The Diversification Properties of US Timberland: A Mean-Variance Approach
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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
1low 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.
22 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.
3Northwest. 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.
43 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
5of 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
6decomposition 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
7portfolio 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
8can 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.
95 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.
10Healey, 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.
11index 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 IndexRegression 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.
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