Risk and required return assessments of equity timberland investments in the United States.
The Capital Asset Pricing Model (CAPM) is useful for estimating the risk and risk-adjusted returns for timberland investments in the United States. However, most analyses predate the existence of empirical, asset-based timberland return series. This analysis estimates timberland CAPM betas based on the National Council of Real Estate Investment Fiduciaries (NCREIF) Timberland Index at the U.S. National, Pacific Northwest, Northeast and South regional levels, utilizing annual returns. In addition, synthetic timberland return series are constructed for 22 regions within the U.S. South, corresponding to Timber Mart-South price reporting areas. CAPM betas are estimated for these areas. We estimate betas of 0.167, 0.349, 0.193, and 0.147 at the National, Pacific Northwest, Northeast, and South areas, respectively, and from -0.137 to 0.279 for regions within the South. Utilizing the estimated betas, we estimate nominal required return rates of 5.8 percent, 6.6 percent, 5.9 percent, and 5.7 percent for institutional timberland investments at the National level, and in the Pacific Northwest, Northeast and South regions respectively. Required rates of return of 4.5 percent to 6.3 percent are estimated for the 22 geographic regions within the South.
Timberland is owned for a variety of reasons. While the financial return from managing the land for harvested timber products is not the only reason people own timberland, and indeed for some it is not a reason at all, for many owners it is the primary objective of ownership. Investment grade timberland serves as an important asset class in well-diversified portfolios of institutional investors. Its use in this role has grown significantly in recent years. DANA Limited (2006) estimates that institutional investors currently own approximately $17 billion of timberland in the United States. One of the prime tools utilized by investors to assess the contribution to a portfolio's risk by the addition of an investment is the Capital Asset Pricing Model (CAPM), developed by Sharpe (1964), Lintner (1965), and Mossin (1966). Previous CAPM analyses have found a wide range of timberland CAPM beta estimates in relation to the broad equities market, from large, negative estimates to moderate, positive figures. These estimates of relative volatility are also used to estimate risk-adjusted returns that timberland investments should be expected to generate. This cost of capital figure can be used to evaluate investments in timberland, as well as periodic silvi-culture investments in the timber management aspect of the business.
Most previous efforts to estimate timberland betas occurred before the existence of a sufficiently long time-series of empirical timberland return data. Instead, various forms of synthetic timberland return indices were constructed for use in estimating the CAPM parameters. The National Council of Real Estate Fiduciaries Timberland Index is the only return index currently in existence for timberland assets. The data now comprise 19 years of returns for most regions. We estimate market risk sensitivities and required rates of return for timberland investments in the broad regions reported by NCREIF--the U.S. South, Northeast, and Pacific Northwest. Since the predominance of investment grade timberland in the United States, and the world, is located in the South, it is worthwhile to explore risk characteristics of timberland within this region. We develop synthetic return series for timberland in 22 different geographic regions within the South, at an annual frequency and covering the period 1987 to 2005. With these data, we estimate market risk sensitivities and required return rates.
The CAPM builds upon the foundation laid by Markowitz (1952), who proved that the risk of an individual investment should not be important to investors, but rather the investment's contribution to the investor's overall portfolio risk. The risk of a financial asset is generally measured as the variability of its returns over time, and is commonly denoted by the SD of periodic returns. Risk can be stratified into two components. Idiosyncratic or firm-specific risk is that component of total risk that is specific to the asset, resulting from actions, events and news pertaining to the specific asset / investment but not to other assets or firms. Firm-specific risk can be removed from the portfolio through diversification. The risk that remains is termed market risk, or systematic risk. This is risk due to economy-wide events and news, and that affects all firms. Systematic risk cannot be removed from the portfolio with diversification.
The contribution of the CAPM is its ability to relate the impact of systematic risk upon the returns of an investment. It does so with the following form:
E([R.sub.i]) = [R.sub.f] + [[beta].sub.i][E([R.sub.m]) - [R.sub.f]], 
where E([R.sub.i]) is the expected or required return on asset i, [R.sub.f] is the risk-free rate of return, and E([R.sub.m]) is the expected return on the total market portfolio of assets. The quantity E([R.sub.m]) - [R.sub.f] is referred to as the market risk premium, or the additional expected return of the market portfolio over the risk-free rate. [[beta].sub.i] is a measure of the sensitivity of the expected returns of asset i to variance in the total market portfolio. It is a measure of the asset's systematic risk, that portion of the asset's total risk that cannot be diversified away. An asset having a beta greater than one is more risky than the market, and commands a higher required return, while an asset with a beta less than one is less risky than the market, and requires a lower return.
CAPM theory states that the market return should reflect the return on all traded and nontraded risky assets, to include human capital. A major criticism of the CAPM is that such a return is of course, unobservable. For empirical work, a proxy is chosen that reflects a broad market portfolio of assets. Historical returns for the S&P 500, or other broad market index are commonly used.
The CAPM was designed as a one-period model. As such, the choice of a proxy for the risk-free rate does not receive much attention. U.S. Treasury securities with a short maturity are usually chosen, the 30- and 90-day Treasury bills being common. These assets are more reflective of a truly risk-free asset than long-term U.S. Treasury bonds. Treasury bonds make periodic coupon payments, which have some degree of reinvestment risk. However, Bruner (2003) and Damodaran (2006a) emphasize that the choice of the risk-free rate should match the return period for the asset data employed. In other words, if the choice is to invest in a closed-end timberland fund having a 10-year horizon, the most appropriate risk-free alternative would be the 10-year U.S. Treasury bond.
