How do you price a forward contract using the no-arbitrage framework? I keep mixing up the cost-of-carry components.

Forward pricing rests on one core idea: you should be indifferent between (a) buying the asset today and holding it, or (b) entering a forward contract to buy it later. If these two strategies don't cost the same, an arbitrageur will exploit the gap until they converge.

The General Formula:

F(0,T) = S0 x e^((r + storage - convenience) x T)

Or in discrete form:

F(0,T) = (S0 + PV(Storage) - PV(Convenience)) x (1 + r)^T

Where:

• S0 = Current spot price
• r = Risk-free rate (financing cost)
• Storage = Cost to physically hold the asset
• Convenience yield = Implicit benefit of holding the physical asset (e.g., avoiding production shutdowns)

Worked Example — Gold Forward:

Gold spot price: $1,950/oz. Risk-free rate: 4.5% annually. Storage: $12/oz per year. No convenience yield. 6-month forward.

F(0, 0.5) = ($1,950 + $12 x 0.5) x (1.045)^0.5

= $1,956 x 1.02225

= $1,999.51/oz

For Financial Assets (equities, bonds):

Replace storage and convenience yield with dividends or coupons:

F(0,T) = (S0 - PV(Dividends)) x (1 + r)^T

Suppose a stock trades at $85, pays a $2 dividend in 3 months, and the risk-free rate is 5%. Price a 6-month forward:

PV(Div) = $2 / (1.05)^0.25 = $1.976

F(0, 0.5) = ($85 - $1.976) x (1.05)^0.5 = $83.024 x 1.02470 = $85.07

Key Intuition: The forward price is NOT a forecast of where the spot will be. It's a mechanically derived price that prevents arbitrage today. If the actual forward trades above this value, you'd sell the forward and buy spot (cash-and-carry arbitrage). If below, you'd do the reverse.

Practice forward pricing with different underlying assets in our CFA Level II question bank.