Journal of Real Estate Portfolio Management: Farmland in a Mixed-Asset Portfolio: A Mean-Semivarianc

Executive Summary, This study uses the downside risk or mean-semivariance (M-S) methodology to evaluate farmland as a component of a mixed-asset portfolio. Results confirm that while a minimal investment in farmland may be warranted, farmland investment does not need to be a substantial part of the core allocations of an optimized mixed-asset portfolio. Although investment in farmland cannot be shown to statistically improve mixed-asset portfolios, which already include allocations to real estate, investment in farmland can be part of the real estate allocation of an optimal mixed-asset portfolio when investors or their advisors have farmland investment expertise. More studies using additional farmland data are required to fully assess direct investment in agricultural land.

Introduction

Real estate investment within a mixed-asset portfolio has been the subject of much research. Most study results indicate that a mean-variance (M-V) efficient portfolio of mixed-assets should have a large concentration of real estate assets and that there are benefits to using real estate for portfolio diversification.1 A high single-digit or low doubledigit allocation to real estate has been shown to be justifiable. Though studies by Pagliari, Webb and Del Casino (1995), Gold (1995, 1996), Liang, Myer and Webb (1996), Ziobrowski, Cheng and Ziobrowski (1997) and Cheng and Liang (2000) question the ability to specifically optimize a mixed-asset investment portfolio, because the range of possible portfolio allocations has been shown to be quite large, the benefit for the inclusion of real estate in mixed-asset portfolio is undisputed.

The present study builds on this existing research concerning real estate in a mixed-asset context by evaluating whether farmland,2 a real estate asset class that has not received much attention by institutional investors, might be used to improve mixed-asset portfolio efficiency. By applying the mean-semivariance (M-S) portfolio construction technique, which allows for consideration of an investor's minimum required return (MRR) and has been used in recent studies by Sivitanides (1998), Sing and Ong (2000), Cheng (2001) and Cheng and Wolverton (2001), the study extends existing research on farmland investment in a portfolio context that uses the mean-variance (M-V) portfolio construction methodology. Unlike prior farmland investment research which, with the exception of Hardin and Cheng (2002), indicates a large allocation to farmland in a mixed-asset portfolio (Webb and Rubens, 1988; Webb, Curico and Rubens; 1988; and Lins, Sherrick and Venigalla, 1992), the present results show that efficient mixed-asset portfolios can be created with no or only minimal allocations to farmland and appear to be in-line with actual institutional investor investment allocations. The results clarify why farmland, which has a market value comparable to the NCREIF and REIT investment universes, has not been seen as a viable real estate investment by most institutional investors. Farmland can best be seen as a possible component of a portfolio of direct investment in real estate, especially for investors with expertise in farmland investment and investors managing funds from states with large agribusiness interests.

Methodology and Data

Unlike prior farmland investment studies that use mean-variance analysis to evaluate mixed-asset portfolio allocation efficiency, this study uses the downside risk or mean-semivariance methodology. Given the well-known limitations in real estate returns data, the data are also evaluated with both actual data and sample data generated using a bootstrap sampling procedure.

The use of the downside risk or M-S methodology (see the Appendix) allows for consideration of an investor's minimum required return (MRR). The downside risk technique optimizes portfolio returns subject to the minimum required return of an investor. In general terms, an investor's minimum required return sets a return benchmark from which portfolio allocations are derived. The asset allocations maximize the probability that the minimum required rate of return will be obtained. The downside risk technique can be considered a more conservative portfolio construction technique than the mean-variance technique in that an investor's tolerance for risk can be made explicit (Cheng and Wolverton, 2001).

As with Tegene and Kuchler (1991, 1993) and Hardin and Cheng (2002), farmland data (Exhibit 1) are from states and regions in the United States with substantial agricultural economies.3 Fifteen states with sufficient long-term data are used to measure farmland return performance. The National Agricultural Statistic Service of the United States Department of Agriculture provides the data. The total return series is created in a method similar to that of Lins, Sherrick and Venigalla (1992) and Hardin and Cheng (2002). National Agricultural Statistic Service data on rental income, land value and the ratio of rental income to farmland value are used to create total returns series with both income and appreciation components. Following Hardin and Cheng (2002), the data is desmoothed using the Geltner (1993) algorithm.4

Common stocks, corporate bonds, Treasury bills and real estate including farmland are evaluated in a mixed-asset portfolio framework. Annual time-series data for these assets from 1968 to 1994 generate twenty-seven annual observations.5 Following prior research, the S&P 500 Index is the common stock measure, the Lehman Brothers' Long Bond Index is the corporate bond measure and the United States Treasury measure is proxied by the one-year T-bill yield available from the Federal Reserve. Because NCRIEF data are not available for the entire period under study, the real estate data is obtained from Evaluation Association, Inc., which reports appraisal-based total property returns aggregated at the national level. This data source has been used by a number of the studies cited in this paper including Ziobrowski, Cheng and Ziobrowski (1997) and Hardin and Cheng (2002).

