The Diversification Properties of US Timberland: A Mean-Variance Approach

Page created by Louis Mccoy
 
CONTINUE READING
The Diversification Properties of US Timberland:
                    A Mean-Variance Approach
                              Bert Scholtens∗ Laura Spierdijk†

                                        January 28, 2008

                                             Abstract

          This paper analyzes the diversification potential of timberland investments in a for-
      mal mean-variance framework. Our starting point is a broad set of benchmark assets
      represented by various global stock, bond, real estate, and commodity indexes. Subse-
      quently, we apply mean-variance spanning and intersection tests to assess whether
      adding US timberland to the investment set improves the mean-variance efficient
      portfolio. Adding timberland to the investment set significantly improves the mean-
      variance efficient portfolio, even if the portfolio already contains a forestry and paper
      equity index. In economic terms the mean-variance contribution of US timberland is
      substantial. Timberland can increase the risk-adjusted excess return per unit of risk
      with more than 40 bp on a quarterly basis. Even if the investment set already contains
      stocks from the forestry and paper sector, the increase is still considerable, namely
      about 35 bp.

          Keywords: mean-variance spanning, portfolio choice, US timberland investments

          JEL Classification: G10, G12

  ∗
     University of Groningen, Faculty of Economics and Business, Department of Finance and CIBIF, P.O.
Box 800, 9700 AV Groningen, The Netherlands. Phone +31 50 363 7064. E-mail L.J.R.Scholtens@rug.nl
   †
     Corresponding author. University of Groningen, Faculty of Economics and Business, Department of
Economics & Econometrics and CIBIF, P.O. Box 800, 9700 AV Groningen, The Netherlands. Phone: +31
50 363 5929. E-mail: L.Spierdijk@rug.nl.
1    Introduction

During the past years investments in timberland have become increasingly popular with

institutional investors both in the Unites 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 dollar, of which 230 billion located in the United States. Within the

US, private landowners’ timberland had a value of 160 billion, forest products companies

owned 52 billion and institutional investors possessed 14 billion.

    Timberland investment returns are driven by four main factors: biological growth,

timber prices, land appreciation, and inflation (Healey et al. (2005)). The popularity of

timberland investments is often explained by its low correlations with more traditional as-

sets, which would make it a suitable diversification instrument for institutional portfolios.

See e.g. Redmond and Cubbage (1988) and Sun and Zhang (2001) who estimate CAPM

models and find negative beta values for various timberland investments. The CAPM

framework is the conventional approach to assess the diversification properties of timber-

land investments from the investor’s perspective. Studies based on the CAPM focus on

excess returns and the risk level relative to the market portfolio. Negative beta’s indicate

that timberland is negatively correlated with the market portfolio, suggesting that there

is some potential for improving the risk and return characteristics of a portfolio by adding

timberland.

    This paper adopt a different approach by analyzing the diversification potential of US

timberland investments in a formal mean-variance framework. Instead of relying on simple

correlations, we apply the mean-variance spanning and intersection tests of Huberman

and Kandel (1987) to assess whether the mean-variance efficient portfolio is improved by

adding timberland to the investment set. Furthermore, we explicitly quantify how much

the risk-adjusted excess return per unit of risk can increase when timberland is added to

an institutional portfolio. Moreover, existing studies on timberland performance generally

use a simple proxy for the market portfolio such as the S&P 500. The resulting low

beta’s in the estimated CAPM models merely tell us that timberland investments have

                                             1
low correlations with such an equity index. By contrast, we consider a well-diversified

investment set consisting of both US and global stock, bond, real estate, and commodity

indexes. As such, our paper presents a more elaborate assessment of the diversification

properties of US timberland.

   The mean-variance framework applied in this paper relies on the assumption that

investment decisions of institutional investors are solely made on the basis of the mean-

variance properties of assets. In reality, also other asset characteristics may play a role,

such as the fact that timberland is often claimed to be a hedge against inflation (see

e.g. Washburn and Binkley (1993) and Healey et al. (2005)). However, this does not

affect our analysis, as our main goal is to substantiate the claims about the diversification

properties of timberland which are merely based on simple correlations between the returns

of timberland and other assets.

