12.1.1 Four Explanations of Commodities as Diversifiers

Commodities are often viewed as an asset class that helps diversify a portfolio of traditional assets (stocks and bonds) through a lack of return correlation between commodities and traditional assets. Here we discuss four reasons why commodity returns may have low correlation with stock prices and bond prices.

First, unlike financial securities, commodities have prices that are not directly determined by the discounted value of future cash flows. Accordingly, commodity prices are not as directly related to changes in forecasted cash flows and changes in market discount rates. Instead, commodity prices are evaluated primarily on forecasts of the commodity's supply and demand. Since commodity prices are driven by different economic fundamentals than are stocks and bonds, they should be expected to have little correlation, or even negative correlation, with the prices of financial assets.

Second, nominal commodity prices should be positively correlated with inflation largely because commodity prices form part of the definition and computation of inflation. Inflation is the decline in the value of money relative to the value of a general bundle of goods and services. A nominal price refers to the stated price of an asset measured using the contemporaneous values of a currency. Thus, the 2015 nominal price of a bushel of corn in U.S. dollars is simply the market price observed in 2015. A real price refers to the price of an asset that is adjusted for inflation through being expressed in the value of currency from a different time period. The 2015 real price of a bushel of corn based on 2010 dollars deflates the 2015 nominal price for the inflation that occurred in the dollar between 2010 and 2015. Since prices of physical commodities such as oil are an important component of the computation of inflation, we should generally expect that the nominal prices of commodities and other real assets would move in tandem with inflation. Thus, real commodity prices would tend to be unaffected by inflation. On the other hand, both the real and the nominal prices of stocks and especially bonds tend to be negatively correlated with inflation because inflation raises the discount rates applied to their valuations. To the extent that changing rates of inflation drive the prices of real assets differently than they drive the real prices of financial assets, there should be low correlation or perhaps even negative correlation between commodity prices and the prices of most stocks and bonds.

A third reason why commodity price changes may be negatively correlated with the returns of stocks and bonds is that they may react very differently at different parts of the business cycle. Stocks and bonds are highly anticipatory in their pricing. The value of stocks and bonds is derived from expectations regarding long-term earnings or coupon payments. Commodities are often priced more on the state of current economic conditions and factors regarding short-term supply and demand. For example, in the midst of a severe and prolonged drought, the price of corn and other agricultural products may be extremely high, despite the long-term expectation that the drought will undoubtedly end and the prices will revert toward more normal levels. Consequently, commodity prices are often at their lowest when economic activity is at its lowest and at their highest when economic activity is at its highest. Traditional financial assets often perform best when the economy is near a low but the prospects for improvement are high.

A fourth argument for low or negative correlation between commodity prices and financial assets is based on commodities being a major cost of some corporate producers. In the short run, a major increase in commodity prices may cause a substantial decline in corporate profits, and a decline in commodity prices may result in an increase in profits. Thus, as commodity prices soar, corporate stocks and bonds may falter (except those of commodity-producing firms). The result is a negative correlation between commodity prices and the prices of financial assets.

All four of these arguments indicate why there tends to be a low or negative correlation of commodity prices and returns to the prices and returns of financial assets.

12.1.2 Commodities as Diversifiers in a Perfect Market Equilibrium

A market is in equilibrium when current market prices equate supply and demand such that further transactions cannot benefit market participants. In an ideal equilibrium, all market participants are well diversified, and the differences between market risk and idiosyncratic risk can be precisely delineated. With a perfect capital market in equilibrium, the role of commodities in diversifying a portfolio is clear, as summarized here.

Diversification is the process of eliminating exposure to idiosyncratic risks while constructing a portfolio that matches the risk characteristics of a perfectly diversified portfolio. In the CAPM (capital asset pricing model), the perfectly diversified portfolio is the market portfolio that contains exposure to all assets and contains exposure to each of those assets in proportion to their total market value (i.e., size). The percentage of the total market portfolio attributable to each asset in that portfolio is known as the market weight. Thus, the market weight of an asset is equal to the percentage of the total global value of that asset relative to the total global value of all assets. For example, if crude oil represents 5% of the total wealth of the world, then a perfectly diversified portfolio of risky assets should have a 5% weight in oil. In a perfect market in equilibrium, any investor with a portfolio of risky assets that has an asset exposure greater than or less than its market weight is speculating on idiosyncratic risk that offers no reward in the form of higher expected returns.

Commodities are a substantial part of total wealth; therefore, commodities should be a substantial part of all portfolios, according to classic equilibrium models such as the CAPM. So, based on the CAPM, the only issue in determining appropriate exposure to each commodity is determining the market weight of that commodity. However, ascertaining the total global market value of a commodity is difficult in practice. Returning to the example of oil, even this simplified view of portfolio allocations introduces a number of difficult questions: How much oil is expected to be discovered? How much oil that is already discovered can be extracted? What price should be attached to oil reserves that are years from being extracted? Further, ascertaining the exposure of financial assets to each commodity is difficult. How much of an oil company's stock price is attributable to oil? How have an oil company's hedging activities modified the company's exposure to oil prices?

12.1.3 Commodities as Diversifiers in the Presence of Market Imperfections

In practice, markets are imperfect and may remain out of equilibrium for extended periods of time. Because shortages and oversupplies of commodities are not quickly corrected through price mechanisms, shortages and oversupplies of some commodities may last a long time. Returning to the oil example, some nations have vast holdings of oil and choose to remain poorly diversified (concentrated), with a very high percentage of wealth exposed to oil prices. If one market participant holds an asset in a higher proportion than its market weight, then some other market participants must hold that asset in a lower proportion than its market weight. Theory is unable to prescribe optimal portfolio allocations in imperfect markets and in markets that are in disequilibrium. In disequilibrium, it is no longer clear that all market participants should include oil or any other commodity in their portfolios with a weight equal to the market weight of that commodity.

Ideally, investors seek to hold commodities in the proportion that provides the highest return-to-risk ratio based on their existing portfolios and such circumstances as the structure of their liabilities. Empirical evidence can be a tool for ascertaining the benefits of diversification for each commodity to each investor. The final section of this chapter reviews the historical properties of commodity returns.

