Abstract
This paper quantifies the diversification potential of timberland investments in a mean-variance framework. The starting point is a broad set of benchmark assets represented by various indexes. Including publicly traded timberland investments in the portfolio does not significantly increase mean-variance efficiency. At first sight, U.S. private equity timberland seems to improve the mean-variance frontier, even if the portfolio already contains a forestry and paper equity index. However, after removing the appraisal smoothing bias from the raw timberland data, there is much less evidence that private equity timberland investments increase mean-variance efficiency. (JEL C14)
I. Introduction
Investments in timberland have become increasingly popular with institutional investors both in the United States and elsewhere in the world. According to the UGA Center for Forest Business, the global timberland market value in 2006 was about $400 billion, of which $230 billion was in the United States. Within the United States, private landowners’ timberland had a value of $160 billion, forest products companies owned $52 billion, and institutional investors possessed $14 billion.1 Timberland investment returns are driven by four main factors: biological growth, timber prices, land appreciation, and inflation (Healey, Corriero, and Rosenov 2005). The attractiveness of timberland for institutional investors is often explained by its low correlation with more traditional assets (such as stocks and bonds), which would make it a suitable diversification instrument. See, for example, Redmond and Cubbage (1988) and Sun and Zhang (2001), who estimate capital asset pricing models (CAPM) and find negative beta values for various timberland investments.
The CAPM framework is the conventional approach to assess the diversification properties of timberland investments from the investor’s perspective. Studies based on CAPM focus on excess returns and on the risk level relative to the market portfolio. The negative beta generally found in the literature suggests that there is some potential for improving the risk and return characteristics of a portfolio by including timberland.
This paper adopts a different approach by explicitly quantifying how much the risk-adjusted excess return will increase when timberland is added to an institutional portfolio. For this purpose, we analyze the diversification potential of timberland investments in a mean-variance framework. We apply the mean-variance spanning and intersection tests of Huberman and Kandel (1987) and Kan and Zhou (2008) to assess to what extent the mean-variance frontier improves by including timberland in the portfolio. In particular, we investigate how much the risk-adjusted excess return on the tangency portfolio (the portfolio with highest possible risk-adjusted excess return) will increase when timberland is included. Existing studies on timberland performance generally use a simple proxy for the market portfolio, such as the S&P 500. The resulting negative betas tell us that timberland investments have low correlations with such an index. By contrast, we consider different investment sets including U.S. and global stock, bond, real estate, and commodity indexes. Moreover, we focus on both private equity and publicly traded timberland investments.
Our results show that adding publicly traded timberland investments from the United States and Canada to the portfolio does not significantly improve the meanvariance frontier. At first sight, U.S. private equity timberland seems to increase meanvariance efficiency, even if the investment set already contains a forestry and paper equity index. Adding timberland to the investment set increases the risk-adjusted excess return on the tangency portfolio with about 10 basis points (bp) per quarter. However, after removing the appraisal smoothing bias from the raw timberland data, there is much less evidence that privately held timberland investments increase mean-variance efficiency. Even under mild assumptions regarding the appraisal smoothing bias, the inclusion of the unsmoothed timberland index increases the risk-adjusted excess return on the tangency portfolio with only 1 bp per quarter.
II. The Data
This section describes the data used for the empirical part of this paper and provides some sample statistics.
Timberland Investments
Our goal is to assess how the inclusion of timberland investments in an institutional investor’s investment set affects the meanvariance efficient portfolio of this investor.
Hence, we have to explain how we represent the institutional portfolio and the timberland investment. With respect to the institutional portfolio, we construct a set of benchmark assets, covering different investment classes in various countries. The asset classes are represented by one or more total return indexes. International diversification is ensured by including both U.S. and global indexes. The assets have been chosen to reflect the elements of a well-diversified portfolio and include U.S. and global (small and large cap) stocks, bonds, real estate, and commodity indexes, but not with the goal to mimic an existing portfolio. The benchmark assets are listed in the first column of Table 1, with a short index description and the data source in the second and third columns, respectively.2
Benchmark and Timberland Indexes
We distinguish between private equity investments in timberland for institutional investors (and wealthy individuals) and publicly traded timberland investments available to any investor. Regarding private equity investments in timberland, there is little choice with respect to available data. As far as we know, there are only two relevant indexes: the Timberland Performance Index and the National Council of Real Estate Investment Fiduciaries (NCREIF) Timberland Index. The former ended in 1999. The latter is a property-based index reporting returns for three regions of the United States: the South, Northeast, and Pacific Northwest. The returns on the NCREIF Timberland Index are determined by the income and appreciation returns on the timberland managed by eight timberland investment management organizations (TIMOs) in the United States.3 The income returns arise from log and stumpage sales, whereas the appreciation returns result from timber and land appreciation. TIMOs are privately owned companies that basically work as timberland brokers for institutional investors. They try to earn cash and capital return for their investors. Also timberland real estate investment trusts (REITs) own and explore timberland properties. They are listed on a stock exchange but are not considered corporations and therefore do not pay corporate income tax. They have to pay out 90% of their profit as dividend to investors. In contrast to TIMOs, REITs do not contribute to the NCREIF Timberland Index. Apart from timberland REITs, there are many publicly traded companies in the paper, lumber, and wood production industry that own or explore timberland and can therefore be regarded as timberland investments.
