<h2>Market Characteristics</h2>
Commodities have specific features that distinguish them from financial instruments.

Financial markets do not have supply side constraints, i.e., their availability in the markets is not restricted by any factors other than the characteristics of the assets they are comprised of and participants who are associated with them like exchanges, governments, traders, etc.  Commodities by their nature are governed by seasonality, production methods, labor costs (to name a few) which determines how they are supplied in the market. On the demand side however both markets tend to be relatively free.

The process by which the commodities are produced and sold often involves storing them as inventories as well and there is a cost associated with this attribute. This maybe due to the seasonality factor, both the supply and demand of this range of products or on the demand side only.

The owner of any commodity can make money by lending and purchasing it back i.e. leasing the commodity in the market.

There are investor specific benefits that result from the ownership of a commodity asset
<h2>Lease Rate</h2>
The lease rate is defined as the rate at which the owner of the commodity lends and buys it back from the investor in the market. During the period when the commodity is leased the ownership does not change hands. The concept is similar to that of the repurchase rate in the bond market. In some cases the market in which such transactions occur is called the leasing market.
<h2>Storage Cost</h2>
When a commodity is being stored it is said to be in the <b>carry markets </b>and it is not generic across each product in the asset class.  The cost of storing it should be factored in the forward price. This makes commodities different from financial assets because apart from the financial cost associated with them there is also a cost of storing them which increases the forward price and makes the forward interest rate curve steeper than the normal curve.
<h2>Convenience Yield</h2>
The benefits from holding the commodity that result from the physical ownership of the asset are termed as the convenience yield. It is owner specific and may or may not be reflected in the forward price.  When the commodity has been loaned out the investor loses out on this yield but saves on the cost of storing the asset.

This property defines range of prices over which the asset can be traded without making an arbitrage profit in the market as it is not necessarily earned back by the investor while engaging in arbitrage.

Basic Commodity Terminology

Cash prices are derived from the futures markets by removing the effect of the cost of carrying the commodity i.e. by stripping out the financial cost of carry price. The driving factors behind the volatility in the prices of the commodities’ cash prices arises because they have different characteristics than financial products.
<h2>Factors that affect commodity prices</h2>
<ol>
	<li><strong>Production related –</strong> Commodities are capital-intensive products i.e. they are influenced by natural factors like weather conditions, crop diseases, size of land cultivated and factors related to production like labor patterns, development in the tools and technologies used. Other than these there are factors like the economic and political environment which manifest itself in the form of trade constraints, subsidies, taxes to mention a few. Altogether these factors affect the cost of producing the commodity and the demand for it in a market where there is more than one participant.</li>
	<li><strong>Storage and Transportation constraints –</strong> All commodities have a real physical form and therefore there is a need for storage prior to distribution. This is not the case of financial products so inventory cost and storage do not have such a large impact on the market prices. This factor does not however affect the prices across all commodity asset classes in the same magnitude but rather depends on the type of commodity in question.</li>
	<li><strong>Economic and Demand related patterns –</strong> In recent times the uncertainties in the global financial system have made commodities a favorable investment alternative to financial instruments.  Typical examples would be gold and silver. The increasing involvement of  developing markets as suppliers expose the prices to the political and production related constraints in these countries like economic policy, infrastructure and labor conditions. This sometimes pushes prices higher.</li>
	<li><strong>Costs involved in storage –</strong> There are two types of costs involved in storing commodities. One is the financial cost and the other is the cost of physical storage and they both need to be factored in when computing the forward prices.</li>
	<li><strong>Seasonality –</strong> Some examples of such factors include weather related patterns, operational risk, climatic conditions and politics.</li>
</ol>
<h2>Commodities Compared</h2>
<ul>
	<li><strong>Gold –</strong> Storage costs are low due to increased durability. There is a lease rate implied in practice. There are two situations. Direct ownership or a synthetic long position. Direct ownership means there is no cost of leasing but storage cost is involved. A synthetic long position means there are no storage costs but there is credit risk exposure.</li>
	<li><strong>Corn –</strong> It is an agricultural commodity it is easily perishable and therefore the price is highly affected by seasonal factors like harvests and yearly weather conditions. These directly influence the storage costs and supply side respectively.</li>
	<li><strong>Natural Gas –</strong> Demand for gas is more in winter than in other seasons. Also the transportation and storage costs are higher than most other commodity types.  The following comparison should explain this characteristic: Agricultural products depend more on supply side rather demand changes as compared to gas which is affected more by demand rather than supply factors.</li>
	<li><strong>Oil –</strong> It is less expensive to transport and easier to store than natural gas.</li>
	<li><strong>Electricity – </strong>Supply side factors like demographics of land and distribution of population, availability of natural resources, political, economic environment and trade policies, type of economy (developed, semi-developed, underdeveloped)  mainly have an influence on the price and availability of this commodity. This is a resource that is required world-wide.</li>
</ul>