12.1.4 Commodities as Diversifiers against Unexpected Inflation

One of the most often cited virtues of commodity investment is its ability to diversify a portfolio against the risk of unexpected inflation. When rates of inflation are steady, asset prices tend to adjust such that the expected nominal returns of each asset reflect anticipated inflation. Therefore, steady and anticipated inflation is not generally a serious investment risk or a determinant of real returns. However, unexpected inflation can be a serious risk to investors. For example, a fixed-income security tends to underperform in an environment of unexpectedly high inflation because the value of the promised future cash flows is being diminished at an unexpectedly high rate.

Real assets in general and commodities in particular offer protection against inflation risk. Inflation risk is the dispersion in economic outcomes caused by uncertainty regarding the value of a currency. Inflation risk emanates from the divergence between realized and anticipated rates of inflation (i.e., unanticipated inflation).

There are two intuitive explanations for the protection from inflation risk provided by commodities. First, commodity prices are an important determinant of the price indices that measure inflation. Therefore, price indices and realized inflation rates tend to be positively correlated with their major component: commodities. Second, the value of a commodity is its perceived ability to provide consumption. Because of their homogeneity and their ability to be transported, commodity prices in each country should adjust quickly to changes in the value of the local currency. For example, when a country's currency experiences hyperinflation, the price of oil in that currency rises, but the price of oil in the currency of other nations is unaffected. The real value of each investor's holdings of oil is unaffected by the inflation rate of the investor's home currency.

12.2.1 Return Enhancement: Alpha

Chapter 11 discussed opportunities to generate alpha through speculation regarding the relationship between futures prices on the same commodity that differ by settlement date (calendar spread). These speculative activities seek to exploit relative mispricing within forward and futures markets as well as relative mispricing between exposure to commodities in derivative markets and exposure to commodities in other markets.

But the primary reason that market participants take on commodity exposure in the pursuit of alpha is to speculate on idiosyncratic movements in the underlying commodity prices. Investors use technical and fundamental analysis to forecast commodity prices and to identify trades with superior risk-adjusted returns. For example, a global macro fund may use fundamental analysis to generate forecasts of when the price of a commodity such as gold will rise or fall due to political or economic factors. Managed futures funds might use technical analysis to forecast trends in natural gas prices resulting from trading activity or seasonal patterns. Futures and forward contracts provide convenient securities through which to manage commodity exposures, but other methods of managing commodity exposures are often available.

12.2.2 Return Enhancement from Beta in Equilibrium

Can commodities offer superior returns to investors in the form of abnormally high rewards for bearing systematic risk? In a perfect equilibrium, the expected returns from commodities and any other assets depend solely on the amount of systematic risk being borne. Thus, higher expected returns to commodities would be generated only by taking high levels of systematic risk, and the higher returns offered by bearing that risk would be no more attractive than the higher returns on other assets containing other systematic risks. Given their inflation-hedging capabilities and their likely protection from downside risk, the systematic risks of commodities are presumably low, and in an informationally efficient market, their expected returns would also be low. Simply put, in a perfectly competitive environment, if the inclusion of commodities in portfolios with traditional assets and other alternative assets offers highly desirable reductions in risk, then their expected returns must be sufficiently low to cause the supply and demand of commodity investing to balance.

The bottom line is this: Commodities do not enhance expected returns when they are efficiently priced and when their systematic risk exposures (betas) are low. If markets are perfect and in equilibrium, market participants should hold exposures to commodities and other asset classes based on market weights, expecting lower returns in exchange for enjoying lower risk. Thus, return enhancement from beta must be attributable to market inefficiencies or markets in disequilibrium.

12.2.3 Return Enhancement from Beta in Disequilibrium

In practice, markets are in a continuous state of disequilibrium, which may offer the opportunity for an asset class to offer benefits as a diversifier without also offering commensurately lower returns. In disequilibrium, participants tend to hold substantially different exposures to various asset classes—especially commodities—than exposures based on market weights.

Suppose, for instance, that commodities are consistently underrepresented in the portfolios of many market participants due to lack of familiarity, expertise, or comfort with commodity investing. In order for the demand for commodities as an investment to equal the supply of available commodity investment opportunities, some market participants need to be incentivized to overrepresent commodities in their investment portfolios relative to market weights. The mechanism by which this would occur is through price adjustments until commodities offered both enhanced returns and diversification benefits sufficient to induce more sophisticated and innovative investors to make large allocations to commodities. Simply put, to the extent that commodity investing is ignored or rejected by some investors, prices would adjust so that other investors would find superior investment opportunities through making higher allocations to commodities. The result would be that commodity beta exposure would offer higher expected returns per unit of risk than would other beta exposures.

The argument that portfolio returns can be enhanced by taking on systematic risks that are inefficiently priced and that offer disproportionately high returns can be argued to be either alpha or beta. In one sense such opportunities are beta, since it is necessary to take on systematic risk exposure to earn perceived superior returns. But such opportunities may also be viewed as offering alpha, since they are perceived to offer superior returns through inefficiencies.

12.2.4 Return Enhancement from Providing Insurance through Commodity Futures

Insurance companies strive to earn profits through providing protection to their customers against risks in exchange for insurance premiums. Commodity futures contracts exist to enable participants to manage their risk exposures to changes in commodity prices, often reducing those exposures through hedging. As discussed in Chapter 11, the quantity of long futures positions in a particular commodity desired by operating firms for hedging purposes rarely matches the quantity of short positions preferred by other operating firms. The gap between the supply of and the demand for a particular commodity futures contract by hedgers is met by speculators. Like insurance companies, speculators meet demand for risk protection in order to earn profits.

Let's examine the case of excess demand for long positions in a commodity futures contract for hedging purposes. As natural demand for long positions drives up the price of particular commodity futures contracts, speculators enter the market to provide offsetting short positions. The narrowly defined purpose of speculators is that they are attempting to earn higher returns by establishing short positions in overpriced contracts and long positions in underpriced contracts. But commodity speculators are performing a broader service to the economy by serving the same role as insurance companies: protecting operating firms against commodity price risks in return for enhanced returns.

Managed futures funds and other traders of commodity futures serve in the role of speculators in order to earn enhanced returns. The primary aggregated source of enhanced returns to speculators is the “insurance premium” that operating firms pay to futures traders who take the offsetting positions of their hedges. Thus, operating firms make insurance-premium-like expected payments to managed futures funds and others who are willing to bear commodity price risk in the pursuit of enhanced returns. Chapter 17 discusses natural commodity hedgers and speculators further.