Privately and publicly held timberland may differ substantially in terms of risk and return profiles. Apart from the appraisal smoothing bias (which we discuss below), several other factors may contribute to these differences. Publicly traded timberland funds are leveraged, while privately owned timberland is not. Leverage generally increases average returns and volatility. Moreover, privately and publicly held timberland investments are likely to differ with respect to the asset composition. For example, timberland located in the South, Northeast, and Pacific Northwest of the United States is overrepresented in the NCREIF Timberland Index. Another factor of potential importance is liquidity. Due to the underlying investment vehicle and the illiquidity of timberland itself, private equity investments in timberland are relatively illiquid. It is usually not possible to sell a sizeable timberland property instantaneously. Publicly traded timberland investments are much more liquid, since investors can sell their shares at any time. Investors generally value the liquidity of an investment. However, privately held timberland is bought by institutional investors with a long-term investment horizon, for whom illiquid assets are not a problem. It is therefore unclear whether the illiquid nature of privately owned timberland negatively affects its risk-return profile. Also, efficiency may play a role. Publicly traded timberland may benefit from economies of scale and greater reporting transparency. Finally, the fee structure could play a role. The TIMOs included in the NCREIF Timberland Index basically act as timberland brokers. They charge their institutional clients a fee that is not corrected for in the reported timberland returns. For a more detailed analysis explaining performance differences between privately and publicly held assets, we refer the reader to Riddiough, Moriarty, and Yeatman (2005) who compare privately and publicly owned commercial real estate.
Description of the Data
The NCREIF Timberland Index has its limitations (see below), but we have few other possibilities to represent private equity timberland investments as an asset class. Although institutional investors will presumably also invest in timberland outside the United States, little or no data is at hand for such investments. For this reason we focus on “institutional” timberland in the United States as represented by the quarterly NCREIF Timberland Index, which has been used in other studies as well (Sun and Zhang 2001; Healey, Corriero, and Rosenov 2005). We focus on the longest sample period for which we have returns on both the NCREIF Timberland Index and our virtual institutional portfolio. The resulting time span runs from the first quarter of 1994 until the third quarter of 2007 and comprises 55 quarterly observations. As opposed to institutional timberland represented by the TIMO-based NCREIF Timberland Index, we also construct three (value-weighted) indexes of publicly traded timberland. (The equally weighted indexes yield very similar results. For this reason, we do not report them. However, they are available upon request). The first consists of the three publicly traded timberland REITs (Rayonier, Plum Creek, and Potlatch). Our second index is broader and covers the largest companies in the paper and paper products industry in the United States and Canada. The third index consists of the major companies in the lumber and wood production industry in these countries.4 For the three indexes of publicly held timberland, the sample period runs from the fourth quarter of 1994 until the third quarter of 2007 (we notice that Rayonier, Plum Creek, and Potlatch became REITs after 1994).
The NCREIF Timberland Index and the Appraisal Smoothing Bias
Timberland properties are not traded frequently enough to construct a transaction-based index. For this reason the NCREIF Timberland Index is based on appraisal values. Timberland properties are appraised on the basis of recent transactions of comparable properties, and these appraisal values are used to construct the index. As a consequence, the NCREIF Timberland Index may suffer from an appraisal smoothing bias and may contain certain inertia. A major concern is that the volatility of the observed index returns is too low compared to the true (unobserved) index. This would seriously distort a meanvariance analysis, resulting in a too optimistic picture of the diversification potential of timberland. We refer to equation [A1], in the Appendix, for a more detailed exposition of the potential problems caused by the use of appraisal values. To avoid analyzing NCREIF Timberland Index returns with too low a volatility compared to the true returns, we consider an unsmoothed version of the index.5 We use the unsmoothing approach introduced by Fisher, Geltner, and Webb (1994); see equation [A2]. The unsmoothed index returns have the same mean as the raw index returns, but a substantially higher volatility. As explained in more detail in the Appendix, the unsmoothing approach involves the problem that the true volatility of the unsmoothed index is unknown. Instead of choosing an arbitrary value for this volatility, we proceed in a different way. For a range of possible volatilities, we obtain the unsmoothed Timberland Index. Subsequently, we apply the tests for meanvariance efficiency (to be discussed in the next section) to the resulting series. To save space, we do not report the results for each of the unsmoothed series. Instead we focus on one version of the unsmoothed NCREIF Timberland Index. We consider the highest volatility for which including the unsmoothed index in the investment set significantly improves the mean-variance efficiency of the tangency portfolio. It turns out that the unsmoothed index significantly increases the mean-variance efficiency of the tangency portfolio for volatilities up to 5.3%. This is the version of the unsmoothed NCREIF Timberland Index for which we will report results in the remainder of this paper. Since the mean of the unsmoothed series is not affected by the unsmoothing procedure, the unsmoothed index will become less attractive in terms of mean-variance when its volatility is increased. Hence, the reported unsmoothed index is based on a relatively favorable choice of the volatility. We emphasize that we do not view the unsmoothed index included in Table 1 as the true index. Instead, we consider it a tool for sensitivity analysis with respect to the volatility of the unsmoothed NCREIF Timberland Index. We will return to this issue in Section V.
