10.1.1 Economic Roles and Vehicles of Natural Resources

A large portion of natural resources is under the earth's surface. In most jurisdictions, private land ownership is limited to surface rights, with the ownership of underground mineral and energy rights retained by governments. However, in the United States, private land ownership has typically included mineral rights. Much U.S. land is publicly owned. For privately owned land, some states allow split estates. A split estate is when surface rights and mineral rights are separately owned.

Public or private owners of natural resources often lease their natural resource rights to developers for eventual extraction. Thus, effective economic ownership of a natural resource is often accomplished through the purchase or leasing of rights rather than through transfer of recorded property ownership.

Pure plays on a private investment in natural resources are rare. A pure play on an investment is an investment vehicle that offers direct exposure to the risks and returns of a specific type of investment without the inclusion of other exposures. Since most underground natural resources are not privately owned and most U.S. privately owned natural resources are commingled with surface rights, there are few institutional-quality investments with returns determined almost solely by the values of the underlying natural resources.

An example of a somewhat pure play on natural resources is Natural Resource Partners L.P., which might also be viewed as a liquid alternative. Natural Resource Partners L.P. is an MLP (master limited partnership) that trades on the NYSE under the ticker symbol NRP. (MLP structures were introduced in Chapter 2 and are further detailed in Chapter 13.) According to the firm, NRP is “principally engaged in the business of owning and managing mineral reserve properties. NRP primarily owns coal, aggregate, and oil and gas reserves across the United States that generate royalty income for the partnership” but also “owns an equity investment in [a] trona/soda ash operation.”¹

In summary, institutional ownership of natural resources can be achieved through land ownership that includes underground rights, ownership of mineral rights, or leasing of mineral rights. There are some opportunities for pure plays on natural resources through private partnerships or listed partnerships (MLPs); however, most global natural resources are either owned by governments or leased to operating firms.

10.1.2 Natural Resources as Exchange Options

Viewing natural resources as options to develop commodities and other real assets offers important insight regarding the analysis of natural resources. A potential developer of a natural resource anticipates expending money to develop the natural resource into a commodity or another improved real asset just as a call option holder anticipates expending cash to acquire an asset. However, an essential element of natural resources as options is that the amount of money necessary to develop the resources is uncertain. Therefore, a key aspect of natural resources as options is that they are better analyzed as an exchange option rather than as a call option with a fixed strike price. An exchange option is an option to exchange one risky asset for another rather than to buy or sell one asset at a fixed exercise or strike price.

The process of developing a resource involves using the mineral rights along with fuel, materials, labor, management, and equipment to bring a commodity to market. It is for this reason that a natural resource should be viewed as an exchange option in which the developer exchanges one set of resources with stochastic prices (the production inputs) to obtain the output (with a price that is also stochastic).

For example, a firm that owns mineral rights to gold ore can be viewed as owning an option to exchange the mineral rights, fuel, mining equipment, labor, management, and materials necessary to extract the gold for a long position in the underlying gold, as depicted more generally in Exhibit 10.1.

The market prices of both the receivables and the deliverables change. As discussed in Chapter 6, like all options, the value of an exchange option depends on volatility. In the case of an exchange option, the volatility depends on (1) the volatility of the price of the asset(s) being delivered, (2) the volatility of the price of the asset(s) being received, and (3) the covariance or correlation coefficient between the prices.

The volatility underlying the exchange option adheres to the familiar formula of Markowitz, which defines the volatility of a two-asset portfolio as depending on both the individual volatilities of the assets and their correlation. If the cost of development is highly correlated with the value of the commodity, the volatility of the value of the exchange will be lower and the value of the option will be lower (everything else being equal). The option can be especially valuable when development costs and commodity prices are not highly positively correlated.

The prices of developing a resource can change due to technological advances and other factors, such as environmental and regulatory concerns. Recent technological breakthroughs in drilling for oil and gas (e.g., hydraulic fracturing, or fracking) have enabled development of resources previously deemed economically infeasible. The transformation of previously worthless shale oil formations into highly valuable producing wells is an illustration of the importance of volatility in development costs that are uncorrelated with commodity prices.

10.1.3 Moneyness as a Crucial Factor in Natural Resource Development

Exhibit 10.2 illustrates a value diagram for natural resource development as an option that is similar to the value diagram of a call option. However, there is an important distinction between the diagram in Exhibit 10.2 and the diagram of a traditional call option (shown in Chapter 6). The horizontal axis of Exhibit 10.2 is the ratio of the current price of the developed natural resource to the current cost of development. The key idea is that both the price of the developed natural resource and the cost of developing the resource are stochastic, so the moneyness depends on the spread between the benefits and the costs of development.