Bruner (2003) surveyed a collection of corporations, financial advisors, academics, and authors of corporate finance textbooks. The survey questions addressed practices used when estimating the cost of capital. When asked the question of which risk-free rate to use when using the CAPM to estimate a required return, the overwhelming response by both corporations and advisors is to use a long-term Treasury bond yield. 70 percent of practitioners utilize a maturity of 10 years or longer, while only 4 percent stated the use of Treasury-bill yields. Bruner concludes with the recommendation of matching the maturity of the risk-free investment to the character of the investment being analyzed, and recommends the yield on the 10-year or longer maturity U.S. Treasury bond for most capital project evaluations.
Estimates of the market risk premium can vary widely, and according to Perold (2004) can be the most difficult component of the model to estimate. Practitioners have a choice of using either an historical estimate of the premium earned by equities over riskless investments, or somehow looking forward to estimate this differential. The obvious assumption in using historical premiums is that future expectations can be reasonably characterized by past experiences. The technique usually involves differencing the average realized return on a risk-free government security from the average realized return on a broad market index. However, Damodaran (2006b) describes three questions the analyst must answer that can significantly influence the result.
First, the number of years of historical returns can have an influence. Using a longer time period yields averages that are much more robust, yet at the cost of including potentially stale or misleading data. Damodaran (2006b) documents that the large standard errors resulting in using time periods of less than 50 years can be larger than the estimated risk premium itself. Second, the choice of short-term Treasury bills as the risk-free asset will result in a market risk premium approximately 1.5 percent larger than if long-term Treasury bonds are used. This choice is easily decided for us, as consistency is required with our aforementioned choice of the risk-free rate that matches the investment horizon.
Third, the choice of using arithmetic vs. geometric averaging of market and riskless returns will make a difference. The arithmetic average is the simple mean return. The geometric average is the compound return, more reflective of an investor's buy-and-hold experience (Bruner 2003). The more variable a return series is, the lower its geometric average will be compared to its arithmetic average. This difference is also more dramatic for longer return series. While U.S. Treasury bonds and bills will not be greatly influenced by this choice, stock indices will because of their increased volatility. The arithmetic average annual return of large capitalization stocks from 1926 to 2005 is 11.6 percent, while the geometric average is 9.6 percent. (1) A requirement of using the arithmetic average of returns is that they be independent over time. However, Fama and French (1988), among others, have documented significant negative autocorrelation of returns over time, making the geometric average the more accurate choice. When analyzing timberland investments, the proper choice is therefore to use a broad-market return index coupled with long-term U.S. Treasury bonds as the risk-free investment, with annual returns for each series averaged geometrically.
While the CAPM is designed to be a forward looking model, it is often used to estimate an asset's beta by evaluating historical returns. We cannot know or observe the expected returns that are required in the model. Following Jensen (1969), the excess returns version of the single-index model regresses historical returns for the asset less the risk-free rate (the asset's risk premium) against the market risk premium:
([R.sub.i] - [R.sub.f]) = [[alpha].sub.i] + [[beta].sub.i]([R.sub.m] - [R.sub.f]) [e.sub.i], 
where [R.sub.i],[R.sub.f] and [R.sub.m] are time series of historical returns for the asset, the risk-free rate and the market proxy, respectively, and [e.sub.i] is an error term. [[alpha].sub.i], or the alpha parameter, is an estimate of the risk-adjusted excess return generated by the asset. If significantly positive, the asset has generated a return in excess of that warranted by its expected market risk. When choosing a risk-free investment for use in the parameter estimation process, a zero-coupon U.S. Treasury security having the same maturity as the frequency of return data should be used.
This required return can be used as a benchmark for measuring potential investments or projects. If evaluating a potential timberland acquisition, the first step would be to estimate the future cash flows for the property, to include timber sales, lease revenues, tax payments, etc. The estimated cost of capital would then be used to discount these figures to arrive at a present value. For an existing property, the required return can be used to evaluate periodic silviculture investments in that asset, such as fertilization or competition control, based on their expected impacts on growth and subsequent cash flow.
Early tests of the CAPM (Fama and MacBeth 1973, Gibbons 1982) have confirmed the positive relationship between beta and asset return. This relationship has also been found to be mostly linear, as the CAPM predicts. Researchers have, however, found the beta-return relationship to be 'flatter' than that predicted by the CAPM (Fama and MacBeth 1973, Black et al. 1972, Fama and French 2004, among others). For example, low-beta assets often have a positive Jensen's alpha, or y-intercept rather than the predicted zero value, while high-beta stocks have been shown on average to have negative Jensen's alpha values. Similarly, betas are expected to migrate toward the mean through time for assets that do not substantially alter their risk with specific events such as changes in capital structure, large divestitures, or acquisitions (Blume 1971).
Fama and French (2004) describe a divergence of opinion among researchers for the imperfect empirical record of the CAPM. Some believe financial markets are not as efficient as once believed, a requirement of the CAPM. Market efficiency stipulates that current security prices reflect all available information regarding the security, resulting in the inability to predict the direction or magnitude of the security's future price movement. Some believe that investors overreact to past stock price performance, which researchers have potentially identified by adding factors to asset pricing models that may capture this behavior (DeBondt and Thaler 1987).
Others believe that more risk factors are required to explain asset prices, in addition to market risk. The three-factor model of Fama and French (1993) is an example. Still others (Roll 1977) believe that the CAPM has never been, nor can be, accurately tested because of the impossible selection of a proxy for the entire market portfolio of assets. While Fama and French (2004) discourage use of the CAPM for empirical work, 80 percent of corporations and financial advisers surveyed by Bruner (2003) nevertheless use the CAPM to estimate the cost of equity capital. One hundred percent of text and trade books included in the survey also recommend primarily using the CAPM for this purpose. With all of its problems noted, the CAPM is still the most used asset pricing model today and has become a standard tool for assessing and understanding financial risk.