Preliminary Data Analysis
The fourth and fifth columns of Table 1 provide quarterly means and volatilities for all asset returns. The last column reports the correlations between the returns on the benchmark assets and the returns on the raw NCREIF Timberland Index. The Dow Jones Canada Index generates the highest average quarterly returns during the sample period, and the Dow Jones U.S. Technology Index is the most volatile. Some indexes are mean-variance inefficient, in the sense that there exists at least one other index with a higher average return and lower volatility. For instance, the MSCI Far East Index is inefficient compared to the MSCI World Index. The means of the raw and unsmoothed NCREIF Timberland Index returns are the same, but the volatility of the unsmoothed index (5.3%) is almost twice as large as the volatility of the raw index (2.7%). The raw and the unsmoothed indexes have about the same correlation with the other assets. Table 2 presents the full correlation matrix corresponding to the benchmark assets, the (raw and unsmoothed) NCREIF Timberland Index, and our three indexes of publicly traded timberland. The latter timberland indexes have a much higher volatility than the NCREIF Timberland Index. Moreover, their returns show weakly positive or even negative correlation with the return on the NCREIF Timberland Index. Also the Dow Jones Forestry and Paper Indexes in our set of benchmark assets have a relatively high volatility and are negatively correlated with the NCREIF Timberland Index.
Correlation Matrix for Quarterly Returns on Benchmark and Timberland Indexes
As a first step, we estimate a simple CAPM model for the raw NCREIF Timberland Index, with the S&P 500 as the market index and the quarterly return on a 1-month treasury bill as the risk-free rate. This results in a beta equal to 0.04 (p-value 0.43) and a risk-adjusted excess return (alpha) of 1.4% (with p-value 0.00). For the unsmoothed NCREIF Timberland Index we find virtually the same results, and also for the three indexes of publicly traded timberland we find betas close to zero (Table 3). This suggests that adding timberland has some potential for improving the risk and return characteristics of a portfolio. However, the key question is whether the beta is indeed low enough. The spanning framework presented in the next section can be used to answer this question in a formal way and to quantify the added value of timberland investments.
Capital Asset Pricing Models Estimation Results
III. Testing For Mean-Variance Spanning And Intersection
Given a collection of benchmark assets, portfolio weights can be chosen in such a way that the resulting portfolio is meanvariance efficient. For a given variance, a mean-variance efficient portfolio has maximum expected return. Stated differently, it has the lowest variance at a given level of return for all possible portfolios. The weights associated with a mean-variance efficient portfolio depend on the degree of risk aversion of the investor. The key question is whether the inclusion of another asset class in the set of benchmark assets improves the mean-variance efficient portfolio. More specifically, we ask: Does the inclusion of timberland to the investment set improve mean-variance efficiency? This question will be answered using the framework of mean-variance spanning and intersection.
DeRoon and Nijman (2001) present a survey of the various methods used to test whether the mean-variance frontier of a set of benchmark assets spans or intersects the frontier of a larger set of assets. Two situations can arise. First, if there is only a single value of the risk aversion parameter for which mean-variance investors cannot improve their mean-variance efficient portfolio by including the additional assets in their investment set, the mean-variance frontiers of the benchmark assets and the extended set of assets intersect. With intersection, the mean-variance frontier of the benchmark assets and the frontier of the benchmark assets and the additional asset have precisely one point in common. Second, if there is no value of the risk aversion parameter for which a meanvariance investor can improve her meanvariance efficient portfolio, the mean-variance frontiers of the benchmark and the extended set of assets coincide. This is called spanning. Spanning implies that the meanvariance frontier of the benchmark assets coincides with that of the benchmark assets and the additional asset. In that case, no mean-variance investor is better off by investing in the additional asset, regardless of the zero-beta rate.