Moneyness in Exhibit 10.2 reflects the direct benefit-to-cost ratio of developing the natural resource immediately. Exhibit 10.2 has three ranges of moneyness: in-the-money (to the right of 1.0 on the horizontal axis), at-the-money (1.0 on the horizontal axis), and out-of-the-money (to the left of 1.0 on the horizontal axis). Being in-the-money means that if the mineral rights are mined at the current price of the commodity (e.g., gold), then the revenues from sale of the commodity will exceed the current costs of developing the commodity (i.e., mineral rights, fuel, labor, management, materials, and equipment).

The option to develop rights to a natural resource may have no expiration date or may be leased on a temporary basis. We examine here the case of a perpetual option. A perpetual option is an option with no expiration date. All perpetual options are American options, since a European perpetual option could never be exercised.

In traditional option theory, most options should be held until expiration. There are limited cases in which an option should be exercised early, such as deep-in-the-money put options and call options prior to ex-dividend dates. Since the option to develop a natural resource is generally a perpetual option, the critical issue is how the owner makes the decision of when to exercise the option.

A natural resource should generally not be developed until the option is substantially into the money. But how far into the money should the option be to justify it being exercised?

Consider the following scenario: A tract of land has moderate quantities of ore containing gold. Suppose that at a market price of $1,500, the gold can be mined at a cost of $1,400 per ounce, for a profit of $100 per ounce. Does it make sense to mine the gold now because of the positive time value of money? The answer is that it depends on three things: the volatility in the price of gold, the volatility in the cost of mining the gold, and the correlation between the two.

10.1.4 Moneyness Differences and Natural Resource Development

Exhibit 10.2 illustrates a key insight into natural resource development when the moneyness depicted on the horizontal axis is viewed as representing different properties. In other words, different properties containing natural resources have different benefit-to-cost ratios from development. Returning to the gold example, consider two properties: (1) a property in a jurisdiction supportive of development, with easily accessible material that is rich in gold ore, and (2) a property with disputed ownership rights, strict environmental regulations, and poorly accessible material with low concentrations of gold ore. Obviously the first property reflects a development option that is deep in-the-money, whereas the second property reflects a development option that is deep out-of-the-money.

Common sense indicates that the first property should be developed before the second property. In economics, this is known as the low-hanging-fruit principle. The low-hanging-fruit principle states that the first action that should be taken is the one that reaps the highest benefits over costs. Thus, the order in which natural resource properties are developed should tend to be driven by the low-hanging-fruit principle.

10.1.5 Why Some In-the-Money Options Should Not Be Exercised Immediately

Option theory guides the distinction between the properties that are sufficiently in-the-money to justify immediate development and the properties for which development should be postponed awaiting subsequent price changes.

The value of delaying a decision to exercise an in-the-money development option, as in all in-the-money options, is based on an analysis of the benefit of awaiting further information. The convex nature of the payoff diagram in Exhibit 10.2 illustrates the asymmetric payoff to options. A long position in an option has increased value at an increasing rate in one direction (in the case of Exhibit 10.2, moving to the right) and decreased value at a decreasing rate in the other direction. The essence of this convexity to holders of long positions in options is to consider the advantage generated by the volatilities of market prices when deciding on the optimal time to exercise an option.

To illustrate, consider a perpetual option with a current intrinsic value of $100. An intrinsic option value is the greater of $0 and the value of an option if exercised immediately. The option's owner believes that future changes in the moneyness of the option are random and, for simplicity, are symmetric. If the moneyness of the option grows substantially higher by increments of, say, $200, then the option's intrinsic value will rise to $300. But if the moneyness falls by the same amount ($200), the option's intrinsic value will not fall to –$100; it can only fall to $0.

These numbers illustrate why the owner of the option should be reluctant to exercise the option. If the owner exercised the option now, it would be worth $100. But the owner might very well prefer a 50% chance of receiving $300 and a 50% chance of having an out-of-the-money option that might become valuable someday.

In this simplified analysis, the option should not be exercised until the time value of the option is zero. The time value of an option is the excess of an option's price above its intrinsic value. The sum of an option's intrinsic value and its time value is equal to the option's total value (or price), as depicted in Equation 10.1:

(10.1)

Returning to Exhibit 10.2, the point at and above which a development option should be exercised is depicted by point A, where the time value of the option is zero. Above that point, the developer gains more wealth from immediately reaping the profit of development than from delaying the decision to exercise the option and potentially benefit from the option's convexity and stochastic market prices. The financial economics are similar to the decision to exercise an American put option early.

