### What is a Convenience Yield?

A convenience yield is the benefit or premium associated with holding an underlying product or physical good, rather than the associated derivative security or contract.

Sometimes, as the result of irregular market movements such as an inverted market, the holding of an underlying good or security may become more profitable than owning the contract or derivative instrument due to its relative scarcity versus high demand. Consider purchasing physical bales of wheat rather than wheat future contracts. If there’s a sudden drought, and the need for wheat increases, the difference between the first purchase price of the wheat versus the price after the shock would be the convenience yield.

### Convenience Yield Explained

The storage of a physical good or commodity closely relates to the convenience yield of products. However, there’s an inverse correlation between commodity prices and storage levels. Based on the levels of supply and demand, when storage levels of a commodity are scarce, the commodity's price tends to rise. The opposite is also true; when a commodity's storage levels are plentiful, the price typically decreases.

Convenience yields tend to exist when the costs associated with physical storage, such as warehousing, insurance, security, etc., are relatively low.

### Convenience Yield and Cost of Insurance

Investors can calculate the convenience yield as the cost of insurance against price risk. The formula is calculated by multiplying the price of a front-month futures contract by the capital cost of money that is tied up in inventory, or Euler's number raised to the borrowing rate multiplied by the time to maturity, then adding the storage cost and subtracting the price of the futures contract for the back-month contract. Next, divide this calculation by the price of the front-month futures contract and add one to the quotient. The resulting value is raised to the power of 365 divided by the number of days to maturity. Finally, subtract one from the resulting value.

### Key Takeaways

- A convenience yield is a premium associated with holding an underlying asset, rather than the associated derivative security or contract.
- Convenience yields typically arise when costs associated with physical storage are low.
- Investors need to know the commodity's future price, spot price, borrowing rate and time to maturity to calculate the convenience yield.

### Real World Example of Convenience Yield

The convenience yield is simple to calculate if a commodity's future price, spot price, borrowing rate and time to maturity are known. The futures price is calculated as the spot price multiplied by Euler's number, or the mathematical constant e, raised to the power of the difference between the borrowing rate and the convenience yield multiplied by the time to maturity. Consequently, the convenience yield is solved to be the difference between the borrowing rate and one divided by the time to maturity multiplied by the natural log of the futures price divided by the spot price. This formula is used for continuously compounding rates and yields.

For example, let’s say that a trader wishes to calculate the convenience yield of West Texas Intermediate (WTI) crude oil for delivery one year from today. Assume that the annual borrowing rate is 2%, the spot price of WTI crude oil is $50.50 and the futures price of crude oil contracts expiring one year from today is $45.50. Therefore, the convenience yield is calculated to be 12.43% continuously compounded per year, or 0.02 - (1/1) * LN($45.50/$50.50).