Factors Affecting Commodity Market Prices

The concept of basis risk in the commodities markets is similar to basis risk in financial products.  It occurs when spot price and the futures price do not converge when the futures contract expires. This happens in two situations. In the first case the risk associated with a commodity price exposure cannot be entirely hedged using  any of the commodity futures contracts trading in the market due to a quantity mismatch. The second case is when cross-hedging needs to be resorted to when there are no available future contracts trading on the market for the commodity in question. Cross-hedging happens when either the maturity, quantity or the quality of hedge cannot be matched with the price exposure to that needs to be hedged.
<h2>Definition</h2>
Basis is defined by the following equation:
<blockquote>
<p align="center"><strong>Basis=Cash Price (S)- Futures Price (F) </strong></p>
</blockquote>
On the day when the position is bought into the books the basis is unknown.

The day when the hedge is lifted is normally unknown and is a random variable unless the day is the same as the futures contact delivery day and the underlying instrument of the futures contract is the same as the commodity being hedged.

There is always basis risk in the case of cross-hedging.
<h2>Market Examples</h2>
The most common reason why it is not possible to hedge all the price risk in a commodity cash position is that it is not always possible to find futures contracts based on the underlying that trade in the market. In this situation the objective is normally to hedge away as much of the exposure as possible by trading contracts on related assets. This is most common reason why basis risk arises and two examples when this happens in the market are cited below.
<ol>
	<li>There is no futures contract for jet fuel so in the market oil and gasoline futures are used for hedging exposure to jet fuel prices. The types of organizations that have a requirement for this are airlines. There is of course not a strong correlation between the prices of oil and gasoline futures, alone or in combinations and the market price of jet fuel. So although it is possible to hedge most of the price risk there will always be some remaining exposure.</li>
	<li>Most of the crude oil futures contracts being traded in the market are based on the West Texas intermediate crude and for oil that is produced in a different region or of a different grade the hedge using these futures will always be imperfect.</li>
</ol>

Basis Risk in Commodities Hedging

A commodity is said to be in carry when it is being stored rather than traded. The concept is similar to financial markets where this term is called the financial cost of carry. In the case of commodities this becomes more obvious since the process of producing and distributing them involves storing them as well.

The costs that are incurred in the carry markets affect the forward price of the commodity that will be traded in the future.
<h2>Forward Price of a Commodity</h2>
The forward price of a commodity is derived using the following formula:

<img class="aligncenter size-full wp-image-10410" alt="fp1" src="https://financetrain.com/wp-content/uploads/fp1.gif" width="270" height="69" />

Where r is risk free rate at which the value of an asset grows in the market.

In financial markets δ is normally associated with the returns that arise from holding the asset. An example would be when an asset pays the dividend. This is called the dividend yield.

Commodities have the characteristic that they can be lent and bought back in the active market. This is called the act of leasing the instrument and the rate of return achieved from it is called the lease rate. The dividend yield in the financial markets is called the lease rate in the commodities market.
<h2>Impact of Storage Costs and Convenience Yield</h2>
The price of the commodity calculated in the future must factor in both the financial cost of carrying the commodity as well as the physical cost of carry i.e. the cost of storing the commodity.

The impact of the storage cost is to make the graph of interest rates for commodities steeper than the normal interest rate structure. The advantage of lending a commodity is that the owner saves on the storage costs. However there is a disadvantage that the owner loses on the benefits of holding the commodity which in markets terminology is called the convenience yield.

In other words when a commodity is leased out, there is saving on storage costs but the benefits due to holding the commodity i.e. the convenience yield is lost.

This relationship is represented by the following equation –

<img class="aligncenter size-full wp-image-10409" alt="fp2" src="https://financetrain.com/wp-content/uploads/fp2.gif" width="183" height="65" />

Where δ is the lease rate, <i>c</i> is the convenience yield and λ indicates the storage costs.

The lease rate can also be represented as the difference between the commodity discount rate <i>α</i> and the expected growth rate of the commodity price <i>g</i>.

<img class="aligncenter size-full wp-image-10408" alt="fp3" src="https://financetrain.com/wp-content/uploads/fp3.gif" width="204" height="67" />

The commodity discount rate is the required rate of return on the commodity.

