Abstract

Short-term return predictability

To investigate the short-term return predictability of investor sentiment on timberland assets, we apply the VAR model. Through the VAR model, the short-term interactions between investor sentiment and timberland investment returns are examined. The model is estimated as follows

where R_t is a k-dimensional vector of asset return, sentiment index, and returns of control variables; φ₀ is a k-dimensional vector; Φ_j is a k × k matrix, where j can be 1, 2, . . . ,  p; and {a_t} is a sequence of serially uncorrelated random vectors with mean zero and covariance matrix Σ. To determine the number of order p, selection criteria such as the Akaike information criterion (AIC), Hannan-Quinn information criterion (HQ), and Schwarz information criterion (SC), are used. Under the null hypothesis, behavioral forces have no influence on asset valuations. That is, investor sentiment has no significant effect on asset returns. Under the alternative hypothesis, overreactions caused by current optimism would increase asset prices and thus lower the subsequent future returns. Accordingly, negative coefficients on sentiment are expected. Brown and Cliff (2005) claim that control variables that capture the rational predictability of asset returns should be included because investors' reactions to the market can be a combination of rational reflections of the market and irrational expectations for the future. Sentiment variables may contain information from risk factors that are used to predict assets' future performance. Thus, to examine the predictability of sentiment on asset returns, the irrational part of sentiment variables is tested by incorporating the systematic risks induced by several control variables. On the other hand, investor sentiment may be affected by market performance. Therefore, the effect of timberland market on the sentiment is also tested by the VAR system.

Long-term return predictability

Intuitively, a bullish market attracts more investment, and investors become more optimistic about the market. The effect of sentiment can be persistent. Therefore, investor sentiment may show some importance in predicting long-term returns. The relationship between long-term timberland investment returns and investor sentiment is examined by the following regression.

where R_i,t+1, R_i,t+2, . . . R_i,t+k, are the successive k period future log returns of asset i; S_t and Z_q,t are the sentiment index and control variables at time t; and and are the intercept and error term of the regression. Parameters and are the sensitivity coefficients on the sentiment index and control variables. Similarly, the null hypothesis indicates that is not significantly different from 0; while the alternative hypothesis states that is negative.

Nevertheless, the method of generating the multiperiod future returns causes an econometric problem. Strong serial correlation in the residuals will be produced after running the ordinary least squares (OLS) regression of overlapping dependent variables so the asymptotic assumptions of the OLS are violated. Although the coefficient estimates are unbiased with serial correlations, the estimated standard errors calculated by the OLS formula are incorrect. To fix the problem, the Newey-West serial correlation consistent standard errors are calculated (Newey and West 1987). The corresponding Newey-West t statistics are calculated as the ratio of the coefficient estimate and the Newey-West standard error.

Asset performance in low- and high-sentiment periods

Previous studies indicate that sentiment investors are reluctant to sell short, and these investors are found to be more active in the run-up market. There is also evidence showing that sentiment investors check their portfolios more frequently during high-sentiment periods than in low-sentiment periods (Yuan 2008, Karlsson et al. 2009). Thus, stocks or portfolios may perform differently with respect to low- and high-sentiment periods. To study the financial performance of timberland investment in different sentiment periods, the average returns of timberland investment as well as the variances of returns are compared. However, the widely used Student's t test is not appropriate here because the sizes and variances of the two samples are usually different. To solve the problem, the Welch's t test is adapted to the Student's t test (Welch 1947).

The NCREIF Timberland Index

Provided by the NCREIF, the NTI tracks total returns from a large sample of geographically diverse timberland properties in the United States. As of 2014Q2, the NTI represented over 13 million acres with a market value of about $23 billion (NCREIF 2014). The NTI includes both income return,¹ which comes from operating activities such as timber sales, and capital appreciation, which is from the partial or complete property sales and/or appraisals if the property is not completely sold during the period.

The formulas used to calculate the index are

where IR_t and CR_t are the income return and capital return, respectively; CI_t equals the capitalized expenditures (e.g., forest regeneration); PS_t equals the net proceeds from land sales; PP_t equals the gross costs of new land acquisitions; and MV_t equals the market value of the property (Binkley et al. 2003).

Owing to the fee-based nature of the NTI, the gross returns measured by the NTI are before investment advisory fees. In addition, the NTI excludes the effects of leverage. To deal with these concerns, the NCREIF released the Timberland Fund and Separate Account Index (NTF) in 2012. The NTF reflects returns of a portfolio of timber funds and accounts and is available both gross and net of fees back to 1988Q1 (NCREIF 2012). In this study, the net of fees NTF is used to represent real business returns of timberland investments. For both the NTI and NTF, logarithm is taken for the return data.

