Implied Rate: Definition, Calculation With Formula, and Example

What Is the Implied Rate?

The implied rate is the difference between the spot interest rate and the interest rate for the forward or futures delivery date.

Understanding the Implied Rate

The implied interest rate gives investors a way to compare returns across investments and evaluate the risk and return characteristics of that particular security. An implied interest rate can be calculated for any type of security that also has an option or futures contract.

For example, if the current U.S. dollar deposit rate is 1% for spot and 1.5% in one year's time, the implied rate is the difference of 0.5%. Alternatively, if the spot price for a currency is 1.050 and the futures contract price is 1.1071, the difference of 5.71% is the implied interest rate. In both of these examples, the implied rate is positive, which indicates that the market expects future borrowing rates to be higher than they are now.

To calculate the implied rate, take the ratio of the forward price over the spot price. Raise that ratio to the power of 1 divided by the length of time until the expiration of the forward contract. Then subtract 1.

• Implied rate = (forward / spot) raised to the power of (1 / time) - 1

where time = length of the forward contract in years

Implied Rate Examples

Commodities

If the spot price for a barrel of oil is $68 and a one-year futures contract for a barrel of oil is $71, the implied interest rate is:

Implied rate = (71/68)^(1/1) -1 = 4.41%

Divide the futures price of $71 by the spot price of $68. Since this is a one-year contract, the ratio is simply raised to the power of 1 (1 / time). Subtract 1 from the ratio and find the implied interest rate of 4.41%.

Stocks

If a stock is currently trading at $30 and there is a two-year forward contract trading at $39, the implied interest rate is:

Implied rate = (39/30)^(1/2) - 1 = 14.02%

Divide the forward price of $39 by the spot price of $30. Since this is a two-year futures contract, raise the ratio to the power of 1/2. Subtract 1 from the answer to find the implied interest rate is 14.02%.

Currencies

If the spot rate for the euro is $1.2291 and the one-year futures price for the euro is $1.2655, the implied interest rate is:

Implied rate = (1.2655 / 1.2291)^(1/1) - 1 = 2.96%

Calculate the ratio of the forward price over the spot price by dividing 1.2655 by 1.2291. Since this is a one-year forward contract, the ratio is simply raised to the power of 1. Subtracting 1 from the ratio of the forward price over the spot price results in an implied interest rate of 2.96%.