Timberland return drivers
Timberland investment returns are generated through two components: income and capital appreciation. Income is received primarily from the periodic sale of timber, which in turn is used in the manufacture of lumber; panel products such as plywood, oriented strandboard (OSB), and fiberboard; paper; packaging; and several types of specialty chemicals. An attractive characteristic of selling timber is that it can be withheld from the market during times of low prices at little cost in many cases. There is a minimal storage fee in the form of an opportunity cost, and in fact the timber continues to grow and appreciate until more favorable market conditions return. Annual income is also often received from the leasing of recreation rights on the land, primarily for hunting.
Capital appreciation is realized from the continuous biological growth of the trees. In addition, larger trees are more valuable per unit than are smaller trees. This is because telephone poles, plywood veneer, and the larger sizes of lumber--some of the highest valued products made from trees-can be made only from larger trees. Therefore, as a tree crosses certain thresholds from one size class to another, its value per unit increases. For southern yellow pine species, there are three predominant size classes: pulpwood, chip-n-saw, and sawtimber. Pulpwood is used to make paper and OSB, and is the smallest and least valuable size class. Chip-n-saw is used to make small dimension lumber. Sawtimber is used in the manufacture of larger dimension lumber and poles, and is the most valuable size class.
The price paid for timber varies by tree size, region, and season. Finished good prices also have an impact on timber prices. However, Binkley (2000) showed how the price of southern pine sawtimber has increased at a compound annual real rate of 2.6 percent from 1910 to 2000. This increase is exhibited in both the income component of timberland returns and in the capital appreciation component, as a key element of the capital appreciation of timberland is the increase in the value of the land itself (Caulfield 1994). This increase is attributable to two factors: first, the increase in the value of the land for producing timber due to price increases (Washburn 1992), and the conversion of a portion of a timberland portfolio to a higher-valued use than the production of timber, such as residential or commercial development, during the investment period.
Timberland return data
The only timberland return index currently in existence2 that is based on actual timberland transactions and appraisals is the National Council of Real Estate Investment Fiduciaries Timberland Index (NCREIF 1994). NCREIF publishes historical return data for timberland investments managed by its members, at two geographic levels: the United States, and three regions within the U.S.: the Pacific Northwest, the Northeast and the South. The NCREIF Timberland Index segregates a total return into income and capital appreciation elements, and is based on actual data reported by its members managing timberland investments.
Hancock Timber Resource Group (2003a) describes how NCREIF began compiling and publishing a quarterly index of timberland property returns in 1994, with data retroactive to 1987 for the Southern and Pacific Northwest regions, and 1994 for the Northeast. This index tracks the changes in value of timberland properties that are (a) held in a fiduciary environment, as opposed to the myriad other ownership objectives shared by many other timberland owners; and (b) "marked to market" at least annually. If the property does not experience a change in ownership during a year via a sale, then it is appraised at year-end to yield a new value. As a timberland investment organization joins NCREIF, it submits historic returns for its properties to augment the index.
This index is built and maintained similarly to NCREIF's other commercial real estate indices. The index has four basic components: the market value of all properties in the index; the EBITDDA return for the properties; the capital return; and the total return. The EBITDDA return is based primarily on the sale of harvested timber during the quarter. However, many timberland property owners lease recreation use rights to clubs or individuals, the income from which is also included in the EBITDDA portion of the total return. It must be noted that the EBITDDA figure is gross of applied management fees charged by the property manager, and therefore overstates the true net income received by the investor (Healey et al. 2003). The capital appreciation component is basically the ratio of the difference in period-to-period property market value, minus capital expenditures in the current period, to the market value of the previous period. Timberland appraisals usually occur on an annual basis and often in the fourth quarter. For time series analyses the quarterly returns are therefore less meaningful, since they will often display an artificial spike in one quarter per year, reflecting the appreciation due to the annual appraisal. For analysis purposes, it is recommended that annual returns be used (Hancock Timber Resource Group 2003a).
The United States-wide timberland index is subdivided into three regional indices: South, Pacific Northwest, and Northeast. Table 1 lists the annualized returns for the four NCREIF Timberland series. The NCREIF return data provides a significant improvement over the use of synthetic proxies for timberland returns. However, it still has two drawbacks that limit its utility in assessing inferences about the performance of timberland investments. First, a portion of the periodic return is based on appraisals rather than market transactions. Second, the reporting frequency is only useful on an annual basis, resulting in a paucity of data points relative to the daily, weekly, or monthly returns of more traditional continuously traded financial assets.
Investing in timberland by institutions is relatively new. It can be tracked to the passage of the Employee Retirement Income Security Act (ERISA) in 1974 that required institutional investors to diversify their portfolios away from traditional common stocks and fixed income securities to broader classes (Healey et al. 2003, Zinkhan 2003). Investments in timberland by institutions grew by a factor of 10 during the 1990s to some $17 billion by 2005 (DANA Limited 2006). This is reflected in the time span of the NCREIF Timberland Index. Although the NCREIF series are regarded as the best data available describing the performance of institutional investments in timberland, the need to analyze the financial performance of timberland predates the existence of this index. Before this time, most analysts constructed synthetic return indices with several management assumptions for use in timberland investment analyses.