Investor sentiment

To proxy investor sentiment, the monthly orthogonalized investor sentiment index constructed by Baker and Wurgler (2006) is used and compounded into quarterly data. The composite index of sentiment is formed from the first principle component of six lead or lag underlying proxies for sentiment. The six sentiment measures include the CEFD, the NYSE share turnover, the first-day returns of IPOs, the number of IPOs, the share of equity issues in total equity and debt issues, and the dividend premium. By principle component analysis, the idiosyncratic noise and non–sentiment-related components are filtered out and common variation is captured. Moreover, to distinguish a common sentiment component and a common business cycle component, the business cycle variation from each sentiment proxy is removed prior to the principle component analysis.² Figure 1 plots the monthly orthogonalized investor sentiment index from 1988 to 2010. It is obvious that the index captures some fluctuations in sentiment. In the early 2000s, owing to the Internet bubble, investor sentiment exploded and reached the highest value. Around 2008 to 2009, because of the subprime mortgage crisis, people lost their confidence about the market. Therefore, their sentiment dropped from positive to negative.

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Control variables

Following the suggestion of Brown and Cliff (2005), in order to control the information that the sentiment index may contain about the rational reflection of the market, risk factors that are used to predict the future performance are considered. These control variables are motivated by the previous asset pricing literature. Market return (MKT) is a risk factor used in the capital asset pricing model (Sharpe 1964, Lintner 1965). It is approximated by the value-weighted returns on all NYSE, American Stock Exchange, and National Association of Securities Dealers Automated Quotations stocks and comes from the Center for Research in Security Prices (CRSP). The size and value factors approximated by the Fama-French factors small minus big (SMB) and high minus low (HML) are considered as significant risk factors and included in the Fama-French three-factor model (Fama and French 1993). They are constructed using value-weighted portfolios formed by size and book-to-market ratio and are obtained from French (2012). Other control variables include risk-free rate, term spread, and default spread. Risk-free rate is approximated by the 1-month Treasury bill rate (Campbell 1991, Hodrick 1992), which is obtained from the CRSP. Term spread (TERM) is the yield difference between the 10-year Treasury bond and the 3-month Treasury bill (Fama and French 1989). Default spread (DEF) is the yield difference between the AAA bond rate and BAA bond rate (Keim and Stambaugh 1986, Fama 1990). These data are from the H.15 database of the Federal Reserve Board. In summary, quarterly data ranging from 1988 to 2010 are used. The descriptive statistics of the data and the correlation matrix of the sentiment index and control variables are reported in Tables 1 and 2, respectively.

Table 1 Descriptive statistics of the quarterly returns for timberland assets, sentiment index and control variables from 1988 to 2010.^a

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Table 2 Correlation matrix of the quarterly orthogonalized sentiment index and control variables.^a

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Results of short-term return predictability

Table 3 presents the result from the VAR model, which shows the interactions between the sentiment and timberland investment returns in the short run. The number of lags are determined by the AIC, HQ, and SC. AIC and HQ suggest p = 8, while SC suggests p = 1. For parsimonious purposes, we stick to a smaller order model. Therefore, a lag of one is chosen. This table only lists the estimation results for the timberland investment returns and sentiment index. From the estimation results in Table 3A, we find that the one-lagged investor sentiment index is an important factor that predicts the future returns of the NTI. The coefficient on the sentiment index is negative and significant at the 10 percent level. Although control variables such as the risk-free rate and term spread also show significance to the future timberland investment returns, they do not affect the significance of the sentiment index. This result confirms the trueness of our alternative hypothesis and suggests that overreactions caused by current optimism would increase the asset price and lower the subsequent one-quarter future returns. The R² indicates that by using the lagged variables, 21.5 percent of the total variation in the timberland investment returns are explained. Moreover, based on the F test result, the VAR(1) system is a valid model for testing the predictability of sentiment. However, there is no evidence that timberland investment predicts the sentiment, but the sentiment predicts itself. Similar results for the NTF are shown in Table 3B, which confirms that the current sentiment significantly negatively predicts the future timberland investment returns in the short run.

Table 3 Short-term return predictability of investor sentiment to the NTI and the NTF with control variables from 1988 to 2010.^a

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Results of long-term return predictability

To examine the long-term predictability of investor sentiment on timberland investment returns, the k period future return is regressed on the sentiment index and control variables. The results of the long-term return predictability with horizons of 1, 2, 3, and 5 years are presented in Table 4. The k period future return is calculated as the arithmetic average of the log returns. Tables 4A and 4B represent the coefficient estimates of the sentiment index and control variables. For all regressions, the dependent variables are the k period future returns of the timberland assets. The sentiment index and all the control variables considered in the short-term return predictability section are included in the regressions as independent variables. The correlations among the sentiment index and control variables, which are reported in Table 2, are relatively small. Therefore, multicollinearity is not a concern for the regression model that we fit.

