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

Backwardation: downward-sloping forward curve

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

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 donâ€™t cost as much as the previous contracts so you save money.

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.