Explain carrying costs and how they shift the forward price
The idea
The forward price equals the spot price compounded at the risk-free rate, adjusted for anything the underlying costs or yields while it is held. Storage and insurance raise the forward price because the seller must be compensated for carrying the asset; dividends, coupons and convenience yield lower it because holding the spot asset confers a benefit the forward holder does not receive. Where benefits exceed financing and storage costs the forward price falls below spot, which is the condition usually called backwardation.
Formulas
Forward price with carry costs and benefits
F₀ = (S₀ + storage − income) × (1 + r)ᵗ
- S₀
- the spot price today
- storage
- the present value of the cost of holding the asset
- income
- the present value of what holding it pays - dividends, coupons, a convenience yield
- r
- the risk-free rate
- t
- the years to delivery
Costs of carry raise the forward price and benefits lower it, because the buyer of the forward avoids the one and gives up the other. Income large enough makes the forward cheaper than the spot.
A practice question
What do dividends and coupons do to a forward price?
- Raise itWhy not: They accrue to whoever holds the asset, not to the forward buyer, which lowers what the buyer pays.
- Lower it - correct
- Leave it unchangedWhy not: Income is part of the cost of carry and moves the forward price down.
Dividends (cash paid by a company to its shareholders) and coupons (fixed interest paid by a bond) go to whoever owns the asset. The forward buyer owns nothing until delivery and gets none of this income. Forward price = Spot x (1 + r)^T - Income received. Because the buyer misses out, the price they agree to pay must be lower. So income on the asset lowers the forward price.
A harder one
What is convenience yield?
- The interest earned on margin posted against the forwardWhy not: Margin interest is a financing matter between the trader and the broker.
- The cost of storing the underlyingWhy not: That is storage, which works in the opposite direction on the forward price.
- The benefit of physically holding the asset rather than a claim on it - correct
Convenience yield is the benefit of holding the physical asset itself, for example a factory owner who keeps production running when supplies are short. Only the person holding the asset gets this benefit, so it works like a dividend. Forward price = Spot x (1 + r)^T + Storage costs - Convenience yield. It is subtracted, so it lowers the forward price. Storage costs work the opposite way and raise it.
The hardest tier
A commodity's forward price sits below its spot price. What does that imply?
- That the market expects the price to fallWhy not: Forward prices come from carrying costs and benefits, not from forecasts, so a forward below spot does not signal an expected fall.
- That holding benefits exceed carry costs - correct
- That storage costs are unusually highWhy not: High storage would push the forward price above spot, not below it.
Forward price = Spot + Financing cost + Storage costs - Benefits of holding the physical asset (such as convenience yield or income). If the benefits are bigger than the costs, the forward price ends up below spot. This is called backwardation. For example, spot $100 plus $5 financing less $9 of benefits gives 100 + 5 - 9 = $96. This only describes the cost and benefit of holding the asset. It is not a forecast that the price will fall.
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