   Our results show that the mean-variance efficient portfolio is significantly improved

by adding US timberland (represented by the NCREIF Timberland Index) to the invest-

ment set, even if the portfolio already contains a forestry and paper equity index. In

economic terms the mean-variance contribution of timberland is substantial. Timberland

can increase the risk-adjusted excess return per unit of risk with more than 40 bp per

quarter. Even if the investment set already contains stocks from the forestry and paper

sector, the increase is still considerable, namely about 35 bp. Our findings contribute to

the existing literature focusing on the added value of timberland investments. Instead of

relying on CAPM or multifactor models, we explicitly assess whether and to what extent

US timberland investments improve the mean-variance efficient portfolio.

   The setup of the remainder of this paper is as follows. Section 2 describes the data

and provides some sample statistics. The mean-variance framework and the tests for span-

ning and intersection are explained in Section 3. Section 4 discusses the empirical results.

Finally, Section 5 concludes.

                                             2
2     The data

This section describes the data used for the empirical part of this paper and provides some

sample statistics.

2.1    Description of the data

Our goal is to assess the impact of including timberland in an institutional portfolio on the

mean-variance efficient portfolio. Hence, we have to set clear how we represent an institu-

tional portfolio and a timberland investment. With respect to the institutional portfolio,

we construct a set of benchmark assets, covering different investment classes in various

countries. Asset classes are represented by one or more indexes. International diversifica-

tion is ensured by including both US and global indexes. Obviously, our benchmark assets

have not been selected with the goal to precisely mimick the composition of an existing

institutional portfolio. They merely reflect the elements of a well-diversified portfolio. The

collection of 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 column, respectively. Apart from

the indexes in Table 1, we also considered several other indexes. Eventually, 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 in our subsequent analysis, we do

not include these indexes in our investment set.1

    Regarding timberland investments, there is little choice with respect to available data

since there is no centralized trading platform for timberland assets. Although there are

some publicly traded timberland companies, they own a relatively small part of total

timberland. Two relevant US timberland indexes exist: the Timberland Performance Index

and the National Council of Real Estate Investment Fiduciaries (NCREIF) Timberland

Index. The former has been discontinued since 1999. The latter is a property-based index

reporting returns for three regions of the United States: the South, Northeast and Pacific
   1
     Indexes we omitted because of collinearity with other benchmark assets are e.g. the MSCI Europe,
Dow Jones US Small Cap, Dow Jones Euro Small Cap, Dow Jones Adia/Pacific, Lehman Global Treasury,
Lehman Investment Grade, Lehman US Treasury, Lehman US Corporate Investment Grade, Lehman US
Government Aggregate, and Lehman US Aggregate.

                                                 3
Northwest. The index has two contributors, Hancock Timber Resource Group and Forest

Investment Associates. Although this index has its limitations (Lutz (1999)), we have

few other possibilities to represent timberland as an asset class. Although institutional

investors will presumably also invest in timberland outside the USA, little or no data is at

hand for such investments. For this reason this paper focuses on timberland in the USA

as represented by the NCREIF Timberland Index. This index has been widely used in

other academic studies as well; see e.g. Sun and Zhang (2001) and Washburn et al. (2003).

Therefore, we think it is appropriate to use it for our analysis as well.

   The Timberland Index is available at a quarterly level. We focus on the longest sample

period for which we have returns on both the Timberland Index and our virtual institu-

tional portfolio. The resulting time span runs from the second quarter of 1994 until the

third quarter of 2007 and comprises 56 quarterly observations.

2.2   Sample statistics

The fourth and fifth column of Table 1 provide quarterly means and standard errors for all

assets under consideration. Finally, the last column reports the correlations between the

benchmark assets and the NCREIF Timberland Index. In the period under consideration,

the Dow Jones Canada Index generates the highest average quarterly returns, whereas

the Dow Jones US Technology Index is most volatile. Some indexes are mean-variance

inefficient, in the sense that there is at least one other index with a higher return and

lower volatility. For instance, the MSCI Far East Index is inefficient compared to e.g. the

MSCI World. The Timberland Index has the highest correlation with the MSCI World

Index and the lowest correlation with the Lehman Aggregate Bond Index. Strikingly, the

Timberland Index is negatively correlated with the Dow Jones Forestry & Paper Indexes,

which illustrated the performance difference between institutionally owned timberland

and listed companies in the forestry and paper sector. For completeness, Table 2 presents

the full correlation matrix corresponding to the benchmark assets and the timberland

investment.

                                             4
3    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 mean-variance efficient. For a given variance, a mean-variance

efficient portfolio has maximum expected return. The weights associated with a mean-

variance efficient portfolio will depend on the degree of risk aversion of the portfolio holder.