Timberland returns value to the owner through a combination of periodic income and capital appreciation, as previously discussed. Therefore, the common return formula is applicable for measuring timberland returns:
[R.sub.t] = [NI.sub.t] + [CV.sub.t]/[CV.sub.t-1] - 1, 
[R.sub.t] = total return per acre of the asset during period t;
[NI.sub.t] = net income received per acre of the asset during period t;
[CV.sub.t] = capital value per acre of the asset during period t.
Many assumptions about forest management practices must be made when developing a synthetic timberland return series. One that is common among most authors is that the hypothetical forest being modeled is fully regulated. This implies that the volume of timber harvested each period is equal to the volume grown. The standing volume of timber in the forest is therefore static over time. So harvest is static, which will minimize volatility and may lower estimates of beta. This allows any capital appreciation of the forest to be reflective of timber or land price appreciation, inflation, or some other factor, but not from any implied change in the inventory of the asset. Revenue realized from the sale of harvested timber represents the periodic income component. Missing from this model of returns is a provision to reflect the occasional sale of small parcels of a property, commonly referred to as a real estate component.
Redmond and Cubbage (1988) constructed species-based synthetic timberland return series for 22 commercial timber species in the United States. Four of the product series' beta estimates were positive, and only two were significant at the [alpha] = 0.05 level. Zinkhan (1988) utilized a synthetic annual return series for southern pine from 1956 to 1986, developed by a timberland investment firm, to estimate a timberland beta of -0.21. Statistical significance was not stated. Washburn and Binkley (1990) studied 11 sawtimber annual stumpage price series reported by the USDA Forest Service and the state of Louisiana. For southern pine sawtimber in Louisiana they estimated insignificant betas of between 0.17 and 0.18, while for southern pine sawtimber on national forests they estimated insignificant betas of 0.35 to 0.37.
Binkley et al. (1996) created synthetic timberland return series for the Pacific Northwest, Northeast and South to estimate timberland systematic risk measures and excess returns. Their model, the John Hancock Timberland Index (JHTI) (3) uses one time series data component: the quarterly stumpage price of the appropriate timber species group for the region modeled. For the U.S. South, the stumpage price is a composite price equal to the equally weighted average price of pine pulpwood and sawtimber. The return income component is simply the quarterly stumpage price multiplied by a subjective factor that represents the regional ratio of periodic income to the capital value of the representative forest. The capital value component is a weighted average of the previous eight quarters' stumpage prices, with progressively less weight given to each preceding quarter's price. Each year's four quarterly returns were then averaged to yield an annual return. Binkley et al. (1996) estimated return series from 1960 to 1994. The authors used a portfolio of large and small company common stocks, corporate bonds, and U.S. Treasury securities of varying maturities for the market portfolio proxy. U.S. Treasury bills of unspecified maturity were used for the risk-free rate. The authors found significant betas of-0.88 ([alpha] = 0.05), -0.54 ([alpha] = 0.05), and -0.21 ([alpha] = 0.10) for the Pacific Northwest, South, and Northeast, respectively. Significant alpha estimates of 10.2 percent, 5.9 percent, and 2.8 percent were found for the same regions ([alpha] = 0.05).
Sun and Zhang (2001) compared CAPM and APT estimates for eight forestry-related investment classes. Two of the investment vehicles modeled were the now-defunct Timber Performance Index and the NCREIF timberland index. NCREIF quarterly returns from 1987 to 1997 were used as a return series. The S&P 500 composite index was used for the market proxy, and U.S. Treasury bills of unspecified maturity were used for the risk-free rate. Sun and Zhang estimated an insignificant beta of -0.05 for the NCREIF Timberland Index. By using quarterly rather than annual returns for the NCREIF series, the beta estimate must be considered suspect. This is due to the aforementioned common practice of appraising timberland properties in the fourth calendar quarter, resulting in an artificial change in capital value during that time.
[FIGURE 1 OMITTED]
Synthetic return series for areas within the South
In addition to estimating CAPM betas and required returns for timberland investments at the major regional level, we also analyzed timberland performance within the U.S. South. The John Hancock Timberland Index (JHTI) model of timberland returns was used as a template to construct synthetic return series for 22 different areas within the U.S. South for 1987 to 2005, where the areas correspond to those defined by Timber Mart-South (TMS 2006a) (Fig. 1). Timber Mart-South divides each of 11 Southern states into two areas, and reports both stumpage and delivered prices for southern pine and hardwood species groups, and for the major product classes. Prices are reported on a quarterly basis. Similar to Hancock Timber Resource Group (2003b), we utilize pine stumpage prices to estimate an annual return series.
Aside from using regional rather than South-wide prices, our series differs from Hancock's in four ways. First, we include pine chip-n-saw as a product component because of the increasing prominence of small-diameter sawtimber in most southern regions. Second, we estimate unique harvest weights for the three pine product classes in each region to apply to the quarterly prices, rather than using an equal weighting factor. Third, we estimate the income rate, representing the quarterly ratio of periodic income to capital value of an investment-grade forest, based on a comparison of our series to the reported NCREIF South return series from 1987 to 2005. Finally, we utilize the composite stumpage prices of the 12 previous quarters for the capital value component rather than 8 quarters. By using the 12 previous quarters, volatility of the return series is reduced slightly, as measured by the SD of returns, and is closer to that of the NCREIF South series.
