Cash and Carry Arbitrage

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Last Updated:January 7, 2024

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What is Cash-and-Carry Arbitrage

Cash and carry arbitrage (C&C) is an arbitrage technique resulting from differences in expected future prices and the current spot price of the commodity. C&C are exploitable and can result in risk-free arbitrage but require calculation and timing.

The arbitrage is derived from the spot market of the commodity and the expected future price. C&C is used when the spot price is deliberately lower than the futures price. This is intentional, as this strategy involves going long on spot markets and short on futures.

More intentionally, the market requires it to be in contango. This means the spot price is lower than the commodity's futures price.

What this strategy entails is to deliberately exploit the difference or delta between the two prices that exist. With contango, the future price will tend to the commodity's spot price as time progresses. Under the right market conditions, the investor can make a risk-free profit.

Essentially, this strategy entails the investor going long on the commodity; at the same time, he goes short on the futures with the commodity he is long as collateral.

When the difference between the futures price and the spot price is extremely close to zero, he settles the short contract using the commodity he is long, resulting in a profit of precisely the difference of prices when he bought the contract and the commodity, and with all positions closed.

This strategy is market neutral as there will not be any positions in the market after C&C is conducted.

Of course, since there are commodities involved, along with the holding period required for the commodity before it can be settled with the short contract, there are several costs involved in this C&C arbitrage that investors should take note of that do not supersede the difference of prices.

If these costs exceed the difference between prices, the investor will get a net loss in terms of profits.

Key Takeaways

Cash and carry arbitrage exploit price differences between a commodity's spot and futures markets.
It involves going long on the commodity in the spot market and short on futures to profit from price convergence.
Factors such as riskless rate, time, commodity beta, market risk premium, storage costs, convenience rate, commodity discount rate, and exponential growth rate should be considered.
Careful evaluation of costs is crucial to ensure they do not exceed the price difference between spot and futures markets.
Risks include changes in storage rates, convenience rates, and other factors that can impact profitability.
Cash-settled futures or non-commodity equity can be used as alternatives to mitigate risks.
Reverse cash and carry arbitrage, going long on futures and short on spot markets, is less common but used in markets experiencing normal backwardation.

Spot and forward markets

Take note that although the term “spot price” refers to commodities immediately bought at the current market price due to delivery times, forwards can also be used as an almost equivalent term for “spot” markets.

Although “spot prices” indicate commodities for immediate delivery, in this case, the producer cannot immediately issue the commodity for delivery and might have the requisite delivery time required to deliver the product above one day.

For instance, in the crude oil market, owing to the time required to deliver the oil to investors, the oil (barrel) would usually be delivered to the investor who goes long in the spot markets for oil in about a month. Going long in a forward contract would achieve the same result.

Hence, for the market for crude oil, the forward and spot prices are the same, as well as the delivery time. Forward prices are contingent on market conditions at the time of the transaction, and spot prices are treated the same in this respect.

Factors affecting cash and carry arbitrage profits

To identify arbitrage opportunities, the commodity's futures price must be considered. In essence, this is finding the outright asset purchase price of the commodity and holding it from now until the expiration date of the future.

Various factors should be taken into consideration for holding outright asset purchases:

Factors To Be Considered For Holding Outright Asset Purchase
Factors	What Is It
Riskless rate	The riskless rate of holding securities that ensures returns with no risk, for instance, US T-bills
Time	The time period of holding the commodity
Commodity beta	How volatile the commodity is vis-a-vis the market’s volatility
Market risk premium	The delta between the expected return from the increase in returns against the risk-free rate
Storage costs	Compared to the total cost of buying the commodity, the costs required to hold the commodity until the expiration date of the future
Convenience (lease) rate	A convenience rate is levied if the commodity is used by the investor before the expiration date or for any other more convenient uses that arise by just holding the commodity
Commodity discount rate	The commodity is discounted to net present value, discounting the time value of money to the current value of a commodity
Exponential growth rate	Assuming the value of the commodity grows at an exponential rate, this is what we use to calculate the futures price of the commodity with current information

Take note the commodity discount rate is calculated like so:

Commodity discount rate = riskless rate + (commodity beta * market premium)

The exponential growth rate of the commodity is calculated as follows:

Exponential growth rate = commodity discount rate - convenience rate + storage costs

The expected futures spot price is:

Expected futures spot price = Spot price * e^{(exponential growth rate * time)}

The expected futures spot price is rather volatile and changes according to market conditions at the date of the transaction. However, the expected future spot price will not always align with the implied futures price (from current conditions).

Note

Identifying the costs required to hold/store the commodity, calculating it, and ensuring that this cost is less than the futures contract provides a risk-free, arbitrable commodity that investors should buy hedging positions of and settle the position upon ensuring profits.

To find out what is deviating:

[ln(Expected futures spot price/ Spot price)]/ time = exponential growth rate

Other conditions are given in the market, such as time till expiration, the spot price of the commodity, and expected futures spot price (as given by how the market prices the commodity).

The only thing that could cause the expected futures spot price to deviate from implied futures is the exponential growth rate, which would have to be wrong for arbitrage opportunities to exist.

