Roll Return Calculation

CFA Level III
#1

Contract price Spot price

March 1,289 1,244

April 1,132 1,101

May 1,215 1,195

Assue all prices and contract expiration are at month’s end and the risk-free rate is 2%. Estimate the roll return for June.

The answer is -20, why?

#2

Where did you get this question from?

#3

1215 - 1195

since you are not wanting to take delivery of the 1m barrels of oil, your only choice is to sell on the spot market (at a loss)

we ignore transaction costs, margin funding etc. thats why they say estimate

#4

The risk-free rate is useless here?

#5

Kaplan Practice Exams

#6

Yes: the risk-free rate doesn’t enter into it.

#7

wait, I thought Roll Return = Change in Futures - Change in Spot ?

#8

Yes !

#9

Then why isnt the answer -11?

(1215 - 1132) - (1195 - 1101)

#10

Because somebody . . . um . . . erred.

#11

Then why aren’t you writing these exams S2000 Magician?

#12

Ain’t that just the question?

#13

  1. that would be for may

  2. your formula says are rolling the futures position, but you are also rolling a short physical position, so the 1101 must be invested at rfr.

  3. roll yield only involves futures, not taking a physical position.

can I have my charter now?

#14

Hi ,

The Roll Return for the month of June is the difference between the spot as of end of may (begining of June ) and the Futures price for the June contract as of End of May. The spot is 1,195 and the futures price is 1,215.

If you Buy the Futures contract you have to pay 1,215 at the end of June for the asset which will be delivered to you. The Spot is 1,195. If the Spot doesnt change, your Futures Contract one second prior to maturity is worth the spot price (convergence of futures to spot). WHich means the Futures that you bought for 1,215 will be worth 1,195 even if the spot price doesnt move a penny. So you have lost 1,195 - 1,215 = -20 on the contract due to Roll Return : Spot - Futures.

to fully get this, imagine the spot closed at 1,200 at the end of June. So the spot appreciated by +5. Your futures one second prior to its maturity in June has the same price as the spot i.e. 1,200. You bought your futures for 1,215 remember, and it is now worth 1,200. You lost 15 on this trade. Notice however that the spot appreciated by +5. You still lost -15. Thats because the spot return is 5 but the roll return as explained above is fixed if you hold to maturity your contract and is -20. so +5 - 20 (spot return + roll return) sums up to your return and this futures trade.

dont forget that if collateral was posted for that trade, the return on that collateral (in the form of T bills for example) would be added to the futures return to compute the TOTAL return on the trade i.e. spot return + roll return + collateral return. Only the first 2 (spot and roll returns) are components of the future returns. the third one is the collateral return and is a component of TOTAL retrun.

hope that helps.

cheers

#15

Thank you, but I do have a follow up question. How would I differentiate within the question between: Roll Return = Change in Futures - Change in Spot and Roll Return= Spot - Futures contract price?

#16

Roll Return is the same and the 2 formulas above refer to the same concept.

take an example:

Spot Gold today is 100

Futures 1 month Gold = 102

The Roll Return if you buy this futures and you hold to maturity is Spot - Futures = -2. The reason was explained above since even if the spot doesnt change and remains at 100, the futures at maturity would converge to the spot and would be 100 too. So you bough ta futures for 102 and at maturity it is worth 100 so you lost 2 henc ethe Roll Return of -2.

This - 2 will always be the difference between the change in Futures and Change in Spot at maturity for any closing price.

Example: Spot closed at 106, so it changed by +6

Futures converges to spot at maturity so it is also worth 106. You bought it at 102 so change is +4

Roll Return is - 2 of course.

You should understand that the -2 is a loss on your futures contract that you will incurr for sure if you hold to maturity. its simply because futures was in contango and you’re buying the futures for more than the spot. since at maturity futures and spot are the same, there is a full +2 increase in the spot that you can’t capture. i.e. the change in the futures would always lag the change in spot by the 2 dollars which simply are the difference between spot and futures.

final example to consolidate:

Spot closed at 102. So spot increased by +2. Futures at maturity is = spot = 102. NO GAINS ON FUTURES. because you bought it for 102. notice how the +2 increase in the spot wasnt captured because the futures started at 102. any increase beyond 2$ by the spot would be captured in the futures.

hope that helps.

cheers

#17

Thanks CFALEB!

#18

Very good explanation