From Eq. , the net income and capital value components for region r in quarter t are:
[NI.sub.rt] = [P.sub.rt] Income Rate, 
[CV.sub.rt] = ([11.summation over (n=0)] (12 - n)[P.sub.r(t-n)])/78, (5)
[P.sub.rt] = [W1.sub.rt][ppwd$.sub.rt] + [W2.sub.rt][cns$.sub.rt] + [W3.sub.rt][pst$.sub.rt], 
and [ppwd$.sub.rt], [cns$.sub.rt], and [pst$.sub.rt] are the pine pulpwood, chipn-saw, and sawtimber prices reported in Timber Mart-South for region r in period t.
Region-specific product harvest weights (W1-W3) were estimated from USDA Forest Service's Timber Product Output (TPO) data (USDA Forest Serv. 2006). The Forest Service periodically surveys mills throughout the South to determine the quantity of wood consumed by product type, and if known, the county of origin. They then estimate the origination of these volumes based upon Forest Service Forest Inventory and Analysis (FIA) inventory data, along with assumptions regarding mill basin radii, etc. The result is a table of estimated timber volume harvested by species group and product class. This table is reported for each county of each southern state. TPO data exists for each state for three different points in time. For most states, the data reflect conditions in 1995, 1999, and 2003, with the exception of Louisiana and Arkansas, for which harvest data are reported as of 1996, 1999, and 2002.
The Forest Service also segregates the data by ownership class. The class most representative of investment-grade timberland is the Forest Industry ownership group. There is not an ownership group specifically representing institutional, or investment-grade, timberland. However, much current investment-grade timberland was at one time owned by an integrated forest products company, and was therefore in the Forest Industry group at one time. Where that was not the case, both groups nevertheless manage timberland similarly (Siry 2002, Clutter et al. 2006). Due to legislative protocol, the Forest Service does not report timberland data of any sort at the county level, and segregated by ownership group. Data are only reported by ownership group at the statewide level. Therefore, a special request was made of the Forest Service's Southern Research Station. A file was sent to them containing a Timber Mart-South region designation (1 or 2) for each county in each Southern state. Forest Service personnel then aggregated harvest volume data by ownership group for all counties in each TMS region, and returned this to us. We therefore received harvest volume data at the TMS region level by ownership group, without violating Forest Service protocol.
The Forest Service TPO data include only one size class for pine sawtimber. They do not segregate pine sawtimber into two size classes. The Southern Forest Products Association (SFPA) 2002 Annual Mill Survey (Southern Forest Products Assoc. 2003) was referenced to provide an empirical method of apportioning regional sawtimber removal volumes. This survey reports pine sawtimber consumption by U.S. South sawmills, by size class. This survey reports the consumption by size class at the South-wide level. By special request, the SFPA agreed to disaggregate this data by state. The number of responding mills in the survey was quite small when viewed at the individual state level, and expert judgment was used to refine this data. It should be noted that this sawtimber size class apportionment represents a single point in time, yet was used to apportion sawtimber volumes for the duration of each time series modeled.
The final parameter needed for estimating the return series is the Income Rate, which is a South-wide, static estimate of the quarterly ratio of periodic income from a timberland investment to its capital value. This parameter was estimated by first aggregating the 22 area harvest volume product weights into South-wide weights over time. These weights were utilized in our quarterly return model, along with TMS southwide stumpage prices to estimate a south-wide return series from 1987 to 2005. The quarterly return series was then annualized. The annual returns from this series were differenced from the NCREIF South series, and squared. The sum of these squared differences was minimized by adjusting the Income Rate in the South-wide synthetic series. The resulting Income Rate value was 1.49 percent. Figure 2 shows the NCREIF South Timberland Index and our South-wide synthetic timberland return series from 1987 to 2005. These two return series have a correlation coefficient of 0.710 for the total 19year history and 0.936 for the most recent 9 years. The Income Rate value was then used in the calculation of each of the 22 area synthetic return series. Table 2 shows the average annual synthetic returns and SDs.
[FIGURE 2 OMITTED]
The similarity of our synthetic, South-wide return series with the NCREIF South Timberland Index is quite good, especially for recent years. Although it is generally understood that timber prices are a significant determinant of timberland prices, other factors exist that influence timberland returns that are not modeled in our synthetic return model. Specifically, timberland owners periodically sell small tracts of land that are worth more for other purposes than timber management, for example real estate development. Such tracts are termed Higher and Better Use, or HBU. NCREIF members report the proceeds from HBU tract sales, which are then included as a portion of the capital return component of the regional return series. We do not attempt to capture this impact.
CAPM estimation and discussion
A significant assumption necessary when estimating required returns utilizing a beta estimated in an ex post fashion is the assumption of the similarity of future and historical asset performance. A trade-off with respect to accurate beta estimation vs. the applicability of that beta in estimating a required return concerns the length of the time series used to estimate the beta. Going further back in time by using more historical returns strengthens the precision of the beta regression estimator. However the future performance of the asset class may not be accurately reflected by historical performance reaching to a point in the past that may reflect a different economic environment for the asset class. The requirement to use annual return data for the NCREIF series yields only 19 data points (11 for the Northeast index), which is small compared to the typical 60 monthly returns used with conventional financial asset beta estimates. Recognizing this trade-off, we chose to use the entire time series to ensure the most precise estimates.
The excess returns version of the single-index model  was used to estimate alpha and beta parameters for the four NCREIF and 22 subsouth synthetic timberland return series. The S&P 500 index was used as the market proxy, along with yields for the 1-year U.S. Treasury bill as the risk-free rate. Ordinary least squares regression was used to estimate the model if the Durbin-Watson (DW) statistic for first-order autocorrelation of the error was within its upper bound for significance at the [alpha] = 0.05 level. If the DW statistic was not within the upper bound, the SAS MODEL procedure (SAS Institute Inc. 1999) was used to estimate the model with a first-order autoregressive error structure. Table 3 documents the regression results.
