# Why: Backwardation --> Roll Yield > 0 ?

Could someone please explain why roll yield is positive in case of backwardation? Ideally, explain mathematically, i.e. using some formula or equation. Thanks!

(Opposite for contango)

To get you started, we know

1. Backwardation: downward-sloping forward curve

2. Roll yield = change in futures price - change in spot price

Thanks!

Backwardation = rolling down the hill. When you roll down the hill you pick up positive roll yield.

As an investor, you may have to continually roll over your contracts as time passes. These contracts don’t cost as much as the previous contracts so you save money.

Spot curve is upward sloping (usually).

Futures curve is downward sloping in backwardation ( a longer out futures contract has a lower price than a more near term one).

But one aspect of the futures contract is that at expiration the futures contract price must converge to the Spot.

So that convergence gives u a higher return (resulting in a positive roll yield).

In backwardation futures price is downward sloping:

F0 < S0

On maturity date, futures price will converge to spot price

Ft = St

Implies:

St - S0 < Ft - F0 (Ft - F0) - (St - S0) > 0

Or if you think of it from this perspective. If futures price is below current spot price and at maturity futures price converges to spot price. Then futures price must increase more (or decrease less) than spot prices.

I like the way you prove this formula :D, so easily understand in terms of formula Thanks so much :x

perfect - i had a question whose answer would be exactly this. thanks a lot