From the above relationships it becomes clear that the forward price moves in an opposite direction to the convenience yield and this is opposite for the storage costs.
<h2>No-Arbitrage Trading Range</h2>
The convenience yield of the commodity cannot be earned by the average investor while trading in the no-arbitrage market. This results in a no-arbitrage trading range rather than a no-arbitrage price for the commodity.

The no-arbitrage trading range is the range of possible prices while factoring in the convenience yield for the pricing of the commodity.

<img class="aligncenter size-medium wp-image-10407" alt="fp4" src="https://financetrain.com/wp-content/uploads/fp4-300x42.gif" width="300" height="42" />
<h2>Example</h2>
The following details are available about corn:
<ul>
	<li>Spot price (Current price in the market) = $5 per bushel</li>
	<li>Rate of interest prevailing the market (r) = 6%</li>
	<li>Storage cost = 15%</li>
</ul>
The 1 year forward price is then calculated as follows:

<img class="aligncenter size-medium wp-image-10406" alt="fp5" src="https://financetrain.com/wp-content/uploads/fp5-300x46.gif" width="300" height="46" />

If the convenience yield of holding the commodity is 4% then the forward price gets impacted:

<img class="aligncenter size-medium wp-image-10405" alt="fp6" src="https://financetrain.com/wp-content/uploads/fp6-300x34.gif" width="300" height="34" />

From the relationships described, it can be deduced that the forward price is negatively impacted as a result of the introduction of the convenience yield i.e. it reduces in value.

Carry Markets and Forward Prices

The forward price of a commodity is calculated much along the lines of that of a financial product except for the fact that by virtue of its physical form and characteristics a commodity incurs different types of storage and holding costs as compared to a financial product and the factors that affect the commodities forward price are much different from those that affect the price of a financial forward.
<h2>The Equations</h2>
The equilibrium formula for the calculation of the forward price of a commodity is as follows:

<img class="aligncenter size-full wp-image-10456" alt="cf1" src="https://financetrain.com/wp-content/uploads/cf1.gif" width="227" height="69" />

Where r is the risk-free interest rate in the market, δ is the lease rate and T is the time between the current date and the future date at which the transaction is supposed to take place.

In financial markets the lease rate is associated with the rate at which returns have been obtained for owning the asset i.e. the dividend yield.

In the commodities market the lease rate arises because the asset can be loaned out in the market as each and every commodity has physical characteristics.

Let’s assume that g is the rate at which the commodity price grows and α is expected rate of return on the commodity price. The lease rate is represented by the following equation:
<p style="text-align: left;" align="center"><img class="aligncenter size-full wp-image-10455" alt="cf2" src="https://financetrain.com/wp-content/uploads/cf2.gif" width="177" height="59" />There is another way of representing the lease rate. When it is lent out storage costs are saved but the benefits of holding the commodity i.e. the convenience yield is forgone. The borrower of the commodity pays a lease rate that is equal to the convenience yield minus the storage costs.</p>
Let us assume that c is the convenience yield and λ are the storage costs. The lease rate is given by:
<p align="center"> <img class="aligncenter size-full wp-image-10454" alt="cf3" src="https://financetrain.com/wp-content/uploads/cf3.gif" width="171" height="51" /></p>
This is also called the cost of carrying the commodity.
<h2>The Derivation</h2>
If the actual storage cost of the commodity is e<sup>λT</sup> where λ is the storage cost rate and T is time to maturity then the storage cost can be derived from the spot prices in the market and the prices shown by the warehouses. If the futures price is such that:
<p align="center"><img class="aligncenter size-full wp-image-10453" alt="cf4" src="https://financetrain.com/wp-content/uploads/cf4.gif" width="252" height="64" /></p>
The rate in the exponential on the left is the risk-free rate for discounting. A trader might then borrow an amount of money on the right hand side, purchase the commodity and pay for the storage upfront and enter into a short position in the future at time T. Given that all this is satisfied the cashflow is as follows:
<p align="center"><img class="aligncenter size-full wp-image-10452" alt="cf5" src="https://financetrain.com/wp-content/uploads/cf5.gif" width="297" height="69" /></p>
There is a possibility of arbitrage in this scheme of things so trade that happens would be one that is of the highest quantity available in the market such that there is a pressure on the movement of the prices such that there is a situation where making risk-free profit does not exist.