    Now a key question arises. ‘Does the inclusion of another asset class in the set of

benchmark assets improve the mean-variance efficient portfolio?’ More specifically, in the

context of this paper: ‘Does the inclusion of US timberland to the investment set improve

mean-variance efficiency?’ These questions will be answered in the framework of mean-

variance spanning and intersection.

    DeRoon and Nijman (2001) present a survey on 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. Basically, two cases arise. First, if there exists only a single

value of the risk aversion parameter for which mean-variance investors cannot improve

upon 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. Second, if there is no value of the risk aversion parameter for which

a mean-variance investor can improve his mean-variance efficient portfolio, the mean-

variance frontiers of the benchmark and the extended set of assets coincide. This is called

spanning.

    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

vector Rt and the returns on the additional asset by the scalar rt . We consider the regres-

sion of rt on Rt , i.e.

      rt = α + βRt + εt ,                                                                       (1)

where α is the intercept and β represents a K-dimensional vector of coefficients. In terms

                                                 5
of parameter restrictions the hypothesis of intersection is stated as
                  K
                  X
      α − η(1 −         βk ) = 0,                                                       (2)
                  k=1

where η equals the zero-beta rate (which we assume to be known). The hypothesis of

spanning implies that restriction (2) hold for all values of η and reduces to
               K
               X
      α = 0,         βk = 1.                                                            (3)
               k=1

The above parameter restrictions are intuitively very clear. They state that if there is

spanning, then the return on the additional asset (timberland in our case) can be written

as the return of a portfolio of the benchmark assets, plus an error term with mean zero

and orthogonal to the benchmark returns. Such an asset will only add to the variance of

the portfolios comprising the benchmark assets, and not to the expected return. Hence,

mean-variance optimizing agents will not include the additional asset in their portfolio. A

similar interpretation holds for the intersection restrictions. The widely applied Wald test

(see e.g. Greene (2007)) can be used to test the spanning and intersection hypotheses.

4     Empirical results: spanning and intersection hypothesis

Using the historical returns on the benchmark assets and the Timberland Index, we test

for spanning and intersection in the regression framework of Section 3. Also, we assess the

economic impact of adding US timberland to the investment set.

4.1   Testing for spanning and intersection

For the benchmark assets listed in Table 1, we test for spanning and intersection with

respect to adding timberland to the investment set. We do this by estimating the regression

model in Equation (1) and subsequent testing of the parameter restrictions (2) and (3) by

means of a Wald test.

    To make sure that the benchmark assets in our analysis are not collinear, we follow the

procedure proposed by Belsley et al. (1980) and inspect the condition indices and variance

                                             6
decomposition proportions corresponding to the matrix of benchmark returns. We do not

find any evidence for multicollinearity.

    Initially, we do not include the Dow Jones Forestry & Paper Index in our set of bench-

mark assets. Hence, we regress the Timberland Index on the returns of 13 benchmark

assets. We find that the adjusted R2 corresponding to the regression model of Equa-

tion (1) equals 0.13, see Table 3 for some relevant estimation output. Moreover, the Wald

test rejects the hypothesis of spanning at each a 5% significance level. Hence, we conclude

that adding US timberland to the investment leads to an improvement in mean-variance

efficiency.

    In a second step we repeat the former analysis, but first add the Dow Jones Forestry

& Paper Index to our collection of benchmark assets. This allows us to assess whether

US timberland improves the mean-variance efficient portfolio when the set of benchmark

assets already contains forestry-related investments. Since the regional and global Forestry

& Paper indexes are highly correlated, we only include one of them at a time. The adjusted

R2 of the regression model of Equation (1) increases to 0.14 (American Forestry & Paper

Index) and 0.15 (Global Forestry & Paper Index). But, again, the hypothesis of spanning is

rejected at a 5% significance level (even at the 1% level); see Table 3. Thus, even when the

investment set already contains stocks from the forestry and paper sector, the Timberland

Index still improves the mean-variance efficiency of the portfolio.

4.2    Economic gains of investing in US timberland

The spanning tests point out that adding US timberland improves the mean-variance

efficient portfolio. But how large is the resulting increase in mean-variance efficiency? In

other words, what is the economic benefit of adding US timberland to the set of benchmark

assets?