Mixed-Asset Portfolio Efficiency Using the Mean-Semivariance Technique

The conventional wisdom is that for diversification to be beneficial, assets in the investment opportunity set must have low or negative correlations. Consequently, the total return series for farmland is constructed based on historic cash rent and land value and the correlation coefficients among farmland and the typical assets found in mixed-asset portfolios are calculated.6 Results are provided in Exhibit 2. Farmland has low and negative correlations with stocks and bonds with the negative correlation between farmland and bonds being statistically significant at the 0.05% level. The farmland returns do not evidence a negative or low correlation with the real estate return measure.

Since institutional investors are concerned with whether farmland should be part of a mixed-asset investment portfolio, optimized M-S portfolios with farmland are generated over three levels of risk tolerance. The lowest level of risk tolerance (T = 0.00%) allows for no capital loss, the intermediary level of risk tolerance is the average T-bill rate during the period under study (7.05%), while the final level of risk tolerance exceeds the average T-bill rate by almost 300 basis points (10.00%). Concurrently, a base M-S efficient frontier is developed for optimized portfolios consisting of common stocks, corporate bonds, T-bills and commercial real estate without farmland.

Exhibit 3 provides evidence of the potential benefits of farmland in a mixed-asset portfolio. Allocation inferences can be made within the downside risk framework with farmland being added to the mixed-asset investment opportunity set and with farmland being excluded from the investment opportunity set (Exhibit 4). As has been found in the existing studies using M-V analysis, farmland appears to improve portfolio efficiency with implied large allocations to farmland as investors become more risk tolerant and have higher expected portfolio returns. Over all three levels of risk tolerance, but especially at the highest level of risk tolerance (T = 10.0%), and with higher expected portfolio returns, large allocations to farmland are indicated. The allocation to farmland peaks over all three levels of risk tolerance at the highest level of expected portfolio return with an implied maximum allocation to farmland of 84.9% of the assets in a mixedasset portfolio. When compared to M-S portfolios without farmland shown in Exhibit 4, it appears that the investment allocation to farmland is generated by higher allocations to bonds and T-bills and lower allocations to stocks and real estate. The real estate allocations across the three levels of risk tolerance and various expected portfolio returns are greater in the absence of the farmland option. Farmland appears to be somewhat of a substitute for stocks and other forms of direct investment in real estate. Using the optimized point estimates for asset allocation generated from the returns series, high portfolio allocations to farmland are implied as has been the case with prior research. The actual stability of the mixed-asset allocation weights is addressed in the following section.

Simulated Mean-Semivariance Mixed-Asset Portfolio Efficiency

While the point estimates discussed earlier infer a large allocation to farmland in a mixed-asset portfolio, additional assessment is necessary to fully determine if farmland is required in an optimized mixed-asset portfolio. Due to the limitations found with real estate and farmland performance measures caused by return construction methodology, the small number of actual observations, the potential for sample selection bias and the welldocumented appraisal smoothing problem, further statistical analysis is warranted. Specifically, the M-S methodology suffers from the same decisionmaking weakness found with M-V analysis as only point estimates are generated, which do not describe the portfolio well in statistical terms. Lacking the true distribution of portfolio weights, the point estimates and weights generated by the data are insufficient for portfolio evaluation. It is now common knowledge that efficient frontiers and portfolio compositions are not precise. As is the case with M-V analysis, this lack of precision in the data can be modeled within the M-S framework by using a bootstrap simulation technique that provides more meaning to the initial portfolio allocations.

Random re-samples of the existing sample of farmland returns are generated by a bootstrap procedure. An M-S analysis is performed on each of 1,000 re-samples and a set of optimal downside risk portfolios are generated at each of the three levels of risk tolerance. Thus, randomly generated weights proxying each asset's weight at a targeted expected portfolio return for a given level of downside risk are created.

The mean-semivariance analysis is applied to each V^sup b^ to generate optimal portfolio asset weights.7 The procedure is repeated 1,000 times so that inferences can be made that are based on the empirical distribution of these simulated asset weights. Simultaneously, confidence intervals for asset allocation weights are developed from the bootstrap simulation. The larger the confidence intervals generated, the less precise the portfolio weights. Also, if the range of the weights has a lower bound of greater than 0.0%, then it may be inferred that some allocation to that asset class is warranted.