12.3.1 Investing in Physical Commodities

An investor can purchase and physically hold an underlying commodity to gain economic exposure to commodity returns. Physical ownership of commodities can be problematic, however. Storage and transportation costs associated with direct investments in commodities make this an unattractive alternative for most investors. Most investors are not familiar with the financing, storage, and transportation issues of physical commodities, let alone willing to bear costs of ownership associated with possession of physical commodities.

Convenience yield is the marginal economic benefit that an investor obtains for having physical ownership of a commodity rather than synthetic ownership through futures contracts or other financial securities. Some investors prefer physical ownership of a commodity because they perceive high value from possessing physical inventory (and are perhaps able to maintain an inventory of the commodity at below-average storage costs). An example is a manufacturer with excess storage capacity and with concerns that commodity supply disruptions (e.g., transportation failures) could disrupt vital operations.

While users of commodities typically derive convenience yield from inventories, speculators or investors who hold inventories of commodities that they do not use are wasting the convenience yield of the commodity. To the extent that convenience yield is efficiently priced, firms that perceive no convenience yield from a particular commodity should prefer investing in commodities in a form other than physical ownership.

Some firms are purely in the business of storing commodities. Natural gas is an example of a commodity held by storage operators that do not consume commodities in their business. The seasonal nature of natural gas demand causes annual periods of physical inventory buildup and drawdown. Natural gas storage operators possess the option to receive natural gas during low-demand periods (summer) and deliver the gas during high-demand periods (winter).

The essential point is that physical ownership of commodities offers the benefit of convenience yield but also the costs of storage and transportation. Physical storage of commodities is typically a poor method of obtaining commodity exposure for investors without a competitive advantage to storing the commodity and without a high convenience yield for the commodity (relative to other market participants).

12.3.2 Investing in Commodity-Related Equities

Another way to gain exposure to commodities is to own the securities of a firm that derives a substantial part of its revenues from the sale of physical commodities, such as a natural resource company. A major problem with this approach is that most firms have revenues related to a variety of commodities or have operations that extend outside of activities directly related to the ownership and extraction of commodities. As a result, the share price of most firms will often be poorly correlated with the price of a single commodity.

There are several reasons why even a firm focused on a single commodity might not be a good proxy for a direct investment in the firm's underlying commodity. First, a high correlation between the stock price and the commodity price assumes that the firm has not hedged its exposure to the commodity through short positions in forward or futures contracts. Also, the firm must own the underlying commodities (or rights) rather than purchasing the commodities or leasing the rights at market prices.

Next, consider how the price of a common stock can be viewed as the product of the earnings per share (EPS) and a price-to-earnings (P/E) ratio. Although the EPS of a commodity-producing firm may be somewhat highly correlated to the price of the underlying commodity, the P/E ratio may not be. If the stock market declines quickly, P/E ratios fall. When commodity prices and inflation are increasing, the decline in overall market P/E ratios could arguably lead to a decline in the P/E ratio of the commodity-producing firm. A decline in overall P/E ratios could lead to a scenario in which the stock price of a commodity-producing firm underperforms the change in commodity prices. Commodity equities may be viewed as having two betas: one to the underlying commodity market and a second to the equity market. Only the first is attractive for investors with a goal of direct exposure to a commodity. If the goal of commodity investment is to diversify the portfolio away from equity market exposure, commodity-related equity investments may retain more equity market risk than is desirable to meet this diversification goal.

Also, a firm's financial and operating leverage may vary and affect the returns of an investment in a way that is uncorrelated with the price of the commodity that the firm produces (e.g., oil). Finally, note that investments in commodity-producing firms can have substantial stock-specific risks. For example, there are operating risks associated with an investment in an operating company, such as those associated with a major accident, a strike, or management mistakes. The firm may have other operations with substantial exposures to other risks.

Note that most diversified investors in the stock market already have a substantial exposure to commodity-related equities. For example, in the United States, the Russell 1000 Index (consisting of roughly the largest 1,000 U.S. stocks) has a weight of approximately 12% on firms that produce energy, metals, and materials.

As a result of these complexities, equities of operating firms do not generally provide pure exposure to commodity prices.

12.3.3 Exchange-Traded Funds

One of the easiest ways to invest in a basket of commodities or in some individual commodities is through an exchange-traded fund (ETF). There are several structures through which commodity ETFs can obtain exposure to commodity prices: futures markets, equity markets, and physical ownership. They can offer broadly diversified commodity exposures, exposures to specific sectors, or, in some cases, exposure to individual commodities. Some of the ETFs offer leveraged returns, whereas others offer bear exposures (exposures negatively correlated with commodity prices) by holding short positions in futures contracts. Most ETFs tend to be cost-effective for retail investors but may not be adequately cost-effective for institutional-sized portfolios.

Exchange-traded notes (ETNs) are similar to ETFs. Whereas investors in ETFs have a direct claim on an underlying pooled portfolio, investors in ETNs purchase a debt security with cash flows that are directly linked to the value of a portfolio. This debt security is typically issued by an investment bank or a commercial bank that agrees to pay interest and principal on the debt at a rate tied to the change in price of a referenced portfolio. Investors need to be aware of a key difference between ETNs and ETFs: ETNs incur the credit risk of the issuing bank (i.e., counterparty risk), whereas ETF investments do not. The risk of ETNs was highlighted during the 2008 bankruptcy of Lehman Brothers, when related ETNs were delisted as exchange-traded products, and investors holding these notes became general creditors of the firm. Both ETNs and ETFs can have underlying commodity exposures diversified across energy, metals, and agricultural commodities; can focus on a specific commodity sector, such as energy; or can invest in a single commodity, such as gold.

Exchange-traded funds investing directly in physical commodities have become extremely popular in recent years, especially in the metals markets. The largest gold ETF has held more than $50 billion in client assets. Those ETFs based on physical commodities typically invest in a single commodity, such as gold or silver. Investors in these ETFs hold a share of a physical stock of bullion held in a secure warehouse.

