If the present value of storage costs exceeds the present value of its convenience yield, then a commodity’s forward price is most likely:

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When evaluating forward prices for commodities, the cost-of-carry framework tells us that forward price F0 is influenced by the spot price growth at the risk-free rate plus adjustments for storage costs and convenience yield.
Option 1: 'Higher than the spot price compounded at the risk-free rate' — This aligns with the usual cost-of-carry formula: if PV of storage costs exceeds PV of convenience yield, the net carry cost is positive, pushing the forward price above the risk-free-compounded spot. In other words, storage costs add a premium to carrying the commodity, so F0 > S0 e^{rT} (or S0(1+r)^T in discrete terms).
Option 2: 'The same as the spot price compounded at the risk-free rate' — This would imply zero net carry, meaning storage costs perfectly offset convenience yield benefits. That would require PV(storage) = PV(convenience yield). The given condition states the opposite (storage costs dominate), so this option is inconsistent with the scenario described.
Option 3: 'Less than the spot price compounded at the risk-free rate' — A forward price below the risk-free-compounded spot would indicate a net negative carry (benefits outweigh costs), which would occur if convenience yield is large relative to storage costs. However, the premise states storage costs dominate the reduction, not the increase, so this option contradicts the stated condition.
In summary, the relationship between PV(storage) and PV(convenience yield) determines the forward premium or discount: a higher PV(storage) relative to PV(convenience yield) implies a positive carry, hence F0 exceeds the risk-free growth of the spot price. The other options either imply a neutral carry or a negative carry, which do not fit the given comparison of present values.

BU.232.710.W1.SP25 Final Exam

If the present value of storage costs exceeds the present value of its convenience yield, then a commodity’s forward price is most likely:

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