We use the regression framework of Huberman and Kandel (1987) to test for spanning and intersection. We denote the returns on the K benchmark assets by the K-dimensional column vector Rt and the returns on the additional asset by the scalar rt. We consider the regression of rt on Rt, namely,
[1]where a is the intercept and b represents a K-dimensional row vector of coefficients. In terms of parameter restrictions, the hypothesis of intersection is stated as
[2]where g equals the zero-beta rate (which we assume to be known). The hypothesis of spanning implies that restriction [2] holds for all values of g and reduces to
[3]As shown by Kan and Zhou (2008), testing a = 0 boils down to testing whether the tangency portfolio (i.e., the portfolio with the highest possible Sharpe ratio) has zero weights in the N test assets. Furthermore, the restriction kK~1 bk ~1 is a test of whether the global minimum-variance (GMV) portfolio has zero weights in the test assets. From the two-fund separation theorem (Tobin 1958) we know that if there are two distinct minimum-variance portfolios that have zero weight in the N test assets, every portfolio on the minimumvariance frontier of the N + K assets will also have zero weights in the N test assets. This explains why the two restrictions in equation [3] are sufficient to test for meanvariance spanning. However, not all portfolios on the mean-variance frontier are equally relevant. According to the CAPM model, each investor will hold a combination of the risk-free asset and the tangency portfolio.6 For this reason, the tangency portfolio is considered to be a more relevant portfolio than the GMV portfolio. Therefore, we can refine the original “overall” spanning test by testing separately whether the inclusion of timberland improves the tangency portfolio or the GMV portfolio, or both. If the overall spanning hypothesis is mainly rejected due to a large improvement of the GMV portfolio, the added value of timberland is limited despite the formal rejection of spanning. Adding timberland to the investment set pays off only if it results in a substantial improvement of the tangency portfolio. In this context Kan and Zhou (2008) propose a step-down approach, which consists of testing the restriction a = 0 followed by kK~1bk~1 conditional on a = 0. The first step-down test assesses whether the tangency portfolio is improved by adding timberland to the investment set, the second whether the inclusion of timberland improves the GMV portfolio. Spanning is not rejected if both tests are not rejected.7 To get a complete picture of the impact of timberland on the mean-variance frontier, we will apply both the overall spanning tests and the stepdown approach. A Wald test will be used for this purpose (see, e.g., Greene 2007).
If the spanning tests show that the meanvariance efficient portfolio is improved by adding timberland to the portfolio, we would like to quantify the resulting increase in mean-variance efficiency. In other words, we want to assess the economic benefit of adding timberland to the set of benchmark assets. To this extent, we consider the Sharpe ratio (Sharpe 1966). The Sharpe ratio of a portfolio with return Rtp is defined as the expected portfolio excess return (relative to the risk-free rate Rtf ) divided by its standard deviation:
[4]This reward-to-volatility ratio is a performance measure that can be used to compare different portfolios in terms of their risk-adjusted excess return. To assess the economic benefit of investing in timberland, we consider the change in the Sharpe ratio for the tangency portfolio caused by adding timberland to the investment set. For completeness, we also report the resulting change in the Sharpe ratio of the GMV portfolio.
IV. Empirical Results: Spanning and Intersection Tests
Using the historical returns on the benchmark assets and the NCREIF Timberland Index, we test for spanning and intersection and assess the economic relevance of adding timberland to the investment set.
Testing for Spanning and Intersection
We first assess how the NCREIF Timberland Index performs in relation to each of the asset classes under consideration. We estimate the regression model of equation [1] and subsequently run the overall spanning tests and apply the step-down approach. We first take the raw NCREIF Timberland Index as the test asset. Table 4 shows that all spanning and step-down tests are rejected at a 1% significance level. As a second step, we include all assets listed in Table 2 in the benchmark portfolio. Subsequently, we test for spanning and intersection with respect to adding timberland to the full set of benchmark assets.8 Initially, we do not include the Dow Jones Forestry and Paper Index. Hence, we first regress the NCREIF Timberland Index on the returns of 13 benchmark assets. The Wald test rejects the hypothesis of spanning at a 1% significance level. Assuming that the zerobeta rate equals 3.9% per year on the basis of historical yearly returns on a 1-month treasury bill during the period 1994-2007, we reject the intersection hypothesis at a 1% significance level. Hence, we conclude that adding timberland to the investment set results in a significant improvement in mean-variance efficiency. Moreover, the step-down tests for the tangency and GMV portfolios are rejected at the 1% level. This leads to the conclusion that adding timberland to the investment set improves not only the mean-variance efficiency of the GMV portfolio, but also that of the tangency portfolio.