Exposure to commodities obtained through ETFs investing in commodity futures can be complicated by a lack of correlation between futures returns and spot returns due to changes in the basis. When the basis in futures markets changes, the returns to a futures contract can be substantially different from spot returns. Investors in ETFs who primarily follow the spot market may struggle to understand the difference between the returns on the ETF and the change in the commodity price in the spot market. For example, when futures prices are in contango, ETF prices are likely to underperform spot prices of the commodity.

Finally, some commodity ETFs obtain commodity price exposure by investing in the equity securities of commodity-producing firms. These ETFs may be diversified across commodity sectors or focused on the producers in a single sector, such as energy, metals, or agriculture. Similar to investments in commodity-producing equities, these ETFs are correlated to both the equity market and the commodity market. In a falling equity market, equity-based commodity ETFs can decline in value, even if prices of commodities are rising in the spot or futures markets.

12.3.4 Commodity-Linked Notes: Overview and an Example

A commodity-linked note (CLN) is an intermediate-term debt instrument whose value at maturity is a function of the value of an underlying commodity or basket of commodities. CLNs are often structured products created through financial engineering so that the commodity risk exposures are generated through positions in commodity derivatives. CLNs are often issued by large banks to meet the risk and return preferences of investors; however, they can also be issued by firms that produce the commodities as a source of financing. The advantage to a commodity-producing issuer of a CLN is being better able to match the risks of its assets and liabilities. For example, a gold-mining firm has assets and revenues highly correlated with the price of gold. A CLN offers the firm the opportunity to be financed with debt securities having coupon or principal payments directly related to the same commodity price that drives its revenues. Whether issued as innovative sources of financing for a commodity-producing firm or financially engineered as structured products, CLNs are closely linked to commodity prices but may also contain the idiosyncratic default risk of the issuing firm.

CLNs have several advantages to some investors over long positions in futures contracts. First, an investor does not have to execute the rolling of commodity futures contracts to maintain exposure. If the CLN uses futures contracts to obtain its commodity exposure, the mechanics of rolling the positions becomes the problem of the issuer of the note (who must roll futures contracts to hedge the commodity exposure embedded in the note). Second, the note is, in fact, a debt instrument. Although some investors may have investment restrictions on direct positions in futures contracts (due to their implicit leverage and potentially large losses), they may be able to obtain commodity exposure through CLNs because they are debt instruments. They are recorded as a liability on the balance sheet of the issuer and as a bond investment on the balance sheet of the investor, and they can have a stated coupon rate and maturity just like any other debt instrument.

For example, suppose that a pension fund is not allowed to trade commodity futures directly (due to restrictions on leverage) but wishes to invest in the commodity markets as a hedge against inflation. To diversify its portfolio, the fund purchases at par value from an investment bank a $1 million structured note tied to the value of an index on commodities, such as the S&P GSCI (discussed later). Assume that the note has a maturity of one year and is principal guaranteed. The principal guarantee means that the pension fund will receive at least the face value of the note at maturity unless the issuer defaults. However, if the S&P GSCI exceeds a prespecified level at the maturity of the note, the pension fund will receive this appreciation. Thus, principal repayment can be higher than the principal, depending on the settlement price of the S&P GSCI at the note's maturity. The pension fund therefore has a call option embedded in the note. If the S&P GSCI exceeds a predetermined level (the strike price) at the maturity date, the pension fund will participate in the price appreciation. However, if the S&P GSCI declines, the pension fund has a promise of receiving the principal amount.

The embedded call option on the S&P GSCI is not free. Thus, an investor such as a pension fund pays for this option by receiving a reduced coupon payment (or no coupon) on the note. When issued, the closer the call option is to being in-the-money (or the further that it is in-the-money), the lower the coupon payment of the CLN. Let's assume that a plain-vanilla note from the issuer might carry a coupon rate of 6%. Under normal circumstances, a CLN with the embedded call option might carry a coupon of only 2%. In this case, the pension fund is sacrificing 4% of coupon income as the price of the call option on the S&P GSCI.

Assume that at the time the note is issued, the S&P GSCI is at $1,000. Further assume that the strike price on the call option embedded in the note is set 10% out-of-the-money, at $1,100. If at maturity of the note the value of the S&P GSCI is above $1,100, in addition to receiving the original principal the investor receives its 2% coupon plus the appreciation of the S&P GSCI above $1,100 (assuming no default occurs). If the S&P GSCI is at or below $1,100, the investor is owed only the original principal and the coupon. Therefore, the final payout of the $1 million CLN with a one-year maturity can be expressed as follows:

where GSCI_T is the value of the S&P GSCI at maturity of the note, and GSCI_X is the strike price for the call option embedded in the note. The $20,000 is found as the 2% coupon multiplied by the $1 million face value of the note, assuming annual coupon payments.

If the option expires out-of-the-money (the S&P GSCI is less than or equal to the strike price of $1,100 at maturity), then the investor receives the return of its principal plus a 2% coupon ($1,020,000). If the option expires in-the-money, then the investor is owed the strike price, the 2% coupon, plus the percentage gain of the index above the strike price applied to the principal. For example, if the S&P GSCI is at $1,210 at maturity, the CLN returns a principal payment of $1,100,000 in addition to the coupon payment of $20,000. The $1,100,000 principal payment is found as follows:

The investor (the pension fund) shares in the upside of the commodity price but is protected on the downside. The trade-off for the upside potential is a lower coupon payment relative to a note without the embedded call option. The issuer of the note presumably purchases a one-year call option on the S&P GSCI as a hedge and, in effect, pays for that call option using savings from issuing a note with a below-market coupon.

The previous example had its principal protected from downside commodity exposure and therefore had the payout of a call option. However, not all CLNs are principal protected. Some notes have principal payments that share fully in the change in value of commodity price changes—up or down. Thus, in this case the value of the principal owed at maturity can be either higher or lower than the note's face value. This may be viewed as a CLN linked to a futures contract instead of an option contract. Further, coupons may be linked to the commodity price or commodity index as well as to the principal.

12.4.1 Why Returns on a Futures Contract Can Differ from the Spot Return

Recall from Chapter 11 that the basis is the futures or forward price minus the spot price. Basis risk is the dispersion in economic returns associated with changes in the relationship between spot prices and futures prices.

Consider a fully collateralized position in a futures contract. A fully collateralized position is a position in which the cash necessary to settle the contract has been posted in the form of short-term, riskless bonds. The total returns from fully collateralized futures or forward returns differ from returns on spot positions on the same asset primarily due to basis risk.

