# Implied Rate

The difference between the forward/future rate and the spot rate

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## What is the Implied Rate?

The implied rate is an interest rate that expresses the difference between the forward/future rate and the spot rate. It serves as a useful tool for comparing returns across different assets and can be applied to any scenario that involves a forward or futures contract. ### Summary

• The implied rate is the difference between the forward/future rate and the spot rate.
• The forward/future rate is the predetermined rate to buy or sell an underlying asset in the future. The spot rate is the current market rate.
• The implied rate is useful for comparing returns across different assets.
• It can be applied to exchange rates, commodity prices, and stock prices.

### Understanding Implied Rates #### Forward/Futures Contracts

Forward and futures contracts are very similar; both engage in buying or selling an underlying asset in the future at a predetermined price or rate. The difference between the two is that the forward contract is over-the-counter (OTC), meaning that it is a private transaction. Therefore, it is more customizable for the parties involved and is settled only at maturity. On the other hand, futures contracts are regulated on options exchanges, less flexible, and settled daily.

Forwards and futures are used to lock in prices or rates in the future for hedging purposes. In the context of the implied rate, both forwards and futures can be used interchangeably.

The forward/future rate represents expectations of future value. For example, if silver is trading today at \$25 (spot price) and the futures contract price is \$30, it means that we expect silver to appreciate in the future.

Therefore, we can understand the implied rate as a way to compare returns across different assets. A positive implied rate means that future borrowing rates are expected to increase, while a negative implied rate suggests that future borrowing rates are expected to decrease.

#### Spot Rate

The spot rate is the current rate offered on the market. It represents the prevailing equilibrium value of supply and demand.

### Practical Examples

The implied rate applies in any scenario that involves futures/forward contracts; it includes exchange rates, commodity prices, and stock prices.

Exchange Rates

The current exchange rate is 1.3 CAD/USD. A forward contract maturing in 3 years comes with a forward exchange rate of 1.4 CAD/USD.

##### Implied Rate = (1.4/1.3)(1/3) – 1 = 2.5%

Commodity Prices

Crude oil is trading at \$52.85 as of April 2021. The futures price is \$60.13, with a settlement date in December 2021 (8 months to maturity).

##### Implied Rate = (60.13/52.85)(1/(8/12)) – 1 = 21.36%

Since the contract matures in less than a year, our T is 8 months out of the 12 months in a year. Our exponent (1/(8/12)) becomes 12/8, or 1.5.

Stock Prices

The S&P 500 Index is trading at \$4180.17 as of April 2021. A futures contract for September 2021 comes with a settlement price of \$4161.75 (5 months maturity).

##### Implied Rate = (4161.75/4180.17)(1/(5/12)) – 1 = -1.05%

Similar to the last example, our T is a fraction of a year. Therefore, the exponent is (1/(5/12)), which becomes 12/5 or 2.4.