Results of Spanning Tests with Different Benchmark Assets (NCREIF Timberland Index)
Next, we repeat the former analysis, but add the Dow Jones Forestry and Paper Index to the benchmark assets. This allows us to assess whether investing in timberland improves the mean-variance frontier if the set of benchmark assets already contains forestry-related investments. Since the regional and global forestry and paper indexes are highly correlated, we include only one of them at a time. Again, the hypotheses of spanning are rejected at a 1% significance level (Table 4). Thus, even when the investment set already contains stocks from the forestry and paper sector, adding the NCREIF Timberland Index still improves mean-variance efficiency of the portfolio. In particular, both the tangency and the GMV portfolio significantly benefit from adding timberland to the investment set. Even when we additionally add our three indexes of publicly traded timberland to the set of benchmark assets, spanning is still rejected.
For the unsmoothed NCREIF Timberland Index the picture is much less favorable. With the complete set of benchmark assets, the overall spanning tests are rejected at the 10% significance level. The same holds for the mean-variance efficiency tests for the tangency portfolio. However, adding timberland to the investment set does not significantly improve the mean-variance efficiency of the GMV portfolio. For the smaller sets of benchmark assets, all spanning tests are rejected at the 5% level.
Finally, we turn to the three indexes of publicly traded timberland. Table 5 reports the results of the spanning and step-down tests with publicly traded timberland as a test asset and the same benchmark assets as before. Adding the timberland REIT index to the investment set improves the meanvariance efficiency of the tangency portfolio (at a 5% significance level) only if the set of benchmark assets consists of the s&P 500 or bonds. Regardless of the set of benchmark assets, the other two indexes of publicly traded timberland do not significantly increase the mean-variance efficiency of the tangency portfolio. Although the mean-variance efficiency of the GMV portfolio often benefits from adding timberland, this portfolio is considered less relevant for investors than the tangency portfolio (see the discussion above). In sum, publicly traded timberland does not add value from a portfolio perspective. Possible explanations for the differences in diversification potential between private and publicly held timberland investments have been addressed in section II.
Results of Spanning Tests with Different Benchmark Assets (Publicly Traded Timberland)
Economic Gains of Investing in Timberland
We assume a risk-free rate of 3.9% per year and calculate the change in sharpe ratios for the tangency and GMV portfolios caused by adding the raw NcREiF Timberland index to the various investment sets. The results in the upper pane of Table 4 show that the increase in the sharpe ratio is often much lower for the tangency than for the GMV portfolio. For example, for the full set of benchmark assets, the increase in the sharpe ratio of the GMV portfolio is slightly more than 30 bp, whereas the rise is less than 10 bp per quarter for the tangency portfolio.9 We propose two additional measures to assess the economic impact of adding timberland to the investment set. First, we consider the weights of the NcREiF Timberland index in the tangency portfolio, which reflect the relative importance of the timberland in this portfolio. Next, we compare the meanvariance frontier based solely on the benchmark assets to the frontier including timberland in addition to the benchmark assets. The (long) position in timberland is second largest among all positions, emphasizing its importance. Furthermore, the mean-variance frontier based on the benchmark assets and the raw index differ substantially from the frontier derived from the benchmark assets only.
We repeat the above analysis using the unsmoothed NCREIF Timberland Index, for which the results are reported in the lower pane of Table 4. Regardless of the benchmark portfolio, the index significantly improves the mean-variance efficiency of the tangency portfolio at a 10% significance level. However, the economic significance of the increase in Sharpe ratios is substantially smaller than in case of the raw index. For example, for the complete set of benchmark assets, including the global Dow Jones Forestry and Paper Index, the rise in the Sharpe ratio of the tangency portfolio is only 1 bp. The corresponding 95% confidence interval around this increase equals [0.02, 13] bp.10 Thus, although the economic relevance of the rise in the Sharpe ratio of the tangency portfolio seems small, it is statistically significant. The limited economic impact of adding the unsmoothed NCREIF Timberland Index to the investment set is confirmed by its relatively small weight in the tangency portfolio. Moreover, adding timberland to the investment set hardly affects the mean-variance frontier.
