Cost of carry: why dividends lower forward prices

Derivatives·July 30, 2026·4 min read

A forward-pricing question gives a spot price of 100, a dividend with a present value of 3, a 5% rate, and a one-year term. A candidate who treats every cash flow attached to the asset as a cost gets 108.15. The correct forward price is 101.85, because the dividend is an ownership benefit rather than an expense of holding the asset.

Carry begins with ownership

Cost of carry is the net economic effect of owning an asset until the forward contract expires. Storage and insurance consume value during that period, while dividends, coupons, and convenience yield provide value to the owner. The forward buyer receives none of those ownership benefits before expiry, so the pricing equation adjusts the spot price for what ownership costs and what ownership gives back.

F₀ = [S₀ + PV(costs) − PV(benefits)] × (1 + r)^T

The timing inside the brackets matters as much as the signs. Each cost and benefit must be expressed as a present value at time 0 before it is added to or subtracted from the spot price. Only that adjusted amount is then carried forward by the interest-rate term. Mixing a future cash flow directly with S₀ would put amounts from different dates into the same calculation.

Present value is doing real work here. The bracket creates a time-0 snapshot of the trade, where the spot price, ownership expenses, and ownership benefits become comparable because every amount has been placed on the same date.

The sign follows the holder

The labels can be deceptive, especially when a question is dense with unfamiliar English. A dividend may look like another obligation associated with the asset, but from the holder's perspective it is money received. That makes it a benefit and places it on the subtraction side. An insurance payment moves the other way: it is money the holder must spend, so it belongs with costs.

This treatment also explains why an ownership benefit lowers the forward price. Someone who buys the asset today receives that benefit during the holding period; someone who agrees today to buy it later does not. The forward price therefore reflects the value the forward buyer missed. Convenience yield follows the same classification even though it is an economic advantage of having the physical asset available, rather than a dividend or coupon deposited in cash.

Worked example

With S₀ = 100, a dividend present value of 3, r = 5%, and T = 1, the dividend enters as a benefit. It is already measured at time 0, so it sits inside the brackets with the spot price before the adjusted amount is compounded for the term.

F₀ = (100 − 3) × 1.05 = 101.85

The tempting 108.15 answer comes from adding the dividend instead. That single sign change treats cash received by the asset holder as though it were a carrying expense, reversing the economics even though the remaining arithmetic is correct.

Quick reference

Convenience yield is the interpretation trap that the formula's compact notation can hide. It may not appear as a payment on a statement, yet access to the physical asset can still be valuable, particularly when immediate availability matters. Classifying inputs by whether the holder gains or gives up value is more reliable than looking only for a visible cash receipt.

This is the same timing trap as discounting the strike in put-call parity: in both, cash flows must be moved to a common date before their signs can be interpreted.

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