    To answer this question we use the Sharpe ratio. This ratio is a performance measure

which can be used to compare different portfolios in terms of their risk-adjusted excess

return per unit risk. We calculate the change in maximum attainable Sharpe ratio that

follows from adding the Timberland Index to the investment set. The Sharpe ratio of a

                                             7
portfolio with return Rtp is defined as the expected portfolio excess return (relative to the

zero-beta rate η) divided by its standard deviation:

                         E(Rtp ) − η
      Sharpe(Rt , η) =                                                                     (4)
                          σ(Rtp )

In this way, the Sharpe ratio of a portfolio reflects the risk-adjusted excess return per unit

of risk. By definition, the maximum attainable Sharpe ratio is the Sharpe ratio of the

minimum-variance efficient portfolio. Rewriting Equation (1) in terms of excess returns

relative to the zero-beta rate η, we obtain

      rt − η = αJ (η) + β(Rt − ηιK ) + εt ,                                                (5)

                           PK
where αJ (η) = α − η(1 −      k=1 βk )   is known as Jensen’s generalized performance measure.

Let θB (η) denote the Sharpe ratio of a mean-variance efficient portfolio based on the

benchmark assets only, for a given zero-beta rate η. The maximum attainable Sharpe

ratio θ(η) based on the benchmark assets and the additional asset satisfies

      θ(η)2 = θB (η)2 + αJ (η)2 /σε2 .                                                     (6)

The term αJ (η)/σε in Equation (6) is often referred to as the adjusted Jensen measure

or the appraisal ratio (see Treynor and Black (1973)) and reflects the distance between

the maximum attainable Sharpe ratio with and without the additional asset. For more

details we refer to DeRoon and Nijman (2001). We use the appraisal ratio to compare the

mean-variance efficient portfolios with and without US timberland.

   The (ex post) appraisal ratio based on our set of benchmark assets (exclusive of the

Dow Jones Forestry & Paper Index) and the Timberland Index as an additional asset

shows that the inclusion of US timberland can increase the maximum Sharpe ratio by 43

bp per quarter. This implies that the risk-adjusted excess return per unit risk can increase

with more than 40 bp on a quarterly basis when timberland is added to an institutional

portfolio consisting of our benchmark assets. However, when the Forestry & Paper Index

is already part of the investment set, the increase in the maximum Sharpe ratio due to

the inclusion of US timberland is lower than before. In this case the Timberland Index

                                                 8
can increase the risk-adjusted excess return per unit of risk with 37 bp (Forestry & Paper

Index, Americas) and 36 bp (Forestry & Paper Index, Global). See Table 3.

   Finally, we make some reservations regarding our analysis. First, we emphasize that

the way the Sharpe ratio is affected by adding the Timberland Index to the investment set

depends on the zero-beta rate, which we assume to be 3.9% a year on the basis of historical

yearly returns on a 1-month T-Bill during the period 1994 − 2007. We also calculate the

change in the maximum Sharpe ratio for zero-beta rates equal to 5.7% and 2.1%, which

reflect the average of 3.9% over the period 1994 − 2007 plus and minus one standard

deviation. The resulting appraisal ratios are also reported in Table 3. With a relatively

high zero-beta rate of 5.7%, the increase in maximum Sharpe ratio is still equal to 28 bp

without the Dow Jones Forestry & Paper Index and 20-21 bp when this index is already

included in the set of benchmark assets. With a low zero-beta rate of 2.1%, these increases

are much higher and equal to 59 and 54 bp, respectively. This sensitivity analysis shows

that the level of the zero-beta rate affects the benefit of adding the Timberland Index to

the investment set. However, we find that even for a historically low zero-beta rate of 2.1%,

inclusion of this index leads to a substantial rise in the maximum Sharpe ratio. Second,

our analysis is based on historical data and ex post Sharpe ratios, assuming that past

timberland returns have predictive power for future performance. Finally, timberland is

a non-traded, illiquid asset. The quarterly historical returns analyzed in this paper could

only be realized by investors with a long-term horizon, such as pension funds or other

institutional investors. Hence, there may be 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 less than ideal to make long-term investment

decisions. As a consequence, a quarterly 40 bp increase in the maximum Sharpe ratio does

not necessarily implies a 80 bp increase on a yearly basis. In practice, 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 e.g. the preferences of

the institutional investor. Without exact knowledge about these preferences it is not even

possible to arrive at an appropriate horizon.

                                              9
5    Conclusions

During the past years investments in timberland have become increasingly popular with

institutional investors both in the Unites States and elsewhere in the world. The popularity

of timberland investments is often explained by its low correlations with more traditional

assets, which would make it a suitable diversification instrument for institutional portfolios.

