Forward price

What is a forward price?

A forward price is the pre-agreed price at which an asset (commodity, currency, or financial instrument) will be delivered at a specified future date under a forward contract. It is set so the contract has zero value at inception and is used primarily to hedge or lock in future prices.

Why it exists

Forward pricing is based on no-arbitrage logic: the forward price reflects the current spot price adjusted for the cost of carrying the asset to the delivery date (financing cost, storage, insurance, etc.) and for any benefits forgone (for example, dividends). One party’s gain in a forward is the other party’s loss — the contract is zero-sum.

Core formula (continuous compounding)

When the underlying pays no dividends and carrying costs are represented by a continuous financing rate, the forward price F is:

F = S × e^(r × t)

where:
* S = current spot price
* r = continuously compounded risk-free interest rate (annual)
* t = time to delivery (in years)
* e = Euler’s constant (≈ 2.71828)

If carrying costs are included as a continuous rate q (storage, insurance, etc.), the formula becomes:

F = S × e^((r + q) × t)

If the asset pays known discrete cash dividends, adjust the spot price by subtracting the present value of expected dividends D:

F = (S − D) × e^(r × t)

and D = Σ d_i × e^(−r × t_i), where d_i and t_i are each dividend amount and time.

Numerical example (no dividends)

S = $100, r = 6% (0.06), t = 1 year:

F = 100 × e^(0.06 × 1) ≈ $106.18

Example with quarterly dividends

Assume S = $100, continuous r = 6%, and four quarterly dividends of $0.50. Compute present value of each dividend:

• PV(d1) = 0.5 × e^(−0.06 × 3/12) ≈ $0.493
• PV(d2) = 0.5 × e^(−0.06 × 6/12) ≈ $0.485
• PV(d3) = 0.5 × e^(−0.06 × 9/12) ≈ $0.478
• PV(d4) = 0.5 × e^(−0.06 × 12/12) ≈ $0.471

Sum D ≈ $1.927. Then

F = (100 − 1.927) × e^(0.06 × 1) ≈ $104.14

Forward vs. spot price

• Spot price: the current market price for immediate delivery.
• Forward price: the pre-agreed price for delivery at a future date, derived from the spot price and carrying/financing adjustments.

Why investors use forward contracts

• Hedging: lock in prices to protect against adverse moves (e.g., farmers, exporters).
• Speculation: take directional views on future price movements.
• Price discovery and planning: enable predictable cash flows and budgeting.

Risks and drawbacks

• Unfavorable price movement: locking a price may lead to opportunity loss if market moves favorably.
• Counterparty/default risk: forwards are typically over‑the‑counter and subject to credit risk (unlike exchange-cleared futures).
• Liquidity and marking: long-dated contracts may be illiquid and harder to offset.
• Model assumptions: misestimating carrying costs, dividends, or discount rates leads to mispriced forwards.

Key takeaways

• Forward price lets parties fix a future delivery price based on spot price and carrying adjustments.
• Continuous-compounding formula: F = S × e^(r t) (adjust for carrying costs or dividends as needed).
• Forwards are useful hedging tools but carry counterparty and market risks that should be managed.