Our unsmoothing procedure is based on relatively mild assumptions regarding the nature of the appraisal smoothing bias (see Section II), resulting in an unsmoothed index with a relatively low volatility. Even under these favorable assumptions, the economic gains of investing in private equity timberland are limited. By contrast, our analysis based on the raw data suggests that the increase in mean-variance efficiency from adding private equity timberland to the investment set is substantial. Strikingly, the appraisal smoothing has been ignored in previous studies using the NCREIF Timberland Index (see, e.g., Sun and Zhang 2001; Healey, Corriero, and Rosenov 2005). The relatively minor diversification potential of the unsmoothed index emphasizes that any results based on the raw index should be interpreted with caution, as they possibly overstate the mean-variance properties of institutional timberland. Hence, our results also serve as a cautionary warning for future studies using the NCREIF Timberland Index.
V. Robustness of The Results
In this section we assess the robustness of several assumptions underlying our analysis.
Risk-Free Rate
The way in which the Sharpe ratio is affected by adding timberland to the investment set depends on the risk-free rate, which we assumed to be 3.9% per year on the basis of historical yearly returns on a 1-month treasury bill during the period 1994-2007. As a robustness check, we calculate the increase in Sharpe ratios for risk-free rates of 5.7% and 2. 1%. These figures reflect the average of 3.9% over the period 1994-2007 plus and minus one standard deviation, respectively. In the first part of Table 6 we report some results for the full set of benchmark assets, including the global Dow Jones Forestry and Paper Index. We first consider the raw NCREIF Timberland Index. The increase in the Sharpe ratio of the tangency portfolio equals 0.2 bp with a 5.7% risk-free rate and 21 bp with a 2.1% risk-free rate. We emphasize that the 0.2 bp increase is still significant, with the 95% confidence interval equal to [0.02, 1 1] bp; again, we obtained this confidence interval by means of a wild bootstrap. For the unsmoothed NCREIF Timberland Index the rise in the Sharpe ratios is even smaller, but again statistically significant. Hence, even for a historically low risk-free rate of 2.1%, inclusion of this index in the investment set leads to a significant increase in mean-variance efficiency. Nevertheless, for the tangency portfolio the economic significance of the increase in the Sharpe ratio is very small.
Results of Sensitivity Analysis
Wald Test
Kan and Zhou (2008) show that the asymptotic chi-square distribution of the Wald statistic is not always accurate for small samples with a substantial amount of benchmark assets. Therefore, we use a bootstrap approach to obtain the smallsample distribution of the Wald statistic. To deal with any heteroskedasticity in the error term of the regression model of equation [1], we apply the wild bootstrap (Mammen 1993). For the full set of benchmark assets including the global Dow Jones Forestry and Paper index, the second part of Table 6 reports the bootstrapped p-values for the overall spanning and step-down tests. The asymptotic p-values are very close to the bootstrapped ones and tend to be conservative. We establish similar robustness results for the spanning and step-down tests applied to the smaller investment sets. Therefore, the use of the asymptotic Wald test does not seem to be a problem in our case.
Unsmoothing Procedure
For the complete set of benchmark assets, the inclusion of the unsmoothed NcREiF Timberland index increases the sharpe ratio of the tangency portfolio by only 1 bp. The assumed volatility of the unsmoothed index is relatively low compared to the volatility of publicly traded timberland as reported in Table 1. Even for this low volatility, the increase in the sharpe ratio is small (although statistically significant). For higher volatilities of the unsmoothed NcREiF Timberland index the results are even worse, as shown in the third part of Table 6. Assuming a volatility of 10% for the unsmoothed index (which comes close to the volatility of publicly traded timberland investments listed in Table 1), the spanning tests are not rejected. With fewer benchmark assets the increase in the sharpe ratio is more substantial, but obviously the full set is more representative for an institutional investor’s well-diversified portfolio.
Other Concerns
We present some final reservations regarding our analysis. First, U.s. private equity timberland investments are represented by the NCREIF Timberland Index. This index covers only three regions in the United states and might not be representative for the United states as a whole. second, timberland is a nontraded, illiquid asset. The quarterly historical returns analyzed in this paper can be realized only by investors with a long-term horizon, such as pension funds or other institutional investors. Hence, there may be a discrepancy between the data frequency (and the resulting sharpe ratios) and the investment horizon. As shown by Levy (1972), sharpe ratios computed at frequent intervals are not always the right instrument for making long-term investment decisions. As a consequence, a quarterly 40 bp increase in the maximum sharpe ratio does not necessarily imply an 80 bp increase on a yearly basis.11 Unfortunately, the return history of the NCREIF Timberland Index is too limited to do the entire analysis at, say, the yearly level. Moreover, the relevant investment horizon will depend on, for example, the preferences of the institutional investor. Without exact knowledge about these preferences it is not possible to arrive at an appropriate horizon. Furthermore, the mean-variance framework applied in this paper relies on the assumption that investment decisions of institutional investors are made solely on the basis of the meanvariance properties of assets. In reality, other asset characteristics will play a role as well, such as the fact that timberland is often claimed to be an inflation hedge (Washburn and Binkley 1993; Healey, Corriero, and Rosenov 2005). Finally, our analysis is based on historical data and ex post sharpe ratios, which do not necessarily have predictive power for future performance.