The basis risk that causes realized returns on a fully collateralized commodity futures contract or forward contract to differ from the total return on the underlying spot position may be divided into three primary sources: (1) when the costs of carry to a marginal investor for the spot position are not the same as the costs implied by the basis, (2) when the convenience yield from the spot position differs from its storage costs, and (3) when the basis changes. The first issue would tend to indicate informational market inefficiency in the pricing of the futures contract. The second issue is that, in equilibrium, if a spot position offers a convenience yield that does not exactly offset its storage costs, the spot position must offer an offsetting financial return. The third issue is simply a consequence of uncertainty.

12.4.2 Why Returns on Futures Contracts with Different Settlement Dates Can Differ

Investors seeking risk exposures through futures markets have numerous choices to make in maintaining that exposure, especially with regard to settlement dates. The returns to investing in commodity futures or forward contracts will differ based on the settlement dates chosen.

The excess return of a futures contract may be viewed as depending on the spot return and the change in the contract's basis. Therefore, the excess returns on different futures contracts with different settlement dates may be viewed as varying because calendar spreads change. In other words, futures contracts on the same commodity but with different settlement dates have different excess returns when their bases vary relative to each other, as reflected in changes in the term structure of forward prices.

Thus, returns to investors using futures contracts in the same commodity will vary based on the decisions that investors make in choosing settlement dates. Do they initiate positions with distant settlement dates or nearby settlement dates? Do they hold a position until settlement occurs (or nearly occurs), or do they roll the contract over well before settlement? Do they concentrate their positions in contacts with the same settlement date or spread their positions across a variety of settlement dates?

In summary, the returns to a long-term strategy using futures contracts will be driven not just by the spot prices underlying the futures contracts but also by decisions regarding settlement dates as well as changes in the term structure of forward prices.

12.4.3 Components of Futures Return

There are two especially useful formulas depicting the components of the total return of a collateralized futures position: a two-component formula and a three-component formula.

The return on a fully collateralized position, R_fcoll, can be expressed as the sum of two components:

(12.1)

Equation 12.1 expresses the total return from an unleveraged, fully collateralized commodity futures position as the sum of the interest earned from the riskless bonds used to collateralize the futures contract (the collateral yield) and the percentage price change in the futures contract (the excess return).

As shown in Equation 11.4, the price of a forward contract may be viewed as equaling the spot price minus the basis. Thus, the excess return in Equation 12.1) the change in the futures price) may be broken into the change in the spot price and the change in the basis. By substituting the change in the spot price and the change in the basis into Equation 12.1 in place of the excess return, the total return from this unleveraged, fully collateralized commodity futures position can be expressed as coming from three primary sources. These three primary sources are depicted in Equation 12.2 as (1) changes in the spot price of the underlying commodity, (2) the interest earned from the riskless bonds used to collateralize the futures contract, and (3) changes in the contract's basis:

(12.2)

Each of the three components can be an important part of the return of a commodity futures position. Let's look at each of these three components closely.

The first component in Equation 12.2, spot return, is the return on the underlying asset in the spot market. The returns of unhedged futures positions are primarily driven by the spot return. Exposure to spot price changes is the primary reason that most market participants enter futures contracts, and is also why market participants wishing to gain exposure to commodity prices establish long positions in futures contracts on commodities. It should be noted that there is not a single spot market or a single network of spot markets that provides a single universally recognized spot price for most physical assets.

The second component, collateral yield, is the interest earned from the riskless bonds or other money market assets used to collateralize the futures contract. Positions in futures contracts are often partially collateralized in that they only post collateral that is equal to the margin required by the futures exchanges. Partial collateralization generates leveraged returns, since the value changes of the entire futures position is borne by a smaller collateral amount. Fully collateralized positions are unleveraged, since the cash invested equals the economic exposure of the futures contract. Depending on interest rate levels, the collateral yield can be a substantial part of the total return to a fully collateralized commodity futures position.

The third component of a futures position is changes in its basis, also known as roll yield or roll return. Roll yield or roll return is properly defined as the portion of the return of a futures position from the change in the contract's basis through time. The basis of a futures contract changes for two reasons. First, as time passes, the time to settlement of the futures contract shortens, and the contract's price (and basis) rolls up or down the term structure of forward prices toward the spot price. Second, as components of the cost of carry vary (interest rates, dividend yields, storage costs, or convenience yields), the basis will also vary, since the basis depends directly on the four components of cost of carry. This very important concept is detailed in the next several sections.

12.4.4 Two Interpretations of Rolling Contracts

One of the sources of futures returns just discussed is the roll yield, or roll return, and it is the subject of alternative understandings. Conflicting interpretations of roll return emanate from ambiguity in the concept of rolling a futures position.

Rolling a contract has two common interpretations. Sometimes it is used to describe the transactions involved in switching, or rolling from, a short-term futures contract to a futures contract with a longer term to settlement in the process of maintaining a continuous exposure to the underlying asset. Other times the rolling of a contract describes how its price “rolls up” the term structure of forward prices as its time to settlement nears.

The two interpretations of rolling a contract lead to two interpretations of roll return or roll yield.

When rolling a contract is viewed as holding a futures position while its time to settlement nears and its price potentially rolls up or down the forward curve, then roll return is viewed as the change in the contract's basis through time. This view of roll return tends to be associated with a financial economics view of risk and return.

When rolling a contract is viewed as a transaction, then roll return is viewed as the profit or loss recognized at the time that a position in a futures contract is rolled from one contract to another. This view of roll return is used to adjust excess futures returns in the process of reporting returns of continuous commodity exposures.

It should be noted that the transactions of closing a position in a short-term contract and opening a position in a longer-term contract do not directly and immediately cause a gain or loss. Rolling between contracts can be viewed as recognizing a gain or loss that was previously accrued. But recognition of accrued gains (and rolling of contracts) does not create wealth or return.

12.4.5 Roll Yield and the Slope of the Forward Curve

Chapter 11 discussed the concepts of contango (an upward-sloping term structure of forward prices) and backwardation (a downward-sloping term structure of forward prices). An important topic in commodity futures is the relationship between the slope of the term structure of forward prices (i.e., the forward curve) and the sources of return from holding a futures contract.

