## Math of Forward Contract

on May 19th, 2022 at %I:%M %pForward contracts are an essential financial instrument that allows individuals and businesses to secure a future price for an asset, commodity, or currency. Forward contracts are customized agreements between two parties, where they agree to exchange an asset or currency at a predetermined price in the future. The math behind forward contracts is a critical component of understanding how they work and why they are so valuable in the financial world.

The formula for calculating the forward price of an asset is straightforward. It is the current spot price of the asset added to the cost of carry. The cost of carry includes the interest rate, the storage cost, and any dividends or income that the asset may generate during the contract period. The forward price is calculated as:

Forward Price = Spot Price + Cost of Carry

For example, let`s say a farmer wants to sell his wheat harvest next year. He expects the price of wheat to decline by the time of the harvest due to an oversupply of wheat in the market. To secure a favorable price, the farmer enters into a forward contract with a milling company to sell his wheat at a predetermined price one year from now. The current spot price of wheat is $5 per bushel, and the cost of carry is 3% per annum. The contract specifies a price of $4.50 per bushel for the wheat.

Using the formula above, we can calculate the cost of carry as follows:

Cost of Carry = Spot Price x Interest Rate + Storage Cost – Dividends

In this case, the formula calculates the cost of carry as follows:

Cost of Carry = $5 x 3% + $0 – $0 = $0.15 per bushel

Therefore, the forward price of the wheat is calculated as:

Forward Price = Spot Price + Cost of Carry

Forward Price = $5 + $0.15 = $5.15 per bushel

The milling company agrees to pay the farmer $4.50 per bushel for the wheat, which is below the forward price. By entering into the forward contract, the farmer secures a price of $5.15 per bushel, reducing his risk exposure if the price of wheat drops in the future.

In conclusion, understanding the math behind forward contracts is crucial for anyone looking to enter into one. The formula for calculating the forward price is straightforward, but the cost of carry can be a bit more complicated, depending on the asset or currency involved. By understanding this math, individuals and businesses can secure future prices for their assets or currencies and reduce their risk exposure in volatile markets.