Summary of commodity futures returns & a question

Just did 2009 AM and f’ed up the futures question massively. A question on that below this summary: Is this an accurate summary of yields on futures? (a) Spot return: 1. Go Long Spot commodity and sit on it, 2. Sell it in the future for a higher amount as implied by forward curve in contango. (b) Collateral Return 1. Go Long futures contract 2. Invest in (discounted) T-bill with face value equal to futures contract which you post as margin(collateral) on your futures (hence the term 'Colateral return). 3. Any dfference between Futures at thime of settlement using the cash you invested and the new spot price is your collateral yield Collateral return being very similar to spot, albeit with the collateral the position becomes physical at the end of the period, not the beginning as with spot. © Roll Return 1 buy a far away futures contract today. Sell the same futures contract in 2 weeks/a month whatever when the expiration date is less far away. Run home grinning to tell your dad that you just cheated backwardation. 2. Reset - repeat step 1. You never actually physically own the commodity - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - So in the 09 AM (Q8) Spot return is +ve because the mg expects SPOT PRICE to rise (somethime between now and the expiration date) Hence he’s buying now before the market prices this into the curve, and selling after it has, when prices are higher. Also, the futures in question is short term, and hence assumed to be highly sensitive to the spot price. He would lose money if he bought after the market had priced this in, because the spot product would be disporportionately priced relative to the futures. I f’ed this because I assumed he wouldn’t have bought until this spot price change had happened…for some reason. Collateral return Similar to the above - the market hasn’t yet reacted to expected price shocks. Hence he locks into a fully collateralise futures price, and so when this goes up, he wins. Question: If his t-bill wasn’t a perfect match for the futures expiration date, there’s be price risk (i.e. a reduction in price) on the bond that would offset the futures gain given the interest rate rise, right? I f’ed this because I assumed that offset I described above would happen. Roll return: Argument is that the backwardation produced by the increased convenience yield magically exactly nets off with the interest rate contango effects.

I can’t answer the question regarding the 2009 exam yet, but the return on a commodity should be in my opinion: -the futures return (including convenience yield) + collateral return (on cash) (assuming no storage costs). It cannot be any other way. If you back out the convenience yield, you can also say that you earn: -the futures return (net of convenience yield) + collateral return + roll return (from convenience yield). They call the first term “spot return” but it is really the spot-return minus RFR. So in my opinion it is then also: -Actual spot return - RFR + collateral return (RFR) + roll return (convenience yield) =Actual spot return (holding the commodity) + convenience yield That would make sense, and it cannot be any other way in my opinion. You can’t earn the actual spot return and then again earn the RFR. What they probably mean in the book with the “spot return” is the short-term futures return (backing out convenience yield, but not doing anything regarding RFR). RFR is then earned on the collateral.

Okay, I think I got it now what they mean in the curriculum. The roll-return is not just the convenience yield but also includes the cost of RFR. That’s their definition, i.e. the change in futures vs. change in spot, therefore the exp(r-y) term in F=S*exp(r-y)(t). So with the RFR backed out of the futures return and put into the roll-yield, the first term is indeed the true spot return. So, adding onto my earlier interpretation: - Actual spot return + collateral return (RFR) + roll yield (conv. yield - RFR) which is again -Actual spot return + convenience yield. This is consistent with reality. So the roll yield goes up with increasing convenience yield, but it is not the same as the convenience yield. If the convenience yield is zero, the roll yield is minus RFR.

Okay, I looked at the 2009 example. It is consistent. -Actual spot return increases due supply shortage. -Collateral return increases due to higher interest rates. -Roll return, would increase with convenience yield and decrease with interest rates. (see my above post). Since we don’t know which one is larger, the best answer would be “No change”.