Implied Rate: Definition, Formula, and Examples
The implied rate measures the percentage difference between a security’s spot price and its forward or futures price over a given time period. It’s a useful way to compare expected returns across assets and to infer market expectations about future interest rates or carrying costs.
Key takeaways
- The implied rate is derived from the ratio of a forward (or futures) price to the spot price, adjusted for contract length.
- It applies to commodities, equities (with forwards), currencies, and any asset with a forward/futures market.
- A positive implied rate indicates higher expected future borrowing or carrying costs relative to the current spot environment.
- Formula: implied rate = (forward / spot)^(1 / time) − 1, where time is in years.
How it works (formula and steps)
- Take the forward (or futures) price and divide it by the spot price.
- Raise that ratio to the power of 1 divided by the contract length in years.
- Subtract 1 to convert the result to a percentage.
Formula:
implied rate = (forward / spot)^(1 / time) − 1
Example interpretation: If the implied rate is 3% for a one-year contract, the market implies an annualized cost or return of 3% embedded in the forward price versus the spot.
Practical examples
Commodities
Spot price for oil = $68
One‑year futures price = $71
Implied rate = (71 / 68)^(1 / 1) − 1 = 4.41%
Stocks (forward contract)
Spot price = $30
Two‑year forward price = $39
Implied rate = (39 / 30)^(1 / 2) − 1 ≈ 14.02%
Currencies
Spot rate (EUR/USD) = 1.2291
One‑year futures rate = 1.2655
Implied rate = (1.2655 / 1.2291)^(1 / 1) − 1 ≈ 2.96%
Uses and interpretation
- Compare returns across different asset classes or contract maturities.
- Infer market expectations of future interest rates or carrying costs.
- Identify potential arbitrage opportunities when the implied rate diverges from financing costs or known carry.
- Applicable whenever a forward/futures market exists; adjustments may be needed for known dividends, storage costs, or convenience yields that affect forward prices.
Bottom line
The implied rate succinctly translates the gap between spot and forward/futures prices into an annualized percentage. It is a practical tool for investors and traders to compare expected returns, evaluate risk/return characteristics, and gauge market expectations of future interest or carry costs.