VI. Conclusion
This paper analyzes the diversification potential of timberland investments in a mean-variance framework. We focus on both U.s. private equity timberland and publicly traded timberland investments in the United states and Canada, where the former is represented by the NCREIF Timberland Index and the latter by three equity indexes. Our approach contributes to the existing literature by explicitly quantifying to what extent timberland investments improve the mean-variance efficiency of a well-diversified portfolio including U.s. and global (small and large cap) stock, bonds, real estate, and commodity indexes.
We find that publicly traded timberland investments from the United states and Canada do not significantly improve the mean-variance frontier. At first sight, adding U.s. private equity timberland to the investment set seems to increase mean-variance efficiency, even if the portfolio already contains a forestry and paper equity index. Including timberland in the investment set increases the risk-adjusted excess return on the tangency portfolio about 10 bp per quarter. However, after removing the appraisal smoothing bias from the raw NCREIF Timberland Index, there is much less evidence that privately held timberland investments increase mean-variance efficiency. Even under mild assumptions regarding the appraisal smoothing bias, the inclusion of the unsmoothed index increases the risk-adjusted excess return on the tangency portfolio by only 1 bp per quarter. Hence, money does not seem to grow on trees.
Appendix
Unsmoothing The Ncreif Timberland Index
This appendix addresses the problems caused by the use of appraisal values for the construction of the NCREIF Timberland Index.
Appraisal Problems
Most timberland properties in the index are appraised only once a year, usually in the fourth quarter and, to a lesser extent, in the second quarter. Properties whose value is not updated in a given quarter are included in the index with the same value as in the previous quarter (Lutz 1999). Consequently, temporal aggregation of individual properties could result in an artificially high quarterly index return variance due to the individual appreciation returns with value zero. Moreover, the seasonality of reappraisals may induce spurious positive fourth-order autocorrelation in the index returns. Second, appraisers tend to smooth or partially adjust property values over time, which leads to appraisal smoothing. As a consequence, the volatility of index returns could be biased toward zero, and the index may lag changes in underlying property values. Similar appraisal problems have been discussed in the context of other appraisal-based property indexes such as the Russell-NCREIF (Fisher, Geltner, and Webb 1994). Biases caused by appraisal smoothing, seasonality in reappraisals, and temporal aggregation may seriously distort any meanvariance analysis, since return volatility may seem lower than it actually is. However, we emphasize that the appraisal problems do not necessarily occur. Edelstein and Quan (2006) argue that appraisal smoothing at the individual level does not always lead to an appraisal smoothing bias at the index level, since individual property appraisal biases may offset in the aggregate. Lai and Wang (1998) show that the use of appraisal-based data can in fact result in a higher variance than that of the true index returns.
Unsmoothing Approach
Fisher, Geltner, and Webb (1994) proposed a method to unsmooth the quarterly Russell-NCREIF Index. This property index suffers from the same potential appraisal problems as the NCREIF Timberland Index. Therefore, we apply the methodology of Fisher, Geltner, and Webb (1994) to remove the autocorrelation from the index returns and to increase its variance (while keeping the mean unchanged). First, it is assumed that the observed index return rt* is a weighted average of current and past true index returns rt2k, that is,
[A1]with w0 a scalar satisfying 0, w0, 1 and w(L)a polynomial in terms of the lag operator. Alternatively, we can write
[A2]To deal with appraisal smoothing and seasonality in reappraisals, we take y(L) = y1 + y4L3 for the lag polynomial y(L). This results in
[A3]with gt = w0rt. We can now write equation [A3] in terms of true returns (rt), assuming E(rt) = m. This yields
[A4]We can estimate the coefficients y0, y1, and y4 from equation [A3] by assuming that true returns (rt) are serially uncorrelated (in which case gt = w0rt is white noise). The value of w0 can be derived only by imposing an additional restriction, for example, that the volatility of the true returns is k%. This yields
[A5]According to Table 1, the volatility of publicly traded timberland is around 7% to 12%, whereas the volatility of the raw NCREIF Timberland Index is only about 3%. Therefore, the true volatility of the unsmoothed timberland index is likely to be in the range of 3% to 12%. We therefore consider a volatility range of 3% to 12% and obtain the unsmoothed index for all (rounded values of the) volatilities in this range using the approach suggested by Fisher, Geltner, and Webb (1994). We take the complete set of benchmark assets and determine the largest volatility for which the stepdown test with respect to the tangency portfolio is not rejected at a 10% significance level. Since the mean of the unsmoothed series is not affected by the unsmoothing procedure, the unsmoothed asset will become less attractive when its volatility is increased. Our results show that the unsmoothed NCREIF Timberland Index significantly increases the mean-variance efficiency of the tangency portfolio for volatilities up to 5.3%. Therefore, we use this version of the unsmoothed index in our analysis. Ordinary least squares estimation of equation [A3] applied to the NCREIF Timberland Index results in the following estimates (p-values based on White’s heteroskedasticity robust covariance matrix in parentheses): y0 = 1.53 (0.005), y1 = 0.04 (0.505), y4 = 0.30 (0.100), and w0 = 0.48.