    This paper analyzes the diversification potential of timberland investments in a formal

mean-variance framework. Our starting point is a broad set of assets represented by various

global stock, bond, real estate, and commodity indexes. Next, we apply mean-variance

spanning and intersection tests to assess whether adding timberland to the investment

set improves the mean-variance efficient portfolio. Moreover, we quantify the economic

benefit of including timberland in the investment set. Our approach contributes to the

existing literature focusing on the added value of timberland investments. Instead of relying

on CAPM or multifactor models, we explicitly assess whether and to what extent US

timberland investments improve the mean-variance efficient portfolio.

    We find that the mean-variance efficient portfolio is significantly improved by adding

the US timberland (represented by the NCREIF Timberland Index) to the investment set,

even if the portfolio already contains a forestry and paper equity index. In economic terms

the mean-variance contribution of US timberland is substantial. Timberland can increase

the risk-adjusted excess return per unit of risk with more than 40 bp on a quarterly basis.

When the investment set already contains stocks from the forestry and paper sector, the

increase is still considerable, namely about 35 bp.

References

Belsley, D., Kuh, E. and Welsch, R. (1980). Regression Diagnostics. Wiley.

DeRoon, F.A. and Nijman, Th.E. (2001). Testing for mean-variance spanning: a survey.

Journal of Empirical Finance 8, 111-155.

Greene, W.E. (2007). Econometric Analysis, 6th edition. Prentice Hall.

                                              10
Healey, T., Corriero, T., Rosenov, R. (2005). Timber as an institutional investment. Jour-

nal of Alternative Investments, Winter 2005.

Huberman, G. and Kandel, S. (1987). Mean variance spanning. Journal of Finance 42,

873-888.

Levy, H. (1972). Portfolio performance and the investment horizon. Management Science

18, 645-653.

Lutz, J. (1999). Measuring timberland performance. Timberland Report 1(2) James. Sea-

wal Company. See http://www.jws.com/pdfs/timberlandreport/v1n4.pdf.

Redmond, C.H. and Cubbage, F.W. (1988). Portfolio Risk and Returns from Timber Asset

Investments. Land Economics 64, 325-337.

Sun, C. and Zhang, D. (2001). Assessing the financial performance of forestry-related

investment vehicles: capital asset pricing model vs. arbitrage pricing theory. American

Journal of Agricultural Economics 83, 617-628.

Treynor, J.L. and Black, F. (1973). How to use security analysis to improve portfolio

selection. Journal of Business 46, 66-86.

Washburn, C.L. and Binkley, C.S. (1993). Do forest assets hedge inflation? Land Economics

69, 215-224.

Washburn, C.L., Binkley, C.S., and Arenow, M.E. (2003). Timberland can be a useful

addition to a portfolio of commercial properties - PREA Quarterly, Summer 2003, 28-31.

                                            11
index                                  description of index                     data source           mean (%)      std.dev. (%)     corr.

       MSCI                                                                            www.mscibarra.com
       World                                  global equity index                                                   2.23            7.50     0.19
       Far East                               regional equity index                                                 0.45           10.22     0.10
       Emerging Markets                       regional equity index                                                 2.08           12.88    -0.02

       Lehman                                                                          Datastream
       Global Aggregate                       global bond index                                                    -1.15             1.73   -0.15

       FTSE                                                                            www.ftse.com
       EPRA/NAREIT Global Real Estate         global real estate equity index                                       2.80             7.57   -0.02
       EPRA/NAREIT US Real Estate             US real estate equity index                                           2.87             6.88    0.07

       Dow Jones                                                                       www.djindexes.com
       AIG Commodity                          global commodity index                                                2.37            6.24    -0.02
       Forestry & Paper (global)              global forestry & paper stocks index                                  1.02            9.86    -0.12

12
       Global Small Cap                       global small cap equity index                                         2.32            8.95    -0.01
       Latin America                          regional equity index                                                 2.04           16.27     0.01
       Canada                                 regional equity index                                                 3.40           10.44     0.10
       Forestry & Paper (America)             regional forestry & paper stocks index                                1.27           11.19    -0.11
       Composite                              US equity index                                                       2.62            7.30     0.15
       US                                     US equity index                                                       2.48            7.99     0.18
       US Technology                          US technology stocks index                                            2.94           16.47     0.07

       NCREIF                                                                          www.ncreif.com
       Timberland                                                                                                   2.39             2.74

