What is the Cost of Carry in Derivatives?

Derivatives, which are the financial instruments derived from underlying assets like stocks, bonds, commodities, or currencies, have recently gained significant popularity. They allow investors to manage risks, engage in speculative activities based on future price movements, and enhance their returns.

Nevertheless, derivatives can be intricate and may pose challenges, particularly for individuals new to finance. One fundamental concept investors should grasp when trading derivatives is the cost of carry. This concept holds significant importance in the pricing of derivatives, and acquiring a clear understanding of it is vital for successful trading within these markets.

What is the Cost of Carry?

The cost of carry in the realm of finance can be described as the expenses incurred when holding an asset over a period of time. Specifically for derivatives, the cost of carry pertains to the expenses associated with holding the underlying asset, which is utilized to determine the price of the derivative. This encompasses factors like the cost of financing the asset purchase, including interest rates and storage costs, and any income the asset generates, such as dividends or interest payments.

The cost of carry holds a greater significance when it comes to pricing and trading derivatives, as it can substantially influence the value of a derivative contract.

How to Calculate the Cost of Carry?

The cost of carry plays a crucial role in determining the price of a futures contract. It is derived by subtracting the current spot price of the underlying asset from the futures price. The cost of carry represents the expenses associated with holding a long position in a futures contract over time, including the cost of financing the position, storage costs, and other relevant expenses.

Calculating the cost of carry requires knowledge of both the current spot price of the underlying asset and the futures contract price. The formula to calculate the cost of carry is as follows:

Cost of carry = Futures price – Spot price

Suppose the current spot price of the Nifty 50 index is 15,000, and the futures contract for delivery in one month is trading at 15,100. To calculate it, for holding a long position in this futures contract, we can use the formula:

Cost of carry = Futures price – Spot price

So, in this case,

Cost of carry = 18,100 - 18,000 = 100

This means that holding a long position in the Nifty 50 futures contract for one month would cost Rs. 100 per index point in financing costs, storage costs, and other expenses.

If it is positive, it indicates that it is more expensive to hold a long position in the futures contract than to hold the underlying asset. Conversely, if it is negative, it indicates that holding a long position in the futures contract is less expensive than holding the underlying asset.

Factors that Affect Cost of Carry

Several factors can affect it for a derivative, including:

Applications of Cost of Carry in Derivatives Trading

The concept of cost of carry holds significant importance in derivatives trading and finds numerous applications across various trading strategies. It is a key factor in basis trading, carry trading, hedging, and arbitrage strategies.

Basis Trading

Basis trading is a commonly employed trading strategy that leverages the cost of carry to capitalize on disparities between the futures and spot prices of an underlying asset. This strategy entails assuming a long position in a futures contract while taking a short position in the underlying asset. The objective is to benefit from the eventual convergence of the futures price and the spot price of the underlying asset.

To illustrate, if the futures price exceeds the anticipated spot price, an investor may choose to go long on the futures contract and short the underlying asset. As the futures contract nears its expiration date, the futures price will gradually align with the spot price, generating profits for the investor.

Carry Trading

Carry trading is a strategy investors employ to take advantage of the interest rate differential between two assets. It involves purchasing a high-yielding asset while simultaneously selling a low-yielding asset. The profitability of this strategy relies on the cost of carry, which encompasses the financing expenses incurred by the investor.

For instance, an investor may buy a currency with a higher interest rate and sell a currency with a lower interest rate, capitalizing on the disparity in interest rates. Nevertheless, the investor must also take into account the cost of carry associated with holding both currencies, which includes financing costs and any applicable storage expenses.

Hedging

Hedging, a commonly employed strategy in derivatives trading, heavily relies on the cost of carry. It involves taking a position in a derivative instrument to mitigate risks associated with the underlying asset.

For instance, let's consider a company susceptible to price fluctuations in a particular commodity. To hedge its position, the company can employ futures contracts. By taking a long position in a futures contract, the company locks in a predetermined price for the commodity, thus protecting itself from potential price fluctuations in the future. The cost of carry assumes a critical role in evaluating the effectiveness of the hedging strategy as it factors in the financing expenses associated with the position.

Arbitrage

Arbitrage is a widely employed strategy in derivatives trading that leverages the cost of carry. It involves capitalizing on price disparities across multiple markets to generate profits. The cost of carry is a valuable tool for identifying potential arbitrage opportunities by assessing whether a specific market is overvalued or undervalued.

For instance, if the cost of carry for a particular futures contract displays a negative value, indicating that the underlying asset is in backwardation, an investor could opt to purchase the futures contract while simultaneously selling the underlying asset. As the futures contract nears its expiration date, the futures price will gradually converge with the spot price of the underlying asset, resulting in favorable returns for the investor.

Futures Cost of Carry Model

The futures cost of carry model is a mathematical framework employed to determine the equitable price of a futures contract by considering the cost of carry. This model operates under the premise that the price of a futures contract should accurately reflect the expenses associated with holding the underlying asset from the current period until the delivery date of the futures contract. By incorporating factors such as financing costs, storage expenses, and other carrying costs, the futures cost of carry model assists in estimating the appropriate futures contract valuation.

The formula for the futures cost of carry model is:

F = Se ^ ((r + s - c) x t)

Where F is the fair price of the futures contract

S - the spot price of the underlying asset

e - the mathematical constant approximately equal to 2.7181

r - the risk-free interest rate, s is the storage cost

c - the convenience yield

t - the time to expiration of the futures contract.

The futures cost of carry model is built upon the assumption that the price of a futures contract is the sum of the spot price and the cost of carry. This cost of carry encompasses various factors, including financing costs, storage expenses, and any other charges incurred while holding the underlying asset until the delivery date of the futures contract. The storage cost represents the expenses associated with storing the asset, while the convenience yield signifies the advantages gained from holding the asset, such as the income generated through leasing.

The risk-free interest rate, which reflects the time value of money, indicates the return rate of a risk-free investment like government bonds. The time remaining until the futures contract expiration date denotes the duration between the present moment and the contract's delivery date.

By employing the futures cost of carry model, traders and investors can compute the fair price of a futures contract and compare it with the actual market price. This evaluation helps determine whether the contract is overvalued or undervalued. The contract is deemed undervalued if the fair price exceeds the market price, potentially presenting a buying opportunity. Conversely, if the fair price is lower than the market price, the contract is overvalued, suggesting a selling opportunity may exist.

Conclusion

Understanding the cost of carry is essential for derivative traders, as it significantly impacts the pricing of futures and options contracts. By grasping the concept of cost of carry, investors can uncover opportunities for profitable trading strategies like basis trading, carry trading, hedging, and arbitrage.

However, it is crucial to recognize the assumptions underlying the cost of carry model and acknowledge its limitations. Investors should also consider additional factors influencing derivatives pricing, including interest rates, volatility, and geopolitical events. Moreover, it is important to be mindful of the risks associated with derivatives trading and establish a robust risk management strategy.

While the cost of carry provides a valuable framework for comprehending derivatives pricing and formulating successful trading strategies, it should be utilized with other analytical tools. Furthermore, investors should exercise caution, carefully evaluate the risks involved, and consider the broader context when trading derivatives.

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