Footnotes
The authors are, respectively, professor and associate professor, Department of Economics, Econometrics, and Finance, University of Groningen, and Centre for International Banking, Insurance, and Finance, Groningen, The Netherlands. The authors would like to thank Jack Lutz and two anonymous referees for useful suggestions. The usual disclaimer applies.
↵1 Source: National Governor’s Association, www.nga.org/cda/files/0407forestryTIMO.PDF.
↵2 Apart from these indexes, we also considered several other indexes. In the end, we did not include them in the set of benchmark assets, as they turned out collinear with one or more other indexes. Since collinearity might be problematic, we do not include these indexes in the investment set. However, we emphasize that our results are robust to the choice of the set of benchmark assets. The indexes we omitted because of collinearity with other benchmark assets are MSCI Europe, Dow Jones U.S., Dow Jones U.S. Small Cap, Dow Jones Euro Small Cap, Dow Jones Asia/Pacific, Lehman Global Treasury, Lehman Investment Grade, Lehman U.S. Treasury, Lehman U.S. Corporate Investment Grade, Lehman U.S. Government Aggregate, and Lehman U.S. Aggregate Index.
↵3 These eight TIMOs are The Campbell Group, Global Forest Partners, Forest Investment Associates, Hancock Timber Resource Group, Molpus Woodlands, Resource Management Service, RMK Timberland, and Timberland Investment Resources. Prudential Timber was one of the founding contributors. Another past contributor is Forest Systems.
↵4 Our Paper and Paper Products Index contains International Paper, Avery Dennison, Sonoco Products, Meadwestvaco, Rock-Tenn, Domtar, Tembec, Potlatch, Mercer International, and Norbord. Our Lumber and Wood Production Index contains Leucadia, Masco, Universal Forest Products, Louisiana Pacific, Weyerhaeuser, Pope Resources, Cross Timbers Royalty Trust, West Fraser Timber, Cascades, Sino-Forest, International Forest Products, and Canfor. We downloaded all total return data from Thomson Datastream. At the end of 2007 (which is the end of our sample period) the Dow Jones Forestry and Paper Index (Americas) contains the stocks AbitibiBowater, Aracruz Celulose, Canfor, Cascades, Catalyst Paper, Domtar, Empresas, International Paper, Neenah Paper, Sino-Forest, Suzano Papel e Celulose, TimberWest Forest, Wausau Paper, West Fraser Paper, Weyerhaeuser. The global Dow Jones Forestry and Paper Index contains quite a few additional companies in the forestry and paper industry located outside America. The full list is available at www.djindexes.com.
↵5 Alternatively, we could apply the approach proposed by Riddiough, Moriarty, and Yeatman (2005), which consists of replicating the NCREIF Timberland Index by means of publicly traded timberland REITs (while correcting for, e.g., leverage). However, it seems difficult to apply this method to the NCREIF Timberland Index, since there are currently only three timberland REITs, who all adopted the REIT structure relatively recently. Therefore, we opt for a different approach and apply the unsmoothing method introduced by Fisher, Geltner, and Webb (1994).
↵6 We notice that, according to CAPM, the tangency portfolio will be a value-weighted mix of all assets in the world.
↵7 Suppose that the significance level of the first stepdown test is a1 and that of the second is a2. Then the significance of the joint step-down test is equal to 1 2 (1 2 a1)(1 2 a2).
↵8 To make sure that the benchmark assets in our analysis are not collinear, we follow the procedure proposed by Belsley, Kuh, and Welsch (1980) and inspect the condition indices and variance decomposition proportions corresponding to the matrix of benchmark returns. We do not find any evidence for multicollinearity.
↵9 We define the increase in the sharpe ratio in basis points as (new sharpe ratio-old sharpe ratio) 10,000.
↵10 We obtained this confidence interval by means of a wild bootstrap (Mammen 1993). We use the same bootstrap procedure to derive the finite-sample distribution of the Wald test in Section V.
↵11 This number is obtained as $80 = 40!4.