The beta estimates for the four NCREIF return series are somewhat higher than those found for timber and timberland by most other researchers. Whether this is due to the use of the NCREIF series vs. stumpage price or synthetic timberland return series, or perhaps that the systematic risk of timberland investments is increasing over time, is inconclusive. However, our NCREIF beta estimates are insignificant at the [alpha] = 0.05 level, (4) consistent with most prior research. Beta estimates for the 22 subsouth synthetic return series are mostly positive, low and not significantly different from zero, with few exceptions. (5) Subsouth regional beta estimates with 95 percent confidence intervals are shown in Figure 3. The average beta of the 22 regions is 0.084 on an equal-weighted basis. This is significantly different from the NCREIF South beta estimate of 0.147. (6) Weighting the subsouth regional beta estimates by an estimate of the amount of investment-grade timberland acres available in each region (7) yields a weighted-average beta of 0.096.
Although timberland owned by institutional investors is quite similar to that owned by traditional forest products companies such as Weyerhaeuser and Temple-Inland, and timberland real estate investment trusts (REIT) such as Plum Creek Timber and Rayonier, the calculated CAPM betas are not directly comparable for two reasons. First, CAPM betas calculated from reported stock returns are equity betas. A firm that is financed to some degree with debt also has a debt beta. By combining the betas for these two sources of financing the beta of a firm's unlevered assets can be calculated as:
[[beta].sub.Unlevered Asset] = Debt/Debt + Equity [[beta].sub.Debt] + Equity/Debt + Equity [[beta].sub.Equity], 
where Debt and Equity represent the long-term debt and market capitalization of the firm, respectively. In practice, the risk of corporate debt is quite low, and can, in many cases, be assumed to be zero (Ross et al. 2002). Incorporating the tax shield for interest paid on debt yields the beta of the firm's unlevered assets as:
[[beta].sub.Unlevered Assets] = [[beta].sub.Equity]/[1 + (1 - [T.sub.C]) Debt/Equity]. 
where [T.sub.C] is the corporate income tax rate. A firm that uses debt to finance some portion of its operations will necessarily have an unlevered asset beta that is lower than its equity beta.
The NCREIF timberland investments are unlevered investments. Therefore our estimated CAPM equity betas are synonymous with the unlevered asset betas. To compare these betas to reported equity betas for publicly owned, vertically integrated forest products corporations and publicly traded timberland REITs, we must first remove the impact of leverage from the equity betas of those firms. Table 4 lists the equity betas of Weyerhaeuser, Temple-Inland, Plum Creek Timber, and Rayonier, four publicly owned firms that own significant amounts of investment-grade timberland. The equity betas, along with long-term debt and market capitalization figures, were reported by Value Line for the end of 2005. Assuming a tax rate of 38 percent for Weyerhaeuser and Temple-Inland, their unlevered asset betas are 0.88 and 1.01, respectively.
Plum Creek and Rayonier are timberland real estate investment trusts, or REITs. As such, they do not pay corporate income tax on timber and timberland related earnings, as long as 90 percent of the income from these assets is distributed to shareholders in the form of dividends (DANA Limited 2006). They do however have some processing assets, the income from which is taxable at the standard corporate rate. According to published company annual reports, Plum Creek had an average effective tax rate of 1.8 percent for 2002 to 2005. Rayonier transitioned to a REIT status effective on January 1, 2004, and had an effective income tax rate of 12.9 percent for 2004 to 2005. Utilizing these tax rates, the unlevered asset betas of Plum Creek and Rayonier are estimated to be 0.68 and 0.86, respectively. These four beta estimates are substantially higher than the NCREIF betas. A second reason making a direct comparison of the NCREIF timberland betas to those of the four publicly owned firms difficult is the heterogeneous composition of the firms' assets compared to the pure timberland represented by NCREIF. These four firms own various types of timber conversion assets in addition to timberland, such as sawmills, pulpmills, and papermills.
[FIGURE 3 OMITTED]
The significantly positive alpha estimates of 5.5 percent to 18 percent for the NCREIF returns suggest that institutional timberland investments have performed above the level warranted by their systematic, or market risk. Of the subsouth regional return series, only the Arkansas-2 area had an estimated negative alpha (-3.0%). Nineteen of the 22 synthetic-return estimated alphas are not significantly different from zero. The average alpha of the 22 regions is 3.6 percent, significantly different than the 5.5 percent NCREIF South estimate. (8) The weighted-average subsouth alpha is 3.4 percent.
With timberland betas estimated from historical data, our attention can now be focused on estimating required returns for future timberland investments. From Eq.  we will need estimates of an applicable risk-free rate [R.sub.f], and the market risk premium ([R.sub.m] - [R.sub.f]). Following Bruner (2003) the current yield on the 10-year U.S. Treasury bond is used as the risk-free rate commensurate with a timberland investment made by an institution that is typically of a 10 year duration. Although certainly many timberland investments are made for longer time horizons, Bruner (2003) points to the often relative flatness of the yield curve beyond 10 years as minimizing the importance of choosing a bond beyond the 10-year rate. Recent yields on the 10-year U.S. Treasury bond have been approximately 5.1 percent.