It is often claimed that holding a long position in a futures contract when a market is in backwardation tends to be a successful strategy because it earns roll return (or roll yield). The idea is that as time passes and the time to settlement of a futures contract diminishes, the future's price rises as the futures contract “rolls up” the downward-sloping curve of a backwardated market. In other words, it is often argued that market participants can earn consistently superior risk-adjusted returns from the positive roll yield generated from long positions in futures contracts when markets are backwardated.

The argument that roll return generates superior returns in backwardated markets for long futures positions implies that roll return generates superior returns in contango markets for short futures positions. Also, roll return could be similarly argued to lead to inferior returns for long positions in markets that are in contango and inferior returns for short positions in markets that are backwardated. Can alpha be consistently generated by alternating between long and short positions based on the slope of the forward curve?

Chapter 11 detailed the pricing of forward contracts in informationally efficient markets. The slope of the term structure of forward prices was shown in section 11.4.2 to depend entirely on the costs of carry. In an informationally efficient market, a nonzero slope of the term structure of forward prices exists to prevent superior risk-adjusted returns. In other words, the term structure takes on a positive or negative slope (contango or backwardated) based on carrying costs, so that the risk-adjusted returns of spot positions and fully collateralized futures positions will be equal.

In an informationally efficient market, roll return is simply the change in the basis that allows identical exposures in cash and futures markets to offer identical total returns. However, no market is perfectly efficient, especially those involving real assets, such as commodities. The next section examines the pursuit of alpha in the complex world of futures contracts on commodities.

12.4.6 Spot Prices, Futures Prices, and Convergence

When a futures or forward contract on a commodity or other asset has zero time remaining until settlement, the price of the futures or forward contract should equal the spot price of the underlying commodity or other asset because the securities are identical (each calling for immediate delivery). The law of one price and the actions of arbitrageurs push spot prices and futures prices toward each other as settlement nears and non-annualized carrying costs approach zero. Convergence at settlement is the process of the futures price nearing the spot price as settlement approaches, and the two prices matching each other at settlement. Thus, convergence means that through time, the basis tends to move toward zero as settlement nears. Visually, convergence may be viewed as forcing the intercept of the term structure of forward prices to equal the spot price.

Convergence allows for the demonstration of an important relationship between spot returns and futures returns. Consider the following riskless position held by Trader I: long a financial asset with the spot price of S₀ (financed with borrowed money) and a short position in a corresponding one-year futures contract held to settlement initiated at the forward price F(T). The aggregated profit or loss of these positions at settlement when the underlying asset is delivered for F(T) can be expressed as follows:

(12.3)

where the carrying costs of Trader I are all the benefits (dividends and convenience yield) of holding the underlying asset minus all the costs (financing and storage costs) of holding the underlying asset, as perceived by Trader I.

In a perfect market, financial futures contracts are all priced efficiently and all traders receive the same risk-adjusted returns, since they observe the same dividend yields and riskless rates. However, in the case of futures contracts on real assets, for which there are heterogeneous carrying costs, individual traders may have different carrying costs, such that the futures basis may offer a trader the opportunity to earn superior risk-adjusted rates of return. Further, to the extent that the markets for futures contracts on real assets are more likely to be informationally inefficient, traders with superior information or methods of analysis may be able to earn consistently positive alpha.

12.4.7 Roll Yield, Carrying Costs, the Basis, and Alpha

There are three ways of expressing the relationship between spot and forward prices through time: (1) the basis, (2) carrying costs, and (3) roll yield. All three of these terms express the same concept.

In an informationally efficient market (and when the carrying costs are expressed as present values rather than as rates or percentages), the absolute value of the carrying costs will equal the absolute value of the basis. The carrying costs and the basis will have different signs, according to the most common definition of the basis being the spot price minus the forward price.

The roll yield is the same as the basis (and the carrying costs) when viewing the return on a futures contract through its settlement. Note that the roll yield is defined as the change in the basis. Since the basis of a futures contact or forward contract is zero at settlement, the roll yield of a futures contract to settlement must equal the contract's starting basis.

In the case of futures contracts on financial assets, the costs of carry for the underlying financial asset are the financing costs expressed as an interest rate (r) and the rate of dividends, coupons, or other distributions (d) that are received and are entered as a negative cost (–d). While r is observable, d is assumed to only be predictable. We assume that all market participants are unanimous with regard to these values and can engage in transactions to receive or pay the same values of r and d. Therefore, the actions of arbitrageurs in these markets should force financial futures toward a high degree of informational efficiency in which roll yield equals the cost of carry, which, in turn, determines (and equals) the basis.

In the case of real assets, the carrying costs of holding the real asset include the storage cost, c, and the convenience yield, y. Storage costs and convenience yields on real assets are heterogeneous between market participants. A heterogeneous value differs across one or more dimensions. In this case, individual market participants may have different costs and benefits (c and y) from holding a real asset. Further, these costs and benefits may be unobservable to others.

A clear benefit of futures markets on real assets is the market's ability to facilitate the efficient bearing of storage costs and reaping of convenience yields. For example, an efficient storage operator of natural gas can store natural gas while hedging its price risk in the futures market. A manufacturer that depends on silver as a raw material can enjoy the convenience of large inventories (e.g., protection from supply disruptions) while hedging the price risk of silver in the futures market.

A major source of potentially superior risk-adjusted returns using futures contracts on real assets emanates from the heterogeneous costs of carry across market participants. The key for a market participant to generate alpha through analysis of carrying costs and the basis is to execute trades when the prices of futures contracts imply costs of carry that deviate from the participant's costs of carry. For example, a trader can generate alpha if his storage costs are less than the storage costs assumed in the price of the futures contract.

12.4.8 The Impact of Rolling Contracts on Benchmarking and Alpha

This section discusses the rolling of futures positions: the closing of a position prior to or at settlement, and the opening of an otherwise identical contract with a later settlement date in order to maintain continuous exposure. There are two important and related issues that rolling futures contracts raises: (1) What is an appropriate benchmark return for a long-term continuous exposure to a commodity, and (2) What is the relationship between risk-adjusted expected returns and the selection of a particular rolling strategy?