From a macroeconomic perspective, the price of the associated commodity rises or falls to either increase or decrease development rates so that the supply of the commodity matches the demand for the commodity.

10.1.6 Implications of Moneyness for Risks of Natural Resources

Exhibit 10.2 and the related discussions provide insight into the risks of natural resources. For natural resources that represent in-the-money development options, the short-term financial risks are primarily driven by the price of the underlying commodity. The steep slope of the option curve in Exhibit 10.2 for options that are far in-the-money indicates that changes in the price of the commodity are the dominant source of short-term volatility in the value of the option to develop the natural resource. Higher moneyness shortens the time horizon of the exercise of the option and reduces the chance that the option's price will be substantially altered directly by changes in the costs of developing the natural resource.

Conversely, natural resources that represent out-of-the-money development options have substantial sensitivity to uncertainty other than the price of the underlying commodity prices. The more distant time horizon for possible development increases the sensitivity of the natural resource's price to changes in development costs, interest rates, and other factors.

10.2.1 Land in Anticipation of Development

A term for investment in and acquisition of undeveloped land or vacant lots is land banking. Land banking is the practice of buying vacant lots for the purpose of development or disposition at a future date. This practice is common in the home-building industry and allows home builders to secure land tracts for eventual use in the fulfillment of housing development pipelines.

Land banking most commonly refers to the acquisition of unimproved or raw land that sits in the anticipated path of residential growth, but the term also references improved vacant lots held by a third-party entity for home builders who have option agreements to use these lots as needed. This has allowed for the more efficient use of capital by home builders. The key investment strategy is to purchase at a relatively low cost land that is vacant, rural, or underutilized and hold it in anticipation of substantial value increases as the location emerges in the path of future development.

The value of land or lots is distinguished not only by location but also by the level of improvement or development. Generally, three types of lots can be purchased for investment:

• Paper lots refers to sites that are vacant and approved for development by the local zoning authority but for which construction on streets, utilities, and other infrastructure has not yet commenced.
• Blue top lots are at an interim stage of lot completion. In this case, the owner has completed the rough grading of the property and the lots, including the undercutting of the street section, interim drainage, and erosion control facilities, and has paid all applicable fees required. At this stage, a home builder can obtain a building permit upon payment of the ordinary building permit fee.
• Finished lots are fully completed and ready for home construction and occupancy. All entitlements, including infrastructure to the lot, finished grading, streets, common area improvements, and landscaping, have been completed. All development fees, exclusive of the building permit and inspection, have been paid.

In times past, home builders banked land and developed lots for their own accounts. As they have become increasingly sophisticated public companies, they have largely changed this practice, relying on joint ventures or third-party investors to bank land for them. Because of this, there has been an increased disintermediation of investment in raw land development. Institutional investors now provide a substantial share of the paper lots and finished lot inventories to home builders on an as-needed basis.

The attraction of land investment is based on the ability to purchase land at an attractive price relative to its potential value in development. However, this is a long-term investment strategy. The key risks depend on the type of residential land purchased and where it is located. Finished lots near a major metropolitan area are safer investments than is raw, undeveloped land. Lots far from urban areas trade at steep discounts to potential value because their development is longer-term and less likely, which implies higher risk and possibly more expenses from, for example, building paved roads and providing electricity and sewerage in a pioneering effort. Unfinished lots also face steep discounts because of the expenses required to develop lots into finished products. These concepts are best understood when land is viewed as a call option.

10.2.2 Land as an Option

Investment in undeveloped land is an option on development much like investment in land with mineral rights.² The strike price of the option is the cost of developing or improving the land (e.g., constructing an apartment building). The time to expiration of the option is typically unlimited. The receivable asset of the option is the combination of the land and its improvement or development (e.g., a finished apartment building with the land beneath it). The payoff of the option is the spread between the value of the completed project and the cost of constructing the project.

The cost of construction (i.e., the strike price of the option) tends to be correlated with the price of improved real estate. This is because the actions of developers tend to arbitrage the relative prices whenever the price of improved real estate substantially increases relative to the cost of development. The value of land as an option on development is therefore positively related to the excess of the value of completed real estate projects over the costs of construction. The volatility of the underlying asset is the volatility of the spread between the costs of construction and the value of the improved property. As with any option, the value of land is positively related to the anticipated volatility in the underlying asset. But since construction costs and completed real estate values are positively correlated, the value of the option is reduced relative to the value that would be obtained if the exercise price (construction costs) were fixed.

