Interest rates and roll return

If we have the following expectations, why does increasing interest rates lead to decreasing roll return? -Electricity supply disruptions in South Africa, the world’s dominant gold producer, will cause gold supply to fall and spot prices to rise. - Interest rates will rise. - The convenience yield on platinum will increase.

Rising interest rates will drive investors out of gold and into bonds, decreasing the spot price.

Maybe I’m completely wrong but:

Roll yield (before expiration) = (Ft - Fo) - (St - So) = Change in forward price - change in spot price. So if the spot price increases (St) the roll yeild decreases.

Howver, at expiration Ft = St, so roll yield = -Fo - (-So) = So - Fo.

If interest rates rise, holding a future rather than the actual commoditybecomes more beneficial, because you get a greater collateral return (invest money you would have invested in commodity at the risk free rate). Due to this, future prices rise, hence decreasing your roll return.

Roll yield = (Future time t - Future at beginning) - (Spot time t - Spot at beginning) If the futures price rises (Future at time t), doesn’t this will increase our roll yield?

Fo = So x e^(r + c - y)(T-t)

Holding So the same, Fo increases when

  • r increases
  • cost of carry increases
  • convenience yield decreases

As Fo increases, these 2 can happen

  • increased degree of contango (where Fo > So)
  • decreased degree backwardation (where Fo < So) or even revert to a contango

in both cases, roll yield decreases as the forward becomes more highly priced relative to the spot