What is a forward price?
A forward price is the delivery price agreed today for buying or selling an asset at a specified future date in an over‑the‑counter forward contract. It reflects the current spot price adjusted for the net cost (or benefit) of holding the asset until delivery (the “cost of carry”) so that the forward contract has zero value at inception under no‑arbitrage.
Key takeaways
– Forward price = spot price adjusted for time value of money and net carrying costs (storage, dividends, convenience yield, financing).
– Common formulas: continuous compounding forms are F = S · e^{r t} (no dividends/carry) and F = (S − PV(dividends)) · e^{r t} (discrete dividends).
– For assets that pay a continuous yield (q), F = S · e^{(r − q) t}. For carrying costs q (positive cost), F = S · e^{(r + q) t}.
– Forwards are OTC and customizable but carry counterparty credit risk; futures are exchange‑traded and marked‑to‑market.
– Investors use forwards to lock in prices (hedging) or to speculate; drawbacks include lost upside if price moves favorably, counterparty risk, and liquidity/rollover issues.
Understanding forward price: core concepts
– No‑arbitrage principle: The forward price is set so neither party can make a riskless profit at inception. That implies the contract’s value is zero at the start.
– Cost of carry: The net effect of financing the purchase, storing/insuring the asset, and any income received while holding it (e.g., dividends or convenience yield). These inflows/outflows change the forward price relative to the spot price.
– Direction of adjustments: Financing and storage costs push the forward price above the spot; expected income (dividends, convenience yield) reduces the forward price.
Common formulas (continuous compounding)
– No dividends or carry: F = S · e^{r t}
– Continuous dividend yield q: F = S · e^{(r − q) t}
– Carrying costs (expressed as continuous yield q): F = S · e^{(r + q) t}
– Discrete dividends (sum of present values D of dividends during life): F = (S − D) · e^{r t}
Where:
– F = forward price (delivery price)
– S = current spot price
– r = continuously compounded risk‑free rate over the contract life
– q = continuous yield (dividend yield, storage yield, or cost expressed as a continuous rate)
– t = time to maturity in years
– D = present value (discounted at r) of discrete cash dividends during the contract life
Practical steps to compute a forward price
1. Gather inputs:
– Current spot price S.
– Time to delivery t in years.
– Risk‑free rate r appropriate for t (use continuously compounded rate or convert appropriately).
– Any expected cash flows from the asset: discrete dividends, coupon payments, storage costs, convenience yield, etc. Decide whether those are best modeled as discrete cash flows (D) or as a continuous yield (q).
2. Choose the right model:
– No income/costs → F = S · e^{r t}.
– Continuous yield (dividend or convenience yield) → F = S · e^{(r − q) t}.
– Continuous carrying cost (storage/insurance) → F = S · e^{(r + q) t}.
– Discrete dividends → compute D (PV of each dividend) then F = (S − D) · e^{r t}.
3. Compute present value of discrete cash flows (if needed):
– For each dividend d(i) paid at time t(i): PV(d(i)) = d(i) · e^{−r t(i)}.
– Sum all PVs to get D.
4. Calculate forward price using the chosen formula.
5. Interpret the result: This is the price that equalizes the value of owning now and financing & holding until delivery versus entering the forward.
Worked examples
Example 1 — No dividends (continuous compounding)
– S = $100, r = 6% (0.06, continuously compounded), t = 1 year.
– F = 100 · e^{0.06 · 1} = 100 · e^{0.06} ≈ 100 · 1.061836 = $106.18.
Example 2 — Discrete dividends
– S = $100, r = 6% (continuous), t = 1 year. The security pays $0.50 every 3 months (four payments).
Step A: PV of each dividend:
– PV(d1) = 0.50 · e^{−0.06·(3/12)} ≈ 0.493
– PV(d2) = 0.50 · e^{−0.06·(6/12)} ≈ 0.485
– PV(d3) = 0.50 · e^{−0.06·(9/12)} ≈ 0.478
– PV(d4) = 0.50 · e^{−0.06·(12/12)} ≈ 0.471
Step B: Sum D ≈ 0.493 + 0.485 + 0.478 + 0.471 = 1.927.
Step C: Forward price: F = (S − D) · e^{r t} = (100 − 1.927) · e^{0.06} ≈ 98.073 · 1.061836 ≈ $104.16.
Example 3 — Continuous dividend yield or convenience yield
– If the asset has continuous dividend yield q = 2% and r = 6%, t = 1 year, then F = S · e^{(r − q)t} = S · e^{0.04}. For S = $100, F ≈ 100 · 1.0408 = $104.08.
Differences: forward price vs. spot price
– Spot price: the price for immediate delivery/settlement.
– Forward price: the pre‑agreed future delivery price. The difference reflects the net cost of carry and time value: F ≈ S compounded at the appropriate net rate over the contract life.
– At contract initiation forward value is zero (no arbitrage); over time it can become positive or negative as spot or rates change.
Why investors lock in a forward price (uses)
– Hedging price risk: Producers, consumers and portfolio managers lock prices to protect margins or asset values. Example: an airline hedges jet fuel, an exporter hedges foreign currency receipts.
– Certainty of cash flows and budgeting: Businesses can lock costs/revenues for planning.
– Speculation: Traders can take forward positions if they expect future spot moves and want customized exposures.
Drawbacks and risks of locking in a forward price
– Opportunity cost: If the spot price moves in a favorable direction, the hedger may miss the benefit.
– Counterparty (credit) risk: Forwards are OTC; the other party may default.
– Liquidity and exit costs: Forwards may be hard to offset early and can require negotiated termination (may be costly).
– Model risk and parameter uncertainty: Wrong assumptions about dividends, rates, or storage costs produce mispriced forwards.
– Basis risk: For hedgers using different instruments (e.g., futures vs. underlying exposure), imperfect correlation can leave residual risk.
Main factors that determine a forward price
– Current spot price S.
– Risk‑free interest rate r over the contract life (cost of financing).
– Expected income from the asset (dividends, coupons).
– Positive carrying costs (storage, insurance) or negative carrying effect (convenience yield).
– Time to maturity t.
– Market liquidity, credit spreads (for OTC forwards), and transaction costs (in practice can cause deviations from simple no‑arbitrage formulas).
Practical checklist before entering a forward contract
1. Confirm inputs: correct spot price, accurate time to maturity, appropriate discount rate.
2. Model the asset’s income and costs carefully (discrete vs continuous treatment).
3. Consider counterparty creditworthiness and whether collateral or credit support annex (CSA) is needed.
4. Compare forward to futures if exchange clearing is preferred (futures mitigate counterparty risk but have daily margining).
5. Evaluate the cost of exiting or rolling the position before maturity.
6. Document the hedge objective and metrics to monitor hedge effectiveness (e.g., hedge ratio, basis risk).
The bottom line
The forward price is the no‑arbitrage delivery price agreed today for a future trade. It is a function of the current spot price, the time value of money, and the net costs/benefits of carrying the asset to the delivery date (dividends, storage, convenience yield, financing). Properly computing and using forward prices allows market participants to hedge, lock in prices, and arbitrage pricing differences—while remaining mindful of counterparty risk and opportunity costs.
Source
Adapted and summarized from Investopedia (Michela Buttignol): “Forward Price” (Investopedia.com). Additional standard results follow from the cost‑of‑carry/no‑arbitrage framework in derivative pricing.