Land that has multiple potential uses is more valuable than land with a single potential use, all other things being equal. As long as the possible values to the various potential uses are imperfectly correlated, multipurpose land will have higher expected payouts and higher values. The reason is that each potential purpose for the land provides possible payouts that, if imperfectly correlated with the payouts of other purposes, generate higher volatility.

While land is generally a perpetual option, it should be exercised (i.e., developed) when the net benefits of development exceed the net value of retaining the option. Therefore, the decision to develop property can be modeled using option theory and depends on the moneyness of the option. The option value also depends on the volatility of the spread; the dividend yield (income) of the completed project; the risk-free rate; and any costs of holding the undeveloped land, such as property taxes, insurance, and maintenance.

10.2.3 Example of Land as a Binomial Option

Chapter 6 discussed binomial tree models and provided a single-period example of pricing an option when the price of the underlying asset for the downward branch had a price of zero. In this section, the binomial approach is expanded to allow nonzero prices for the underlying asset in both branches of the tree.

For simplicity, this example is single period and assumes that the risk-free interest rate is zero. These assumptions allow the use of a simplified version of a powerful option-modeling technique called binomial option pricing. Binomial option pricing is a technique for pricing options that assumes that the price of the underlying asset can experience only a specified upward movement or downward movement during each period.

Consider a parcel of land that can be improved at a construction cost that depends on the overall health of the economy. If the economy improves (the up state), the land can be improved at a construction cost of $100,000 and will create an improved property worth $160,000. If the economy falters (the down state), the construction cost drops to $80,000, and the improved property would be worth $70,000. Comparable improved properties now sell for $100,000.

The first step in valuing the land is to use the current price of comparable improved properties ($100,000) and the two possible values of improved properties at the end of the period ($160,000 and $70,000) to determine the risk-neutral probability that the economy will improve. A risk-neutral probability is a probability that values assets correctly if, everything else being equal, all market participants were risk neutral. A risk-neutral probability may be viewed as being equal to a statistical probability that has been adjusted for risk so that it can be used to price risky assets in a risk-neutral framework. More details are provided regarding risk-neutral probabilities in Part 5. By assuming that the riskless interest rate is zero, we enjoy the simplicity in this example of not needing to discount future cash flows. So the current value of a comparable property must equal its end-of-period expected value based on risk-neutral probabilities, as shown in Equation 10.2:

(10.2)

where UpValue equals value in the up state, DownValue equals value in the down state, UpProb equals the risk-neutral probability of the up state, and (1 – UpProb) equals the risk-neutral probability of the down state (a faltering economy).

Inserting the comparable property's current value and possible property values into Equation 10.2 generates a solution for the probabilities:

Solving this equation generates UpProb = 1/3, which means that the risk-neutral probability that the economy will falter is 2/3.

The second step is to insert the probabilities calculated in the first step into Equation 10.2 to compute the value of the option (the land). The key is to compute the value of the two development outcomes. In the up state, the developer earns $60,000 ($160,000 – $100,000). In the down state, the developer loses $10,000 ($70,000 – $80,000) by developing, so let's assume for simplicity that the developer donates the land to a nature conservancy rather than suffering a cash loss. The value of the option (the land) is the weighted average of the outcomes, since the riskless interest rate is zero.

Thus, the value of the land is $20,000. Simply put, there is a one-third chance that the economy will do well, netting the developer $60,000, and a two-thirds probability that the land will be abandoned to charity. The power of binomial option pricing models emanates from setting or calibrating the probabilities of each path based on market-observed values of efficiently priced assets and then using those probabilities to price an option.

While extremely simplified, this binomial option pricing framework can demonstrate important principles, as illustrated in the following examples.

The option model approach may be used for a variety of purposes, such as computing volatility given an option price and computing probabilities given an option price. The application of binomial option pricing, even in this simplified example, demonstrates the ability of option theory to provide insight into risk. In addition to including a nonzero riskless interest rate, an analyst may wish to consider multiple time periods in applying the option approach.

10.2.4 Risk and Return of Investing in Land

Investment in land is a departure from the traditional forms of real estate investment by institutional investors, who tend to purchase commercial real estate that is then leased, providing both capital appreciation and an annual cash flow. As a result, land development tends to be riskier and more speculative than other real estate investing, owing primarily to its lack of revenue, its long holding period, and its uncertain prospects. However, raw land does not deteriorate in value the way developed real estate does. Whereas developed properties require constant upkeep to maintain their value, the downside risk of owning undeveloped land is reduced.

