll yield.

Yes you are right @cook29, when comparing the futures contracts (the old one and the one to be rolled into) AT or very near expiration (when the future price had already converged to the spot price) then the roll yield will be profit/futureprice (which happened to be equal to the spot price that close to expiration).

If we were to compute the roll yield further out from expiration then i would use the futures prices (which will not have yet convereged to the spot price).

Oh, and i believe my roll yield here is actually 5/95= 5.3%

Take a look at the example it really helps.

If it were 97, then it’s 3%

For the long, roll yield is Δforward − Δspot.

Try some algebra:

Δforward – Δspot = (new forward – old forward) – (new spot – old spot)

= new forward – old forward – new spot + old spot

= (new forward – new spot) – (old forward – old spot)

If you roll the contract forward, then your roll yield is the new forward premium less the old forward premium.

If you don’t roll the contract forward, then you use the fact that the forward price has converged to the spot price: the first term is zero, and your roll yield is the negative of the old forward premium.

I can see that I need to write an article about roll yield.