<img class="aligncenter size-full wp-image-10451" alt="cf6" src="https://financetrain.com/wp-content/uploads/cf6.gif" width="234" height="65" />

If the above inequality is to hold only companies that can sell it and repurchase at a later date because it is not possible to hold negative amounts of commodities and companies do this due to strict industrial requirements. This difference often comes from other industry related requirements and it is modeled via a convenience yield termed as c.
<p align="center"> <img class="aligncenter size-full wp-image-10450" alt="cf7" src="https://financetrain.com/wp-content/uploads/cf7.gif" width="282" height="65" /></p>

<h1>Lease Rate vs. Convenience Yield</h1>
The lease rate is the rate that the borrower pays for the commodity he has taken as loan from the lender. The forward price of the commodity is inversely related to the lease rate much like the dividend yield for financial products. The same holds for the relationship between the forward price and the convenience yield as is implied from the formula.

While the cost to the borrower of the commodity is represented by the lease rate the convenience yield is the benefits that the borrower gains during the loan period as a result of possession of the commodity. So the lease rate means something very different than the convenience yield for the commodity.

Equilibrium Formula for Pricing Commodity Forwards

The concept of hedging in commodities markets is the same as in the financial markets and that is to mitigate the exposure to price movements due to the commodities positions. The most common instruments that are used for hedging purposes are futures contracts as they are highly liquid instruments. Futures contracts are the most popular instruments because their prices are highly transparent and the risk of counterparty default is borne by the exchange where such products normally trade. They are only exposed to movements in market prices or market risk and are highly standardized in nature compared to their OTC counterparts.

In situations where there are no futures on the commodities traded on the market hedging is carried out using futures on related commodities.
<h2>Types of Hedges</h2>
<ul>
	<li>A short hedge happens when a company holds a long position in a commodity i.e. it owns the commodity and has to sell futures contracts in order to hedge its long position.</li>
	<li>A long hedge happens a company takes a long position in a futures contract in order to hedge a short position in commodity (risk due to upward movements in prices).</li>
	<li>A cross hedge happens when there is risk due to market factors that need to be mitigated but there are no futures on the underlying commodities that are available for trading in the market.</li>
</ul>
<h2>Hedging Methods Specific to Commodities</h2>
<strong>Strip Hedge</strong>

A strip hedge happens when futures contracts over many maturities ranges are purchased to hedge the underlying cash positions. In other words strips of futures contracts are used. This normally happens when there is high liquidity for futures contracts over longer time horizons. There is no basis risk due to the strip hedge as the basis becomes locked and changes cannot affect the risk.

<strong>Stack ad Roll Hedge</strong>

This type of hedging involves purchasing futures contracts for a nearby delivery date and on that date rolling the position forward by purchasing a fewer number of contracts. This process then continues for futures delivery dates until each position maturity exposure is hedged. It normally happens when there is no adequate liquidity for the long term futures contract traded in the market. The following are the risks involved in stack hedging.
<ul>
	<li>Basis risk is locked only for the initial contracts and the future basis exposure is locked.</li>
	<li>Liquidity is higher as instruments with short maturity are being used.</li>
	<li>There are high transaction costs due to this type of hedging due to more contracts being required.</li>
	<li>The possibility of conflicting with position limits is high due to the high hedging volumes.</li>
	<li>If the market is in backwardation the stack strategy creates positive cashflows at roll-over dates. A short stack position generates negative cashflows under these conditions.</li>
</ul>
The following points are also to be noted
<ul>
	<li>Accounting regulations impact the profits and losses that are generated from the hedging methods and hence need to be taken into consideration.</li>
	<li>Margin calls on the futures can trigger panic in the market.</li>
	<li>If there are long maturity hedges then it is important to tail the futures position.</li>
</ul>
&nbsp;

Strip Hedge and Stack Hedge in Commodities Market

A spread position is one where trading takes places on many contracts on the same or related commodity. If the price between two related commodities changes then the idea is to profit from the opportunity.

There are two main types of commodity spreads
<ol>
	<li>Inter-commodity spread – In this case a position is taken in two different but related commodities.</li>
	<li>Intra-commodity spread – In this case the position is taken in different maturity months for the same commodity.</li>
</ol>
An example of this would be the case of wheat and corn which are used to ethanol production and cattle feed respectively. A certain relationship exists between the prices of these two commodities i.e. they must follow a certain pattern. Therefore it is easier to trade spread positions on them. These would then be inter-commodity spreads.