The first issue is how to establish a benchmark for a long-term continuous exposure to a commodity. Within futures markets, individual investors roll their futures positions over at different times relative to settlement and may differ in the selection of which settlement date to use for the new positions. Accordingly, it is not possible to identify a pattern of rollovers that is common to all investors and to identify the return of a particular pattern of rollovers as being representative of the returns achieved by all investors. Thus, the specification of index and benchmark returns in forward contracts is specific to a particular rollover strategy. Further, if an index or a benchmark is designed to represent the return of a fully collateralized strategy, then there can be differences with respect to the interest rate that is assumed to be earned on the collateral. Construction and management of index and benchmark returns in commodities assume a particular rollover strategy and collateral yield; thus, the reported returns of each index or benchmark are driven in part by those assumptions.

The second issue is whether a particular rollover strategy can consistently generate attractive risk-adjusted returns (alpha). The difference in returns between two rollover strategies can be expressed as being equal to the returns of a calendar spread. To illustrate, consider two investors with continuous long positions in the same futures contracts. Suppose that Investor A rolls over contracts one month prior to settlement and establishes a new position in the first deferred contract. Investor B rolls over contracts at settlement and establishes a new position in the new nearby contract. As long as the nearby contract has one month or more to settlement, Investors A and B have the same position. However, when the nearby contract has one month or less to settlement, Investor A rolls into the first deferred contract while Investor B remains in the nearby contract. The difference between the returns of the two strategies occurs only during the month prior to settlement and is equal to the returns of a calendar spread.

For purposes of discussion, let's title the strategy followed by Investor B as a classic rollover strategy: Each contract is held to settlement and then is rolled over into the shortest available contract. All other rollover strategies generate a return that is equal to the return of that classic rollover strategy plus, at times, the return of a short calendar spread. If markets are inefficient, it may be possible to earn a consistently superior or inferior risk-adjusted return through the adoption of a particular rollover strategy. However, any alpha generated from selection of a particular rollover strategy is identical to the alpha of an equivalent strategy using calendar spreads. In other words, speculating on rollover strategies is tantamount to speculating on calendar spreads.

It should be noted that, in practice, markets are imperfect and have transaction costs. When transaction costs are included, some rollover strategies may be more cost-effective than others.

12.4.9 Three Propositions Regarding Roll Return

The more common definition of roll return (or roll yield) is that it is the return accrued in a futures position through time, attributable to changes in the basis of the futures contract. This section distinguishes this definition of roll return from the accounting usage of the term regarding the closing of one futures position and the opening of another. The following three propositions highlight these issues and are based on the more common definition of roll return.

PROPOSITION 1: Roll return is not generated when one position is closed and a new position is opened. For example, roll return is not generated by closing the nearby contract at $95 and opening the first deferred contract at $92, for a $3 profit. The lack of logic to that view of rollover is analogous to selling a short-term Treasury bill for $99, buying a longer-term Treasury bill for $98, and claiming that the transaction generated a profit of $1.

Roll return occurs throughout the time that a particular futures or forward contract is held. Roll return can be viewed as the difference between the price at which a particular contract is opened and the price at which that same contract is closed in excess of the return on a spot position in the contract's underlying commodity. The price difference is based on the same contract at two different points in time.

PROPOSITION 2: Roll return is not necessarily positive when markets are backwardated. It is true that roll return is positive in backwardated markets if none of the components of the costs of carry change. However, if the costs of carry change, then even in backwardated markets there is no guarantee that roll return will be positive. In other words, it is reasonably likely for the term structure of forward rates to shift such that roll return will be negative in a backwardated market.

PROPOSITION 3: A position that generated a positive roll return does not indicate that the position's total returns were superior (i.e., that there was alpha). Roll return is a part of the total returns that make futures contracts and cash positions equally attractive. Roll return is usually negative, to punish the forward position (relative to the cash position) for not requiring a cash investment relative to a spot position. But roll return can clearly be positive, when, for example, there is a high dividend or coupon rate on the underlying asset. In the case of a forward contract or futures contract on a financial asset held to settlement, roll return equals carrying costs times –1: (d – r). Thus, if the dividend yield of a financial asset exceeds the riskless rate, then roll return is positive if the position is held to settlement.

12.5.1 Construction and Uses of Commodity Futures Indices

Financial securities are generally traded in centralized spot markets, and so most indices related to traditional investments focus on prices from cash markets. Returns on physical commodities are generally better measured using prices of futures contracts rather than spot or cash prices. Spot prices of physical commodities are not generally traded in a single centralized market, and therefore the spot prices vary between locations (a difference that cannot be arbitraged to near zero due to transportation costs). Also, while shares of a particular security are homogeneous and trade at the same price, some commodities have different qualities or grades that trade at different prices. For these reasons, commodity price indices are commonly constructed using futures prices on commodities rather than cash commodity prices.

The construction and the application of commodity futures indices raise several complexities relative to indices of traditional assets. As discussed in Chapter 3, returns on derivative positions such as futures can be based on fully collateralized positions or on leveraged positions. Commodity futures indices are generally constructed to be unleveraged. The face value of the futures contracts is fully supported (collateralized) either by cash or by riskless bonds (e.g., Treasury bills). Futures contracts are purchased (i.e., hypothetical long positions are established) or swap agreements are entered into to provide economic exposure to commodities equal to the amount of cash dollars being invested in the index. Therefore, every dollar that an investor exposes to the risk of a commodity futures index has generally similar risk to having one dollar invested directly in commodities.

An investment manager can use commodity futures indices in several ways. First, a commodity futures index can be used as a benchmark for investment performance analysis and return attribution. Second, an investable commodity futures index can be used to implement an active tactical bet by the investment manager that the underlying commodities will generate superior expected or average returns. Finally, an investable commodity futures index can be used in a passive strategy of providing reduced risk through portfolio diversification.

