Forward Price
Forward Price
The delivery price at which a forward contract has zero value today: the spot price grown at the risk-free rate less any income the asset pays while held, with continuous compounding. Any other price would let an arbitrageur lock in a riskless profit.
When to use: Use for forwards on stocks, indexes and currencies, where the asset pays a known yield (dividends, foreign interest). For commodities with storage costs use the futures price with cost of carry.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| ForwardPrice | Forward Price | No-arbitrage delivery price | $ |
| S | Stock Price | Current price of the underlying | $ |
| Rf | Risk-Free Rate | Continuously compounded annual risk-free rate as a decimal | % |
| IncomeYield | Income Yield | Continuous yield the asset pays while held (dividend yield, foreign rate), as a decimal | % |
| T | Time to Expiration | Time to expiration in years (e.g. 0.25 for 3 months) | years |
Real-Life Examples
Example 1: One-Year Forward on a Dividend Stock
Stock at $100 with a 2% dividend yield; risk-free rate 5%; one-year forward.
Given
Step-by-Step
The forward is above spot because financing the stock costs 5% while holding it earns only 2%. The holder of the forward gives up the dividends and saves the financing.
Example 2: Six-Month Index Forward, No Income
Index at 2,500, no dividends, risk-free 4%, six months.
Given
Step-by-Step
With no income the forward simply grows at the risk-free rate: $50.50 of carry over six months.
Frequently Asked Questions
Whoever holds the stock until delivery collects the dividends; the forward buyer does not. The forward price is reduced by the value of that income to keep the two positions equivalent.
Under constant interest rates, yes. Futures are marked to market daily, which introduces a small difference when rates and the asset are correlated; the difference is ignored here.