                                                Table 1: Benchmark indexes and timberland index

     This table lists the benchmark indexes and the timberland index, together with a short description (second column), data source (third column),
     mean quarterly return (fourth column), quarterly standard deviation (fifth column) and quarterly correlation with the Timberland Index (sixth
     column) during the period 1994-2007.
1      2      3      4       5       6       7       8      9     10     11     12     13     14     15     16
     1: Timberland                       1.00
     2: DJ AIG Commodity                -0.02    1.00
     3: Global Real Estate              -0.02    0.12   1.00
     4: US Real Estate                   0.07    0.06   0.75   1.00
     5: MSCI Emerging Markets           -0.02    0.12   0.67   0.32    1.00    0.72
     6: MSCI World                       0.19   -0.07   0.59   0.31    0.72    1.00
     7: MSCI Far East                    0.10    0.16   0.54   0.15    0.66    0.67    1.00
     8: Lehman Global Aggregate         -0.15   -0.22   0.08   0.18   -0.06   -0.03   -0.23    1.00
     9: DJ Forestry & Paper (Am.)       -0.11   -0.03   0.64   0.35    0.64    0.66    0.46   -0.02   1.00

13
     10: DJ Forestry & Paper (Global)   -0.12    0.02   0.66   0.37    0.66    0.68    0.59   -0.07   0.95   1.00
     11: DJ Latin Am                     0.01    0.11   0.60   0.36    0.90    0.69    0.50    0.00   0.62   0.60   1.00
     12: DJ Canada                       0.10    0.13   0.63   0.33    0.78    0.83    0.56   -0.07   0.58   0.60   0.77   1.00
     13: DJ USA Technology               0.07   -0.14   0.39   0.12    0.60    0.83    0.51   -0.04   0.48   0.46   0.58   0.73   1.00
     14: DJ Global Small Cap            -0.01    0.06   0.71   0.45    0.79    0.88    0.72    0.01   0.67   0.74   0.75   0.84   0.74   1.00
     15: DJ Composite                    0.15   -0.04   0.61   0.43    0.60    0.86    0.42    0.12   0.71   0.65   0.62   0.73   0.67   0.77   1.00
     16: DJ US                           0.18   -0.15   0.56   0.32    0.66    0.95    0.51    0.06   0.63   0.58   0.66   0.83   0.87   0.83   0.89   1.00

                    Table 2: Correlation matrix for quarterly returns on benchmark indexes and Timberland Index
Regression model:
          rt = α + βRt + εt

          Sample period:                                                    1994-2007
          Frequency:                                                         quarterly

          benchmark assets:
          excl. Forestry & Paper index
          adj. R2                                                                  0.13
          spanning test (p-value)                                                  0.03
          increase max. Sharpe ratio                       43 bp (zero-beta rate 3.9%)
          increase max. Sharpe ratio                       59 bp (zero-beta rate 2.1%)
          increase max. Sharpe ratio                       28 bp (zero-beta rate 5.7%)

          benchmark assets:
          incl. Forestry & Paper index (Americas)
          adj. R2                                                                  0.14
          spanning test (p-value)                                               0.0001
          increase max. Sharpe ratio                       37 bp (zero-beta rate 3.9%)
          increase max. Sharpe ratio                       54 bp (zero-beta rate 2.1%)
          increase max. Sharpe ratio                       21 bp (zero-beta rate 5.7%)

          benchmark assets:
          incl. Forestry & Paper index (Global)
          adj. R2                                                                  0.15
          spanning test (p-value)                                               0.0001
          increase max. Sharpe ratio                       36 bp (zero-beta rate 3.9%)
          increase max. Sharpe ratio                       54 bp (zero-beta rate 5.7%)
          increase max. Sharpe ratio                       20 bp (zero-beta rate 2.1%)

                           Table 3: Outcomes of spanning tests.

This table provides the adjusted R2 corresponding to the regressions of the Timberland Index
returns on the benchmark returns, p-values for the spanning tests, and the increase in maximum
Sharpe ratio due to adding timberland to the investment set. Three situations are considered: (1)
the Dow Jones Forestry & Paper Index is not included in the set of benchmark assets, (2) the
Dow Jones Global Forestry & Paper Index (Americas) is included, and (3) the Dow Jones
Forestry & Paper Index (Global) is included. The Wald-tests are based on White’s
heteroskedasticity robust covariance matrix.

                                               14
You can also read