12.5.2 Popular Commodity Futures Indices

The following three commodity futures indices are among the most widely used indices in academia and industry:

1. The Standard & Poor's Goldman Sachs Commodity Index (S&P GSCI) is a long-only index of physical commodity futures. The S&P GSCI is composed of the first nearby futures contract in each commodity. Perhaps the most distinctive feature of the S&P GSCI is that a futures contract trades on the index itself (on the Chicago Mercantile Exchange [CME]). In other words, investors can purchase a futures contract tied to the spot value of the S&P GSCI. The S&P GSCI is a production-weighted index. A production-weighted index weights each underlying commodity using estimates of the quantity of each commodity produced. A production-weighted index is designed to reflect the relative importance of each of the constituent commodities to the world economy. The weights in the S&P GSCI are heavily dominated by energy commodities (over 70%) due to their dominant role in global production. The S&P GSCI is constructed with 24 physical commodities across five main groups of real assets: precious metals, industrial metals, livestock, agriculture, and energy.
2. The Bloomberg Commodity Index (BCOM), formerly the Dow Jones-UBS Commodity Index, is a long-only index composed of futures contracts on 22 physical commodities. These commodities are diversified and include petroleum products, natural gas, precious metals, industrial metals, grains, livestock, soybean oil, coffee, cotton, cocoa, and sugar. Unlike the S&P GSCI, to determine the weights of each commodity in the index, the BCOM relies primarily on liquidity data, such as trading activity. This index considers the relative amount of trading activity associated with a particular commodity to determine its weight in the index and places an upper limit of 33% for the weight of any one sector.
3. The Reuters/Jefferies Commodity Research Bureau (CRB) Index is the oldest major commodity index and is currently made up of 19 commodities traded on various exchanges. The CRB Index uses a four-tiered grouping system to weight the commodities. The system is designed to reflect the importance of each commodity to global economic development. For example, Tier I currently has 33% of the index weight and includes only petroleum products. The second tier represents highly liquid commodities, whereas Tiers III and IV are included to provide diversification and broad representation for the index.

12.5.3 Comparison of Weighting Methods of Commodity Futures Indices

Commodity indices differ in terms of components, weights, and rebalancing methods. The S&P GSCI, for example, is weighted based on economic importance as indicated by global production levels. The weights in the BCOM are determined by economic importance as indicated by the level of trading activity. The argument for constructing both indices is analogous to that used for the capitalization-weighted S&P 500: The most economically important components should have the most influence. In contrast, the CRB Index follows a more subjective and fixed weighting scheme based on tiers.

12.6.1 Four Commodity Market Event Risk Attributes

As indicated in Chapters 16 to 21 on hedge funds, many hedge fund strategies are exposed to substantial event risk, in which hedge funds generally experience poor returns. For example, analysis of the returns to hedge funds around the financial turmoil of 2008 indicates that most hedge fund strategies experienced substantial negative returns—especially arbitrage strategies. Simply put, when a major global or economic crisis arises, long positions in most risky assets decline in value.

However, there are four characteristics of commodity investments that suggest that many major events actually enhance returns to investors with long positions in commodities.

First, most major global events cause increases in commodity prices due to anticipated decreases in commodity supplies or increases in demand. Events that may lead to unexpectedly reduced supply of one or more commodities include disrupted trade and disrupted production. Events such as trade wars, military wars, major weather events, and political instability can inhibit production and/or trade and drive up commodity prices. Trade disputes, wars, and political unrest tend to drive energy prices higher. Droughts, floods, and crop freezes tend to reduce the supply of agricultural products. Major labor unrest or global political instability can drive up the prices of and demand for both precious and industrial metals.

Second, the commodity price increases due to events tend to be larger and more sudden than the price decreases resulting from events that lower commodity prices. These patterns of the number and magnitude of shocks to the commodity markets should provide long positions in commodities with positively skewed returns.

Third, many commodity shocks are likely to be uncorrelated with each other. For example, OPEC agreements to cut oil production should be uncorrelated with droughts in the agricultural regions around the world or with labor strikes affecting mining. The implication is that the commodity price changes due to major events should be relatively uncorrelated with each other and therefore somewhat diversifiable.

Fourth, shocks to the commodities markets are generally uncorrelated with shocks to the financial markets—or perhaps even negatively correlated. The reason is that most sudden large events have negative short-term implications to global production and trade. These shocks tend to reduce the supply of commodities, causing commodity prices to rise while simultaneously depressing equities and corporate bonds. For example, a shock such as a trade dispute or weather event may cause a sudden decrease in the supply of raw materials, which should have a positive impact on commodity prices but a negative impact on financial asset prices through its anticipated reduction in corporate profits.

In summary, commodity price shocks tend to be positive during major events. Therefore, most major global events provide positive returns for commodities at the same time that they provide negative returns for financial assets. The event risk associated with commodities tends to favor investors in the commodity markets while detrimentally affecting investors in traditional financial markets.

12.6.2 Commodities as a Defensive Investment

Fluctuations in aggregate global wealth are an unfortunate consequence of economic activity. When major declines in aggregate wealth occur, most major classes of investments tend to decline in response. A number of studies have examined the correlation of global equity markets during periods of market stress or decline. The conclusion is that equity markets around the world tend to be more highly correlated during periods of economic stress than during normal times. This means that in bad times, when the benefits of diversification are most needed, equity markets tend to decline at the same time, and global equity diversification fails to protect the investor. The major reason that traditional assets often do not provide downside risk protection is that almost all traditional assets react in similar fashion to major macroeconomic events. For example, a spike in oil prices is felt across almost all traditional asset classes.

Most traditional investments do not offer both protection from global turmoil and attractive returns. This is a major reason that investors are drawn to alternative investing. Hedge funds and other skill-based strategies might be expected to provide diversification by being more market neutral and having returns that are protected from, or even benefit from, market turmoil. In addition to using skill-based strategies, investors can achieve diversification benefits from the passive addition of an asset class such as commodities. The greatest concern for most investors is downside risk. The ability to protect the value of an investment portfolio in hostile or turbulent markets is the key to the value of any macroeconomic diversification. Commodities may be especially useful at reducing downside risk.

12.6.3 Slow Acceptance of Commodity Futures by Institutions

Institutional investment capital committed to commodity futures is considerably smaller than that invested with hedge funds. One reason is the lack of understanding of commodities as an investment product. A second reason is the perception that commodity futures are extremely risky investments, best left to aggressive speculators and short-term traders. However, as large institutional investors seek greater diversification in their investment portfolios, commodity investing is growing to meet the demand. Commodities can be viewed as contributing to the diversification of a portfolio. It is expected that the demand for commodities investing and other real assets will continue to grow as institutional investors become more familiar with the risks of commodity investing through futures contacts and appreciate the potential role of commodities in reducing downside risk.