Land may be viewed as a call option. As with the expected return of a call option on an equity, the expected return of land depends on its systematic risk. The expected return of land is a probability-weighted average of the expected return of the land if it remains undeveloped and the expected return of the land if it is developed:

(10.3)

where E(R_l) equals expected return on land, P_d equals probability of development, E(R_d) equals expected return conditioned on land being developed, and E(R_nd) equals expected return conditioned on land not being developed.

Undeveloped land is sometimes criticized as an investment with poor returns, based on the observation that values of undeveloped land do not increase substantially through time. However, historical returns of undeveloped land may suffer from a negative survivorship bias. A negative survivorship bias is a downward bias caused by excluding the positive returns of the properties or other assets that successfully left the database. In this case, a return index on properties that remained undeveloped excludes the high returns obtained on the properties that were developed.

Returning to the option view of land, land that does not get developed tends to be land that in retrospect was a bad investment (unexercised options). Land that gets developed tends to have been a successful investment (exercised options). Consequently, price indices of undeveloped land tend to understate the expected returns of all undeveloped land because they ignore the success stories, meaning the land that became developed during the period in which the returns are being observed.

In most investment analyses, survivorship bias is positive. In the cases discussed in subsequent chapters, the problem is that the index ignores the negative returns of investments that fail. In the case of undeveloped land, the properties that remain in the category tend to be the failures. By excluding the favorable outcomes, historical indices of undeveloped property may substantially understate mean returns and falsely portray undeveloped land as a poor investment.

10.3.1 Timberland Risk and Return

The pros and cons of ownership of timberland are summarized in Exhibit 10.3. The key potential benefit of timber are returns that have a low estimated correlation with traditional stocks and bonds. However, as pointed out in section 10.5, this apparent benefit may stem from the smoothed pricing caused by the difficulty of measuring the value of illiquid assets, such as timberland. Timber is a renewable resource with flexibility in the timing of its harvesting. On the other hand, timber values are tied to cyclical industries such as housing that can experience prolonged slumps, such as the housing slump that began in 2007.

Perhaps the greatest risk of timber is its long growth cycle and the many adverse events that can occur during that cycle. Rotation is the length of time from the start of the timber (typically the planting) until the harvest of the timber. Natural stands of pine frequently require a rotation of 45 to 60 years. Hardwoods may need 60 to 80 years to produce high-quality saw-timber products. Even though intensive management of planted pine can shorten the rotation to approximately 25 to 35 years, the investment is still very long-term and subject to risk—such as fire, drought, and other natural disasters—as well as obsolescence due to innovation or government restrictions on ownership rights, such as harvesting.

But timber does offer harvesting flexibility, which is a timing option. A harvest schedule can be accelerated or postponed by several years in most cases, giving the owner the opportunity to time a harvest to coincide with personal income needs or to wait for a more favorable price situation. There can be a substantial value to delaying the harvest of timber for an additional year. Depending on age, weather, and location, Forest Research Group estimates that northern hardwood experiences a biological growth rate of 1% to 3.33% per year.⁴ Delaying harvest during a year of low timber prices earns an additional year of growth while waiting for timber to rise to a more profitable sales price. Also, timber can be used for a variety of purposes (firewood, pulpwood, chip-n-saw, home building), offering the option to put the timber into a variety of products. To the extent that the prices of the associated products are imperfectly correlated, the multipurpose option can add considerable value.

10.3.2 Methods of Timberland Ownership

Most timberland is directly owned and privately traded by institutional investors. There are two publicly traded ways to invest in timber. First, at least two ETFs (exchange-traded funds) have been developed to track the S&P Timber and Forestry Index. The ETFs hold the same stocks that are in the timber index and in the same cap-weighted proportion. Unfortunately, the returns of the two ETFs have not matched those of the index very closely. Both ETFs have underperformed the S&P Timber and Forestry Index and done so with greater volatility. Although these ETFs have the same beta exposure as the underlying index, both suffer from a cost structure and a trading reality that do not match those of the timber index. Another way for retail investors to gain exposure to timber is through real estate investment trusts (REITs), which are discussed in Chapters 14 and 15. There are four REITs that specifically invest in timberland.

10.4.1 Financial Analysis of Farmland

Exhibit 10.4 provides an example of the potential return to farmland before income taxes. Assume that farmland costs $10,000 per acre and that the investor purchases 30 acres, for a total investment of $300,000. The landowner finances half the farmland with debt at 8%, for a total interest expense of $12,000 per year. The landowner receives as rent $1,000 per acre, for an annual income of $30,000. There are property taxes of $200 per acre, for a total property tax expense of $6,000. Insurance and other costs are $2,000.

