# 2009 Morning Roll Return

I’m confused about the answer for question 8 on the 2009 morning session.

Roll return = change in Futures price - change in spot price

but the answer only looks at the change in the futures price and doesn’t mention how the change in the spot price would affect the roll return. if the spot price is expected ti increase, wouldn’t that mean that the expectation for the roll return would be to decrease?

Roling return earned due to rolling of futures contract

if Rf > lease rate or convenience yield

then Forward rate > spot rate, so markets are in contango (roll return are +ve)…mean forward rates r higher than the spot rate

if Rf < than convenien yield, markets r in backwardation (means roll return are -ve)

In the ques: Smith expects both interest rate & convenience yield to increase hence ans is NO CHANGE

coz we are not given the magnitude of change in int rate & convenience yield. If Int rate increases more than convenience yield than roll return will increase

I think you may have written that backwards.

Roll return when markets are in contango is negative, and positive when in backwardation.

dapoopa is correct.

In a downward sloping term structure of futures prices (i.e backwardation), closer the contract is to maturity, higher the roll yield. A positive return will be earned from a simple buy and hold.

I realize it.

Yes, if the forward is higher than the spot rate (i.e. contango), rolling return are -ve. The best way to understand this relationship is in example of Stack & roll.

In ques, Covenience yield increase would decrease the forward rate. So rolling return would be +ve. However increase in interest rate is expected to increase forward rate means -ve rolling return.

So, it doesn’t matter what the spot rate does as long as Rfr > Convenience Yield?

My thought was that these factors only affected the futures price - eg No Change. However, if the futures price does not change and the spot prices are expected to increase, then there would be a decrease in the Roll Yield. Why do we not factor in the spot price?

AFAIK, rolling return is what you earn due to rolling of expired future contract with new term futures. So it’s not actually difference due to change in future & change in spot. It is rather earned due to rolling of futures contract.

In terms of financially settled future contract let take an eg: Suppose I have gone short of a future contract expiring in the month of April @100. So on or before expiry, I would require to close this position or square off by taking opposite position. To continue to be hedged I would again take position in the next month. If there is difference i would make gain/loose rolling yield. On expiry lets say April futures is trading @ 102 & May month future @ 103. I would buy April future @ 102 to close (loss 100-102= - 2) & would short May month future @ 103 (rolling gain 103-102). Would continue rolling till the desired period.

However as explained in the text Hedger is looking to hedge for a series of obligation falling every month for one year period (Strip hedge). So he may get position in 12 contracts expiring in the next Twelve months. However far end futures contract are very thinly traded so high spread in Bid n Ask results in higher txn cost. So hedger may choose to take position only for the next month which he will roll over every month to continue to have position in futures in every month (Strap hedge) & may earn/loose due to rolling of futures.

Hope I made my point clear.

Text says

The spot return or price return is calculated as the change in the spot price of the underlying commodity over the specified time period. The spot return measures the change in commodity futures prices that should result from changes in the underlying spot prices, according to the cost of carry model

Now, it means some portion of change in futures is due to change in spot itself. Lets suppose if change in futures is 6 & change in spot is 3. Does this mean that 6-3=3 is due to roll return?

As per formula

Return on commodity return index = spot return+collateral (which is basically risk free return)+roll return. In ehibit 16 (P.No 52) they calculated roll return difference between change in future - change in spot

It also says that if market are in backwardation, positive return will be earned by following Buy & Hold.

If spot are higher than futures & it is expected that future will converge to spot at time of expiry (means will increase). However, Is only one period considered here?

I guess so, otherwise if we have multilple period than we would require to roll & in that case this would not be a buy & hold strategy. Is in it?

buy and hold implies you are always long the first contract .as that contract appears close to expiration you sell and enter the next delivery contract and so on.if the term structure is always backwardated you will derive a positive return simply by earning the roll yield at each and every roll

So it should n’t be taken as (buy & hold) do-nothing strategy because you r rolling at each expiry.

Yes .

If you want the roll return you have to roll.

Also the exchange will usually not let you hold all the way to expiration if you’re not a true hedger. You have to exit about 1 or 2 days prior , if you’re a speculator

Why would you take delivery when your intention is only to profit?

If convenience yield increases and Rfr decreases then Fwd price decreases (change in Fwd price is neg). As long as spot prices stay the same, this means that the roll return becomes more favorable. whether that means going from a return of 1 to 2% or from -3 to -2%. it does not necessarily mean that markets are in backwardation, just trending that way. Now if the spot price moves as well the change in the spot price could cause the market to be further in backwardation, revert back towards contango, or exactly offset the futures price decrease.

I think you have to keep the change in the spot rate in mind when deciding whether the roll return is increasing or decreasing. Is this not correct?

market is said to be in backwardation whenever the futures price is below the spot.

That is an absolute measurement. There is nothing relative about it.

For the futures price to be below spot , the (RiskFree-convenience+storage) has to be negative.

That number is actually the risk premium paid by the hedger to the speculator for buying and storing the commodity and just for the convenience of having it with certainty

The book says that when markets are in backwardation, a positive return is earned from a buy and hold strategy. Backwardation is when Futures price < spot price. Roll return = change in futures price - change in spot. This all makes sense because if the futures price is less than the spot then it rises to the spot price. so say:

Futures price at time t = 2 and spot = 3; then at time t+1 the Futures price would = 3 and roll return would be 1. this indicates a positive roll yield while in backwardation.

next example: If (RiskFree-convenience+storage )))))))=0 then the Futures price is = to the spot. no matter what the spot does (go up, down) the futures price will converge and there will be no roll yield (correct?). so say there is a problem with the orange harvest this year and the spot price goes from 32 to 104, because the futures price will converge to the 104 final spot, the roll yield would be (104-32) - (104-32) = 0.

It doesn’t matter what the expectations are for the spot at time t, if the futures price = the spot at the beginning of the contract then there is no roll yield.