Another example would be the use of pork belly spreads because their prices are easily available in the market and one can expect them to go through reasonable price fluctuations. The normal spread is when the far contract is short sold and the nearby contract is purchased when the premium of the far to near is judged as being too great. These judgments are based on the ratio of premium to transactions and the carrying charges. The three main types of spreads that can occur are as follows:
<ol>
	<li>If the price premium judged is too high then according to this all possible combination of contracts should be spread.</li>
	<li>This is the same as number 1 except for the fact that only one spread is permitted per combination of contracts</li>
	<li>This is also the same as number 1 except for the maximum holding period is determined.</li>
</ol>
<h2>Examples</h2>
AT&amp;T shares sell both on the Mid-West as well as the New York exchanges and the price difference in these two markets very rarely exceed that of the transaction costs in the purchase and sale of the security. If in case the spread does exceed the amount then there will be purchases on the exchange where it is cheapest and sales on the place where it is most expensive. When the buyer receives the stock he can cover the short sale and pocket the profit and this result in the risk-free arbitrage opportunity.

There are cases where there is shorting of the near contract and purchase of the long-term one which is called a reverse spread. Reverse arbitrage is of course very rarely possible.
<ul>
	<li>The inter-commodity spread is formed by the following transactions. In February a July 1 wheat contract per bushel is sold and a July 1 corn contract per bushel is bought. The prices are 500 and 300 cents per bushel respectively. On June 1 wheat contract is bought and 1 July corn contract per bushel is sold at 300 and 200 cents respectively.</li>
</ul>
<p style="padding-left: 60px;">There are losses on corn and gain on wheat due to this.</p>
<p style="padding-left: 60px;">The loss on corn is – 0.1 * 5000 = $500</p>
<p style="padding-left: 60px;">The gain of wheat is – 0.2 *5000 = $1000</p>
<p style="padding-left: 60px;">The total amount gained is $500.</p>

<ul>
	<li>Copper futures prices for three delivery months July, September and December are 57, 57.5 and 60.5 cents per pound. The butterfly spread on this is as follows:
<ul>
	<li>On November 10 sell 1 July contract at 57 cents per pound and buy two September contracts at 57.5 per pound and sell one December contract for 60.5 cents per pound.</li>
	<li>On April 15 buy one July contract at 55 cents per pound and sell two September contracts at 57 per pound and buy one December contract at 58.5 cents per pound.</li>
</ul>
</li>
</ul>
<p style="padding-left: 90px;">The profits and losses for each of the delivery months are as follows:</p>
<p style="padding-left: 90px;">July – 0.02 * 20000 = 400</p>
<p style="padding-left: 90px;">September – (-0.005) *2 *20000 = -200</p>
<p style="padding-left: 90px;">December – 0.02 * 20000 = 400</p>
<p style="padding-left: 90px;">The total profit is the sum of the three which gives us $600.</p>
<p style="padding-left: 90px;">This is an example of an intra-commodity spread.</p>

Define and Compute a Commodity Spread

There are cases where it is not possible to find futures contracts on a particular underlying in order to hedge the exposure to the commodity. In this case futures on the nearest underlying will be used to perform the hedge and this process is known as cross-hedging. Some of the reasons there are problems in cross hedging commodities are due to mismatch in:
<ul>
	<li>Maturity – this happens when the hedging horizon does not match the futures expiry date</li>
	<li>Quantity – the exposure that needs to be hedged cannot be covered by a certain multiples of futures contracts.</li>
	<li>Quality – the characteristics of the commodity to be hedged does not match those in the futures contracts.</li>
</ul>
The question then arises as to which contract should be chosen for the cross-hedging purposes. The answer is that the contract whose prices are highly correlated with that of the underlying asset needs to be used for the hedging. It is very important for this contract to be liquid in nature and the delivery month should be the same or just after the hedge will be lifted.

In a cross hedge there is always basis risk i.e. the risk that prices of the spot and the futures will merge together as the futures nears expiry.
<h2>Examples of Cross Hedging Commodities</h2>
The most common reason why cross-hedging happens is because of the inability to find contracts on the same underlying whose risk needs to be hedged in any of the exchanges. Also this happens when the liquidity of these contracts is not really that great.

A classic example of cross-hedging is in case of West-Texas crude oil future contracts which only trade on those markets so they can only provide as an imperfect hedge for oil that is traded in a different region or of a different grade.

It is also very difficult to find futures contract for Jet fuel so airlines that wish to hedge the price exposure will resort to using crude oil or gasoline futures instead. Although the prices of these commodities are not perfectly correlated with each other so the hedge will never take place for all of the risk rather it will address only much of the risk.

The remaining risk is called the basis risk which is defined as the spot price of the asset minus the futures price. If the asset and the futures contract on that asset are similar then there is no basis risk at all i.e. the basis will go to zero when the contract expires. However, if there is a mismatch the basis will never go to zero so there is always some residual risk.

Cross Hedging Commodities

Commodity Forwards and Futures

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Commodity Forwards and Futures

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