Exhibit 10.4 shows that the return on equity (ROE) (net income/equity) is 6.67%. The return on assets (operating income/assets) is $22,000/$300,000, or 7.33%. In real estate, the cap rate (capitalization rate) or yield is a common term for the return on assets (7.33% in this example). The concept is often used to value real estate so that the value of a property might be viewed as equal to the property's expected annual net operating income divided by an estimate of an appropriate cap rate:

(10.4)

The annual operating income is the income before financing costs. When Equation 10.4 is used to value real estate, the cap rate (or yield) is a ratio based on observation of comparable real estate and professional judgment.

10.4.2 Farmland Prices and Returns

The total returns on farmland depend on cash flows from income as well as changes in market prices of the farmland. Farmland contains the idiosyncratic risks of poor harvests and farm-specific cost inefficiencies. Farmland revenues, returns, and valuations are also driven by macroeconomic factors, including commodity prices.

Farmland may be viewed as a play on the growing global population. The United Nations estimates that the world's population will grow by one-third over the next 40 years. This growing population would require additional food and use additional land. However, advances in agriculture may continue to generate substantial increases in food production per acre of farmland, and additional nutritional needs can be met by scaling back consumption of products that require large amounts of grain and farmland, like meat. Technology has increased the yield per acre of farmland through advances in fertilizers, plant genetics, pesticides, and farming education. Improvement has been dramatic; for example, in some areas of the United States, such as Iowa, the corn yield per acre has more than tripled over the past 60 years.

Another potential boost to farmland prices may result from continuing expansion in farmland as a source of energy through biofuels. Ethanol produced from corn or sugar cane is mixed with gasoline to provide a blend of energy for automobiles. In addition to corn, biodiesel can be produced using soybeans. As more countries around the world search for solutions to their energy needs, traditional crops and agricultural use of land will become more valuable.

Government policies are usually favorable to farmland, including crop subsidies and the ability to rapidly depreciate (for income tax purposes) improvements to farmland, such as drainage systems or levees. However, government actions can also work against farmland values. For example, the U.S. federal government may periodically sell its stores of grains and commodities, depressing commodity prices and farmland values at the same time.

The expected returns and risks of farmland are related to its unique nature and its differences from traditional real estate. First, farmland produces commodities that trade on international markets. Whether it is wheat, corn, soybeans, or some other product, these commodities are quoted on international futures exchanges and are traded and shipped around the world. This makes farmland values much less dependent on local economic conditions. Second, unlike buildings, farmland generally does not deteriorate substantially through time and does not need renovation. Finally, farmland is very scalable; the additional amount of machinery and labor needed to manage and produce crops on additional acreage is not large. Scalability drives competition in the market for leasing farmland.

From a portfolio management perspective, there are risks to farmland. First, like most other forms of real estate investing, farmland is illiquid. Second, transaction costs are high. Sales are arranged through brokers that can charge fees of 3% to 5% for negotiating the sale of the land. In addition, the time to find a suitable buyer can be long, particularly in a recession. Financing can become unavailable at times, which can undermine the value of the land.

10.4.3 Three Factors of Multiple Use Option Prices

The agricultural value of farmland is related to commodity prices and farming expenses, which are in turn related to overall economic factors and governmental policies. Specifically, the agricultural value of farmland is driven by the profitability of its agricultural use. A prolonged surplus of a commodity, like corn, generates substantially lower commodity prices. Lower commodity prices, such as lower corn prices, can lead to depressed farmland prices, especially for land areas where corn production has traditionally served as the land's best use.

This highlights the value and importance of options for multiple purposes. The value of the multiple purposes of farmland is driven by three factors related to the multiple uses (other than the moneyness of the current best use): (1) the current closeness of the profitability of each alternative to each other, (2) the volatility of the profitability of each alternative, and (3) the lack of correlation between the alternatives as to profitability.

For example, suppose that a farmer has two main crops that are suitable for the farmer's land and equipment: corn and soybeans. The option to plant either crop has low value if both crops have very different current levels of profitability, if neither corn nor soybean profitability varies substantially, or if corn and soybean profitability are highly correlated. In all three cases, the option to switch from one crop to the other has very limited value.

Consider a region where planting one particular crop is consistently the best use of farmland. For example, in the United States, there is a major corn-producing region. In this region, other uses of the land often offer substantially lower profitability. In such cases, the options for alternative use may be viewed as being far out-of-the-money. Therefore, the multipurpose aspect of the option has little value, and the land behaves more like a single-use option that is in-the-money. However, having several viable crops with volatile and uncorrelated prices is a valuable option.