From historical return data provided by Bodie et al. (2005), the historical market risk premium of large stocks over long-term government bonds for 1926 to 2005 is 4.25 percent, utilizing geometric mean returns. Using Eq. , along with the CAPM beta estimates, the required return on equity for institutional timberland investments in the U.S. South, Northeast, and Pacific Northwest is estimated to be 5.73 percent, 5.92 percent, and 6.59 percent, respectively. Nationally, the required return is estimated to be 5.81 percent. Utilizing our beta estimates for timberland investments within the South, required return on equity estimates range from a low of 4.52 percent in VA 1, to a high of 6.29 percent in FL 2, with an average of 5.46 percent and a S D of 0.41 percent. The average when weighted by available investment-grade timberland acres is 5.51 percent. The required returns developed here are nominal; no attempt has been made to isolate the real return component. These results are displayed in Table 5.
This study utilized the Capital Asset Pricing Model to assess the risk, risk-adjusted performance, and required return of institutionally owned, equity timberland investments in the United States. Data comprised 19 years of annualized returns for the NCREIF South and Pacific Northwest Timberland indices (1987 to 2005), and 11 years for the NCREIF Northeast index (1994 to 2004). Recognizing the appraisal bias inherent in the quarterly form of the NCREIF data, annualized data were used. Consistent with this return frequency, 1-year U.S. Treasury bill yields were used as the risk-free rate, along with returns for the S&P 500 Composite Index as the market proxy.
The CAPM beta coefficient is the estimate of a security's sensitivity to variance of the overall financial market. We estimate low, positive betas for equity timberland investments, and not significantly different from zero. This implies that timberland investments bear substantially less risk than does the financial market as a whole. These estimates are higher than those found in many previous studies, which often employed different return series, estimation benchmarks and timeframes. Our results suggest the possibility of an increase in recent years of the nondiversifiable, or systematic risk of timberland investments. Future research should explore this possibility, along with identifying possible explanatory factors.
The CAPM alpha coefficient reflects the historical performance of an investment in consideration of its systematic risk. We estimate positive alphas for the NCREIF national and regional return series, significantly different than zero for all but the Pacific Northwest region. Hence, timberland investments have performed above the level warranted by their market risk. This finding is consistent with previous research.
The CAPM was also used to estimate forward-looking, required nominal return rates for timberland investments. The calculated betas were used, along with the current yield on the 10-year U.S. Treasury bond, which constitutes an appropriate risk-free alternative to a typical institutional timberland investment. A market risk premium consistent with historical performance was utilized. Risk adjusted rates of return are estimated to be less than 100 basis points above the risk-free rate for all NCREIF return series except the Pacific Northwest, which is 150 basis points above the benchmark riskless investment.
Synthetic return series were created for 22 geographic regions within the U.S. South, corresponding to Timber Mart-South price reporting areas. CAPM beta and alpha parameters, and required return rates were estimated for these regions, based on annual returns for 1987 to 2005. The intrasouth beta estimates are low, mostly positive and all are statistically insignificant. Risk-adjusted historical performances are low, positive (21 of 22) and mostly insignificant. Required rates of return range from 4.5 percent to 6.3 percent.
Further research may provide insight into timberland investment performance by examining the fundamental components of the return process as they relate to factors within the economy to estimate appropriate risk and required return figures. Market risk premiums estimated by a forward-looking procedure might also prove to be of value. This study provides a firm foundation of risk and required return estimates using a traditional approach, against which future models and results can be benchmarked.
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(1) Data from the Center for Research in Security Prices, University of Chicago, as published in Bodie et al (2005).
(2) The Timberland Performance Index (TPI) (Caulfield 1994) was similar to the NCREIF index; however, it is no longer in existence.
(3) Described fully in Hancock Timber Resource Group (2003b).
(4) The NCREIF-South beta estimate was significant at [alpha] = 0.10.
(5) 18/22 regions positive; FL 2 significant at [alpha] = 0.05, AL 1 significant at [alpha] = 0.10.
(6) t-statistic = -3.13.
(7) USFS FIA (Smith et a1 2004) timberland acres for the Forest Industry ownership group for each southern state, apportioned to TMS area levels by an estimate of the volume harvested in each area.
(8) t-statistic = -3.84.
The authors are, respectively, Manager, Timberland Investment Research, Resource Management Serv., LLC, Birmingham, Alabama (firstname.lastname@example.org); and Dean, Warnell School of Forestry and Natural Resources, Univ. of Georgia, Athens, Georgia (email@example.com). The authors would like to thank Tony Johnson and his staff at the USDA Forest Serv. Southern Research Sta. for their assistance in developing the Timber Product Output data with respect to Timber Mart-South areas. This paper was received for publication in October 2006. Article No. 10265.