The Implied futures price of forward/spot

See the formula as shown:

F0 = S0 e^{(r + u - y)T}

F0 refers to the expected futures price.
S0 refers to the spot price of the commodity.
r refers to the risk-free rate.
u refers to the storage rate.
y refers to the convenience rate.
T refers to the period of time holding the commodity in storage.

Suppose the implied futures price is the same as the expected futures price. In that case, no arbitrage opportunities exist as all storage, convenience, and time rates have already been factored in.

However, if:

F0 > S0e^{(r + u - y)T}

A cash-and-carry arbitrage would be able to exploit the delta between the expected futures price and the implied futures price.

When the futures short is conducted, this creates a sell on the higher-priced future. The long commodity starts as well, and the commodity is held until such a time when the delta between the two decreases to near zero.

The investor then settles the short position with the futures clearing corporation with the long commodity in exchange for the closing of the short position. The investor earns the delta.

Cash and carry arbitrage (Leveraged case)

The above is the case if the commodity is entirely financed without leverage.

In the case where only leveraged is used to finance the commodity, the formula below is used:

F0 = S0(1 + r)T + (u - y)T (1 + r)T

The r in this instance, is not referring to the risk-free rate but the borrowing rate, as the commodity is financed entirely by collateral. The risk-free rate is no longer at play as the leverage is used instead.

Note

Take note that both terms are multiplied by (1+r)^T to ensure that they are at future values (to match up with the calculation of the futures price, which is a future value).

Likewise, to ensure that the arbitrage opportunity exists adequately to ensure that cash and carry can result in risk-free profits for the investor, similar to the above case without leverage:

F0 > S0(1 + r)T + (u - y)T (1 + r)T

This ensures that the above condition of the expected futures price is higher than the implied futures price. Therefore, the price discrepancy shows an opportunity for this to be properly exploited at a risk-free rate for the investor to make profits, even entirely leveraged.

What can influence costs in cash and carry arbitrage?

Take note that all the rates calculated above (convenience, storage, risk-free) are settled as such at the settlement date. However, these rates might still be subject to change and result in deviations from the implied futures price.

For instance, if the storage rate increases above the current storage rate and above the current rate up until expiration, there will be no opportunity for the arbitrager to unload his positions to net a profit.

To mitigate such risks, cash-settled futures could instead be used, or non-commodity equity such as S&P 500 futures against the spot price of S&P as priced by the current market conditions.

However, with low risks come lower rewards. Lower risks of no storage fee result in more participants in arbitrage. This would decrease the yield of such spreads because more participants exploit the price inefficiencies and lower the future price from its original high.

Reverse cash and carry arbitrage

Similar to the case of cash and carry arbitrage, reverse cash and carry is an opposite strategy that uses the direct opposite of the conditions for cash and carry to attain profits.

While C&C saw longs in spot markets and shorts in futures, reverse cash and carry would instead see longs in futures and shorts in spot markets. It depends on the market being in normal backwardation.

Normal backwardation would mean that the expected futures price of the commodity is lower than the current spot price of the commodity. However, since this occurrence is rarer in most markets, C&C is often used instead.

Simply put into equations, the following is displayed:

F0 < S0(1 + r)T + (u - y)T (1 + r)T

Or:

F0 < S0e^{(r + u - y)T}

Take note of the difference in r meanings, with the first formula’s r relating to the interest rate. In contrast, the second equation’s r relates to the risk-free rate.

Conclusion

In conclusion, cash and carry arbitrage takes advantage of price differences between spot markets and future markets of commodities. It involves going long on the spot market and short on futures to profit from the convergence of prices over time.

By carefully considering factors such as:

Riskless rate
Time
Commodity beta
Market risk premium
Storage costs
Convenience rate
Commodity discount rate
Exponential growth rate

Investors can identify arbitrage opportunities and execute risk-free trades.

The success of cash and carry arbitrage depends on the presence of contango, where the spot price is lower than the futures price, making it advantageous to go long in the spot market.

However, costs associated with holding and storing the commodity should be carefully evaluated to ensure they do not exceed the price difference between the spot and futures markets.

Note

It is important to note that spot and forward prices can be used interchangeably in the context of commodities, as delivery times often delay the purchase and actual delivery.

Market conditions, implied futures prices, and the expected futures spot price play crucial roles in determining the profitability of cash and carry arbitrage. While cash and carry arbitrage offers the potential for risk-free profits, it is not without risks.

Changes in storage rates, convenience rates, and other factors can impact the strategy's profitability. Cash-settled futures or non-commodity equity can be used as alternative instruments to mitigate these risks.

Additionally, reverse cash and carry arbitrage, which involves going long on futures and short on spot markets, can be employed in markets experiencing normal backwardation, where the expected futures price is lower than the spot price.

However, this condition is less common, and cash and carry arbitrage is more frequently utilized.

Cash and carry arbitrage is a sophisticated strategy that requires careful analysis, precise timing, and consideration of various factors. When executed correctly, it can provide opportunities for risk-free profits in the commodity markets.