# 2009 exam roll return question

For Question 8Aiii, the answer states that the increase in convenience yield has the effect of increasing the roll return. Looking at thismathemetically makes sense: F = Se^(rfr + cost - conv yield)T, so as conv yield goes up, the exponent goes down, and F goes down, making F < S, and causing backwardation, thereby increasing roll return.

However, if you look at this intuitively I think you get a different result. Roll return is defined (Schweser Book 4 Page 29) as the change in futures price not explained by change in spot price (F-S). So if convenience yield goes up and forces F down, then F is a smaller number, making F-S a smaller number, and thereby decreasing the roll return.

Am I thinking of this the wrong way?

F-S is a flat price equation , while roll return is delta F - delta S . In a backwardated market F starts out lower than S( by definition of backwardation , F is below S) .

As time goes on , and assuming nothing much has happened to S for the purpose of roll yield discusson ), F must roll upwards towards S as futures always convereges to spot near expiry . So delta F is positive and delta S is close to zero per our assumption . So you get a positive roll yield.

By saying your roll yield s F-S you’re misleading yourself . It is the measure of the difference in changes in Futures and changes in spot

I completey agree–I meant to write delta F - delta S.

Maybe the key here to thinking about it in the way I wrote in my second paragraph is that as the convenience yield increases and decreases F, the term structure become more “negatively steep” (i.e. more vertical), since S stays the same but F goes down more.

Then, you can say that delta F - delta S (i.e. roll return) is in fact larger, since each period, F has to “move more” to get to S since the convenience yield has made it lower.

Does that make sense to you?

any thoguhts?

I think you are looking at it just from the point of view of convenience yield which is wrong.

Interest rates will rise -> so rf will rise

Convenience yield will drop - do - y will drop

what will be the combined effect -> unknown - since you do not know the exact magnitude of each change.

cpk,

i understand that there are 2 differing effects that go in opposite directions and thats why the total effect is unkown/unchanged.

in my question, i was only focusing on the part of the answer dealing with the convenience yield, and trying to understand why the convenience yield increase causes backwardation and a roll return.

so the point in my last post was that the increased convenience yield causes F to be smaller, and since roll return is delta F - delta S, it becomes larger since F has to change more and more each period with a steeper negative term structure.

hoping to bump this in case anyone has since looked at the 2009 exam. just trying to fully understand why increase in convenience yield increases roll return, if we consider that roll return is the change in Futures price - change in spot price.

my guess is that since convenience yield decreases the numerator in the futures formula, F decreases. this causes a more negatively steep term structure. since F converges to S over time, each period the delta F is larger as it has to “clumb higher” to reach the spot price, thus increasing the roll return.

does this make sense?

pg 52 in v5 text

bottom of page states “all else being equal, an increase in a commodity’s convenience yield should lead to futures market conditions offering higher roll returns.”

Ok yea so what I wrote is correct. Above that it says "The positive return is earned because as the futures contract gets closer to maturity its price msut converge to that of the spot price of the commodity. Because in backwardation the spot price is greater than the futures price, the futurs price must increase in value.

Thanks.

^good point

you are correct , show NY