how to understand why the roll yield is positive when the term structure of future price is downward sloping?

Assuming spot price stays the same, the futures price will rise to meet the spot price as it approaches. So you will gain by rolling over.

I don’t have the book in front of me, but I’ll post the page where it talks about this later.

So if the curve is backwardated, then the futures price, say 12 months out, is less than the spot price. Assuming the structure stays the same, as we move forward in time, that 12 month future becomes an 11 month future, 10 month, etc. and reprices to reflect the term structure, so you get appreciation as the future moves closer to maturity.

Thanks for the answers.

CFA Institute tells you that the roll yield is calculated as:

roll yield = Δforward price – Δspot price.

While this formula is accurate, it doesn’t provide much insight into what roll yield is. However, a little algebra yields (*pun only partially intended*):

roll yield = Δforward price – Δspot price

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

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

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

= profit on new forward – profit on old forward.

This last formula tells you what’s really happening: you have a positive roll yield when the profit on the new forward contract is higher than the profit on the old forward contract, and a negative roll yield when the profit on the new forward contract is lower than the profit on the old forward contract.

awesome magician , that’s magical

Thanks, janakisri.

This is the sort of thing I try to do in my classes: help make this stuff make sense. I hate the idea of memorizing formulae without understanding why they work.