The possible multipurpose option of farmland often extends well beyond multiple agricultural uses. Land that is currently most profitably deployed as farmland can become more valuable for other uses, such as development (residential, industrial) and mineral rights. Multiple-use options can be especially valuable when they include both agricultural and nonagricultural uses, because the correlation between the profitability of diverse uses tends to be lower than the correlation between the profitability of similar uses. Low correlation of uses generates higher option value, because when underlying assets diverge in profitability or value, the call option holder can benefit from the rise in the value of one use with limited harm from the fall in the value of the alternative use.

10.4.4 Methods of Farmland Exposure

Private farmland ownership is the primary method of obtaining exposure to farmland in particular and agribusiness in general for institutions. Regarding publicly traded alternatives, there are two stock indices that track the farmland and agribusiness industry: the DAX Global Agribusiness Index and the Thomson-Reuters In-the-Ground Global Agriculture Equity Index. The stated goal of both indices is to provide a benchmark for the agribusiness industry. Both indices track publicly traded companies that engage in four areas of the agribusiness industry: (1) agricultural products, (2) seed and fertilizer, (3) farm machinery, and (4) packaged foods.

The Market Vectors Agribusiness ETF (ticker MOO, a creatively descriptive ticker name) tracks the same stocks with the same weights as those in the DAX Index. The ETF began trading in August 2007, and its performance closely tracks that of the DAX Index.

10.5.1 The Impact of Smoothing on Observed Volatility

For simplicity, consider an investment that experiences the following six months of returns (not necessarily in this order): –3%, –2%, –1%, +1%, +2%, and +3%. Since this series has a sample mean of 0%, the sample variance of the series is simply (1/5) × [(–0.03²) + (–0.02²) + (–0.01²) + (0.01²) + (0.02²) + (0.03²)]. The sample volatility (or standard deviation) of the monthly return series is 2.37% (rounded).

Now consider the measured volatility if the returns of the best and worst months are changed to +2% and –2% from +3% and –3%. The sample variance of this new series is (1/5) × [(–0.02²) + (–0.02²) + (–0.01²) + (0.01²) + (0.02²) + (0.02²)], and the sample volatility is 1.90% (rounded).

If the highest and lowest returns are smoothed, the observed volatility can be substantially reduced. In this example, the observed volatility of the smoothed series is approximately 80% of the size of the unsmoothed series. Smoothing also affects the measured correlation between returns on different assets. Continuing with the previous example, suppose that a second asset has corresponding actual monthly returns of –5%, –3%, –1%, 1%, 3%, and 5%. Using unsmoothed returns, the estimated correlation between the two assets is 99.4%. However, if the highest and lowest returns of the first asset are smoothed as described previously, then the measured asset correlation is just 95.8%.

10.5.2 Managed Returns and Volatility

Managed returns are returns based on values that are reported with an element of managerial discretion. There are four primary ways that values and returns can be managed: favorable marks, selective appraisals, model manipulation, and market manipulation.

A favorable mark is a biased indication of the value of a position that is intentionally provided by a subjective source. For example, a trader may ask a brokerage firm to provide an indication of the value of a thinly traded asset for reporting purposes when the trader has reason to believe that the brokerage firm has an incentive to bias the valuation process in a particular direction to assist its client. Favorable marks may be used to obtain high real estate appraisals that enable larger mortgages.

Selective appraisals refers to the opportunity for investment managers to choose how many, and which, illiquid assets should have their values appraised during a given quarter or some other reporting period. Appraisals are relatively expensive, so the normal practice is to appraise a subset of assets infrequently (e.g., annually or even once every three years) and to quote asset values between appraisals using inexpensive internal updates. This practice enables investment managers to alter the timing of appraisals and the selection of properties to be appraised to manage reported returns.

Model manipulation is the process of altering model assumptions and inputs to generate desired values and returns. Model manipulation can occur in complex unlisted derivative transactions and other unlisted assets that are valued using models. The reported values can be manipulated by altering the parameter values that are inserted into the model. For example, use of higher estimates of asset volatilities can generate higher option prices.

Market manipulation refers to engaging in trading activity designed to cause the markets to produce favorable prices for thinly traded listed securities. As an example of this extreme practice, a buy order may be placed very near the close of trading to generate a higher closing price (or, conversely, a sell order may be placed to generate a lower closing price) in order to report more favorable returns for the current period or to smooth price variations, since valuations are frequently based on closing prices. To the extent that investment managers and fund managers are rewarded for exhibiting stable returns, there is an incentive to reduce observed volatility by managing returns. Smoothing can also be generated inadvertently. In the case of real assets, the appraisal process can introduce smoothing, as discussed in the next section.