Table 4 Long-term return predictability of investor sentiment to the NTI and the NTF with control variables from 1988 to 2010.^a

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As predicted by the alternative hypothesis, the results from Table 4A show that the sensitivity coefficients of the sentiment index are universally negative for all horizons considered, ranging from −0.300 to −0.775. The significance levels are determined by the Newey-West t statistics, which are calculated as the ratio between the coefficient estimates and the Newey-West standard errors with lags of 24. The test statistics show that the current investor sentiment significantly predicts future returns of the NTI over the next 1 to 5 years (5% level for the 1- and 5-year horizons and 1% level for the 2- and 3-year horizons).³ Besides the sentiment factor, the market return, value effect, risk-free rate, term spread, and default spread are also significant factors that predict the future returns at a certain point of time.

Table 4B presents the long-run regression results of the NTF. Similar to the results of the NTI, negative coefficient estimates on the sentiment index are obtained. Comparing these results with those in Table 4A, current investor sentiment only predicts the 2- to 5-year future returns of the NTF significantly with values of −0.569, −0.512, and −0.217. In addition, control variables such as the value effect, risk-free rate, term spread, and default spread are significant in the long-term regression for the 2- to 5-year horizons.

The economic magnitude of the coefficients on sentiment is reported in Table 5. The magnitudes are taken by the coefficients on the sentiment index and control variables multiplied by the horizon and the standard deviation of each dependent variable. The standard deviations of sentiment and control variables are reported in the SD column. The values of magnitudes indicate the effect of one standard deviation change of the sentiment index on timberland investment returns. For example, with one standard deviation increase in the current investor sentiment, NTI will decrease by 1.305, 3.195, 4.242 percent per quarter in the first 3 years and decrease by 3.092 percent after 5 years. For both the NTI and the NTF, we obtain an increasing trend of the economic magnitudes in the first 3 years, and the magnitudes decrease thereafter.

Table 5 Economic magnitude of sentiment in the long-term regressions.^a

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Asset performance in low- and high-sentiment periods

In order to study the performance of timberland assets in different sentiment periods, we compare the average returns of the NTI and NTF in low- and high-sentiment periods as well as their variances. In this study, sentiment is defined as low when the values of the sentiment index are below zero and high when the values are above zero. The average returns, variances, numbers of observations, as well as the comparison results are reported in Table 6. Owing to the different numbers of observations in two samples, the Welch's t test is used to compare the sample means.

Table 6 Performance of the NTI and the NTF in low- and high-sentiment periods from 1988 to 2010.

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The results in Table 6 show that during the whole sample period from 1988 to 2010, there are 53 low-sentiment quarters and 39 high-sentiment quarters. Table 6A presents the performance of the NTI in each sentiment period. The variances in low- and high-sentiment periods are 22.252 and 10.749, which are significantly different based on the F test. With higher variance, returns in low-sentiment periods are more volatile than in high-sentiment periods. The average returns are 3.507 and 2.714 percent during low- and high-sentiment periods, respectively. However, the Welch's t test indicates that the average returns of the NTI in low- and high-sentiment periods are not significantly different. Similar results for the NTF are obtained, which are shown in Table 6B. The result confirms the previous finding that timberland investment earns stable long-term returns.

Robustness test

The long-run predicting power of the sentiment index is examined using the overlapping long-run timberland investment returns. In the meantime, investment sentiment index is found to be persistent. Some studies have argued that because of the persistence of the predictive variables and the overlapping observations, the OLS method may provide biased coefficient estimation (Hansen and Hodrick 1980, Stambaugh 1999). To test the robustness of the long-run regression results, the moving block bootstrap (MBB) method, as suggested by Schmeling (2009), is used. The data are split into n − b + 1 overlapping blocks, with n as the sample size and b as the block length. In this study, we set the block length to be 5. We then bootstrapped n/b (an integer is chosen) blocks from the n − b + 1 blocks randomly with replacement to generate 10,000 new time series samples. For each sample, we run the long-run regression and estimate the coefficients. For the results reported, the coefficient estimates are averaged among the 10,000 regressions results, and the standard deviations of the coefficients are also reported. From Table 7 we can see that for both the NTI and NTF, negative coefficients on the sentiment index are obtained for all the long-run horizons considered. The values of the coefficients estimated by the MBB method are almost the same as the ones from the OLS method. In addition, the standard deviations of the coefficient estimates are relatively small, indicating the accuracy of the estimates from the bootstrap samples. This result confirms that our results from the OLS are unbiased and robust.

Table 7 Robustness test of long-run predicting power of sentiment index on timberland investment returns.

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