Table 1.--Annual returns for the four NCREIF timberland indices. Annual returns are compounded reported quarterly returns. Mean return is the arithmetic average of the annual returns. National South Northeast Pacific Northwest Year (percent) 1987 26.5 14.1 36.3 1988 30.1 14.0 71.1 1989 37.4 12.6 74.4 1990 11.1 13.6 7.8 1991 20.3 10.8 29.9 1992 37.3 13.1 60.5 1993 22.4 15.1 27.3 1994 15.4 20.0 14.0 10.7 1995 13.8 13.7 3.3 15.3 1996 10.7 11.5 17.6 8.9 1997 18.9 24.3 18.1 11.6 1998 5.9 10.7 10.7 -2.7 1999 10.9 7.3 27.9 13.7 2000 4.4 2.3 7.5 8.3 2001 -5.2 -4.1 -6.2 -8.4 2002 1.9 2.3 2.8 -1.0 2003 7.7 7.5 12.2 8.6 2004 11.2 9.5 17.4 12.4 2005 19.4 14.3 35.6 Mean 15.8 11.2 11.4 22.1 Std. dev. 11.1 6.2 8.9 23.4 Table 2.--Means and SDs of synthetic timberland return series for 22 areas within the U.S. South from 1987 to 2005. Timber Mart-South Area 1 Timber Mart-South Area 2 State Average return SD Average return SD (percent) Alabama 10.8 8.0 10.4 9.4 Arkansas 11.2 10.4 7.0 18.0 Florida 9.4 8.6 8.3 9.1 Georgia 8.9 10.7 8.0 7.7 Louisiana 11.5 8.0 11.5 9.7 Mississippi 13.0 11.2 11.8 9.7 North Carolina 10.4 9.6 10.5 4.8 South Carolina 8.5 7.5 8.9 6.6 Tennessee 13.3 13.8 12.4 13.9 Texas 12.9 10.2 10.2 11.7 Virginia 10.1 6.0 10.6 6.9 Table 3.--CAPM parameter estimates for NCREIF and synthetic timberland returns. Alpha standard Asset [alpha] error Pr > [absolute value of t] NCREIF National 0.113 0.042 0.015 NCREIF South 0.055 0.012 0.000 NCREIF Northeast 0.059 0.026 0.048 NCREIF Pacific NW 0.180 0.095 0.078 AL 1 0.043 0.029 0.151 AL 2 0.044 0.036 0.242 AR 1 0.023 0.061 0.705 AR 2 -0.030 0.097 0.761 FL 1 0.027 0.031 0.402 FL 2 0.015 0.027 0.586 GA 1 0.033 0.037 0.388 GA 2 0.017 0.029 0.561 LA 1 0.055 0.025 0.042 LA 2 0.051 0.029 0.094 MS 1 0.018 0.066 0.790 MS 2 0.051 0.038 0.195 NC 1 0.048 0.035 0.187 NC 2 0.045 0.018 0.024 SC 1 0.017 0.037 0.658 SC 2 0.013 0.035 0.712 TN 1 0.070 0.034 0.054 TN 2 0.059 0.062 0.359 TX 1 0.070 0.036 0.071 TX 2 0.024 0.052 0.649 VA 1 0.053 0.025 0.053 VA 2 0.053 0.016 0.003 Beta standard Asset [beta] error Pr > [absolute value of t] NCREIF National 0.167 0.120 0.183 NCREIF South 0.147 0.075 0.065 NCREIF Northeast 0.193 0.132 0.177 NCREIF Pacific NW 0.349 0.268 0.211 AL 1 0.179 0.098 0.086 AL 2 0.066 0.129 0.617 AR 1 -0.052 0.109 0.639 AR 2 -0.014 0.165 0.932 FL 1 0.097 0.105 0.371 FL 2 0.279 0.094 0.009 GA 1 0.120 0.121 0.336 GA 2 0.100 0.072 0.186 LA 1 0.160 0.110 0.164 LA 2 0.168 0.137 0.237 MS 1 0.078 0.112 0.496 MS 2 0.079 0.122 0.526 NC 1 0.101 0.122 0.417 NC 2 0.044 0.050 0.382 SC 1 -0.049 0.067 0.474 SC 2 0.045 0.065 0.495 TN 1 0.249 0.203 0.236 TN 2 0.001 0.128 0.992 TX 1 0.093 0.144 0.527 TX 2 0.161 0.115 0.180 VA 1 -0.137 0.080 0.105 VA 2 0.070 0.093 0.452 Asset R-square DW NCREIF National 0.318 1.94 NCREIF South 0.187 1.41 NCREIF Northeast 0.193 2.38 NCREIF Pacific NW 0.292 1.73 AL 1 0.378 1.91 AL 2 0.197 1.47 AR 1 0.395 1.37 AR 2 0.527 1.71 FL 1 0.261 1.65 FL 2 0.465 1.59 GA 1 0.323 2.18 GA 2 0.450 2.10 LA 1 0.232 1.78 LA 2 0.191 1.79 MS 1 0.422 1.46 MS 2 0.225 1.49 NC 1 0.203 1.68 NC 2 0.317 1.83 SC 1 0.430 2.04 SC 2 0.454 1.86 TN 1 0.082 2.39 TN 2 0.464 1.49 TX 1 0.176 1.83 TX 2 0.446 1.85 VA 1 0.224 2.13 VA 2 0.034 1.43 Table 4.--Unlevered asset betas for four publicly-owned corporations having substantial amounts of investment-grade timberland. Long Market term debt capitalization Equity Unlevered Firm beta (M) asset beta Weyerhaeuser 1.15 $8,010 $16,300 0.88 Temple-Inland 1.20 $1,498 $5,000 1.01 Plum Creek Timber 0.80 $2,019 $6,900 0.62 Rayonier 0.95 $555 $3,500 0.83 Table 5.--Required nominal return estimates for NCREIF and synthetic timberland returns. Required return Asset (percent) NCREIF--National 5.81 NCREIF--South 5.73 NCREIF--Northeast 5.92 NCREIF--Pacific Northwest 6.59 AL 1 5.86 AL 2 5.38 AR 1 4.88 AR 2 5.04 FL 1 5.51 FL 2 6.29 GA 1 5.61 GA 2 5.52 LA 1 5.78 LA 2 5.81 MS 1 5.43 MS 2 5.44 NC 1 5.53 NC 2 5.29 SC 1 4.89 SC 2 5.29 TN 1 6.16 TN 2 5.11 TX 1 5.50 TX 2 5.79 VA 1 4.52 VA 2 5.40
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|Title Annotation:||Practicalities and Possibilities|
|Author:||Cascio, Anthony J.; Clutter, Michael L.|
|Publication:||Forest Products Journal|
|Date:||Oct 1, 2008|
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