10.5.3 Appraisals and Smoothing

Listed financial assets, such as the shares of the equity of Exxon, are homogeneous and have observable market prices. Thus, the owner of 1 million shares of Exxon can use observed market prices to value a portfolio. However, many real assets tend to be unique and unlisted. Therefore, the estimation of values for a real asset, such as an oil-producing property, typically requires professional appraisal. Appraisals are professional opinions with regard to value and are discussed in greater detail in Chapter 15. A central issue in the analysis of the risks and returns to real assets is the effect of the use of appraisals on the estimation of returns and the measurement of risk.

Behavioral finance discusses psychological phenomena such as anchoring, detailed in Chapter 15, which can explain smoothing in the appraisal process. Appraisers may inadvertently underprice real assets that experience large upward shifts and overprice real assets that experience large downward shifts. The result is likely to be a highly smoothed price series relative to the price series of similar but listed assets. The essential point is that real asset appraisals can inadvertently cause lower reported volatility by muting large positive and negative returns.

Another problem with valuing real assets is that the extreme illiquidity of these assets means that a period of months typically passes between the agreement on a price for a transaction and the actual culmination of the exchange. Also, the appraised value of an asset is typically a lagged value that is based, to a substantial degree, on the observed transaction prices of comparable assets. Thus, changes in appraised values typically lag changes in actual values by even more than changes in observed transaction prices do.

These two sources of lagged information affect the measurement of return correlations between liquid and illiquid assets. To see this, suppose that a liquid asset has the following quarterly returns:

Suppose further that an illiquid asset has exactly the same true returns, but they are measured and reported one quarter later because of illiquidity lag and appraisal lag:

The true correlation between the returns of the two assets is 100%, but the measured correlations of the reported returns (from periods 2 to 10) is just 29.1% due to the lag in reporting the returns of the illiquid asset. The underestimated correlation implies dramatically greater diversification benefits than truly exist.

10.5.4 Smoothed Returns Compared to Market Returns

The previous section implicitly viewed returns based on market prices as true indications of risk while viewing smoothed returns based on appraisals as underestimating the true risks. However, in some cases, there is considerable debate regarding the reliability of market prices versus appraisals. This section discusses whether the listing of real assets reveals risk or increases risk.

In some cases, such as U.S. real estate, there are reliable data on both appraised prices from unlisted properties and market prices of similar real estate held inside funds that trade in liquid markets. Often the returns computed from appraised values diverge substantially from the returns computed from market prices, even though the underlying real assets are similar. Specifically, the volatility of returns based on market prices is often substantially higher than the volatility of returns based on appraised values. A critical issue is whether the price volatility of listed real assets reflects true changes in the value of the real assets or whether the price changes reflect trading conditions in the equity markets. For example, if the equity market experiences a huge sell-off and the listed prices of real assets similarly decline, do the large losses correctly reflect actual diminished value of real assets or do they overstate the true losses?

Contagion is the general term used in finance to indicate any tendency of major market movements—especially declines in prices or increases in volatility—to be transmitted from one financial market to other financial markets. When comparing the high volatility of listed real estate prices relative to appraised real estate prices, it may be argued that the high volatility of listed real estate prices is driven by contagion effects from other listed securities, such as the equities of operating firms that are listed on the same exchange. Within this interpretation, the high volatility of listed real estate prices would be driven by potentially temporary contagion effects rather than indicating true volatility in the value of the underlying properties. The primary question is: Do listed real asset prices overstate underlying asset volatility because they are unduly influenced by liquidity swings or mood swings in financial markets, or do appraised real asset values understate underlying asset volatility because they fail to reflect value changes on a full and timely basis due to smoothing?

One clue to the resolution of this question can be found in the definition of fair market value, as appraisers seek to measure it. A typical definition is “the amount of cash … that property would bring if exposed for sale in the open market under conditions in which neither buyer nor seller could take advantage of the exigencies of the other.”⁵ For example, a liquidity crisis that motivated an owner to accept a relatively low price to convert a real asset into cash would be explicitly ignored in the process of appraising the value of that asset. In contrast, asset values and returns that are measured using actual transaction prices incorporate events such as liquidity crises, as the market events of October 2008 through March 2009 showed. Such events indisputably affect the values at which assets can be sold.

This issue of whether market prices or appraised values better reflect risk is central to the analysis of real assets and important to consider in the analysis of their risks and returns. In section 10.6, appraised values of real assets are used to estimate historical returns and estimate risk. Clearly, the results need to be viewed in light of the possibility that the reported risks substantially underestimate the true risks because of the use of smoothed valuations rather than market prices.