The bootstrapped mixed-asset portfolio allocations for farmland are shown in Exhibit 5. The panels from the exhibit provide lower bounds (LBs) and upper bounds (UBs) for the three levels of risk tolerance over a large range of expected returns. Two meaningful inferences can be made. The LB quantifies a minimum allocation to the asset class. And, if the range in all asset allocations at any expected return includes 20.0%, then a naïve allocation would provide results similar to an optimized portfolio. Exhibit 5 shows that as an investor's risk tolerance (T) and expected portfolio return increase, the median estimated allocation to farmland generally increases. When using the LB evaluation criteria, however, only minimal allocations to farmland are required. The LB at the lowest risk tolerance level (T = 0.00%) is 0.00%. The LB at the intermediate risk tolerance (T = 7.05%) level is 3.00% and lower bound (LB) is only 5.00% at the moderate risk tolerance level (T = 10.0%). This minimal allocation is further confirmed when the range of asset allocations is analyzed. At all levels of risk tolerance and expected portfolio returns, the range of optimal allocations for each potential asset in the mixed-asset portfolio includes 20.0%, which implies that an optimized allocation does not outperform a naïve allocation.

Finally, in Exhibit 6, M-S efficient bootstrapped mixed-asset portfolios with and without farmland are compared.8 There is no statistical difference between with and without farmland bootstrapped MS efficient portfolios. This strongly suggests that it is not necessary to add farmland to a mixed-asset portfolio that already includes real estate. This does not, however, mean that farmland cannot be used as a component of an optimized mixed-asset portfolio, but rather implies that substantial reallocations to farmland are not necessary. In short, when investment managers have expertise in farmland investment, then such investments can be used as a part of an optimized mixed-asset portfolio. Optimized mixed-asset portfolios, however, can be created without the addition of farmland as a separate asset class.

Conclusion

This study provides additional insight into the ability of farmland assets to improve mixed-asset portfolio efficiency by using the downside risk or mean-semivariance methodology for measuring portfolio efficiency. The study results contrast with prior research by showing that investment in farmland is not required to improve mixed-asset portfolio efficiency when real estate is already a component of the mixed-asset portfolio. Within a mixed-asset portfolio, M-S optimized portfolios with farmland cannot be statistically differentiated from portfolios without farmland. While it appears that a very small asset allocation to farmland might improve portfolio efficiency, the additional marginal costs of making such an investment may offset any potential gains. While institutional investors with expertise in farmland investment can justify some allocation to farmland based on strategic choices and the investment goals of the institutions for which they manage assets, investment managers in general need not increase the complexity and portfolio construction and maintenance costs of mixed-asset portfolios by adding farmland as a separate asset class.

One must also consider the potential biasing effect of a lack of sufficient return data for alternative real estate-oriented investments like farmland on portfolio analysis. Although newer statistical techniques can be used to evaluate smaller data sets, the collection and generation of better data will make the assessment of alternative real estate investments more meaningful. Advocates of nontraditional or non-core real estate mixed asset investment options must take pro-active steps to see that sufficient data is available for analysis. Specifically, for farmland investments, greater amounts of data will allow a fuller assessment of the asset class and may increase our ability to make statistical inferences implying that farmland can improve mixed-asset portfolio efficiency. Additional studies should be completed with other farmland returns series including those from NCREIF, Ibbotson and proprietary sources.

Endnotes

1. See Seller, Webb and Myer (1999).

2. In this analysis, the term farmland is operationalized by cropland properties. Cropland is generally denned as land that is used for row crops. This is differentiated from other types of agricultural land that might include pastureland, orchards or other more specific delineations of the asset class. Cropland and most other farmland assets are characterized by lease cash flows and price appreciation returns. The majority of row crop production in the U.S. is on leased land. Similar to other real estate investment types, investor returns come from rental cash flow and asset appreciation.

3. Tegene and Kuchler (1991, 1993) and Hardin and Cheng (2002) indicate that a reduced data set better measures agricultural land investment performance. In this study, cropland returns are used to represent farmland investment returns. Investment in agricultural land can also include other sub-types of property such as orchards, pastureland, and nuts and by actual crop in production. California and Texas, which both have substantial agricultural production, are excluded from the data.

4. There is continued debate as to the use of smoothed and unsmoothed total real estate return indices. The analysis was done on both smoothed and unsmoothed indices with no differences in the study results.

5. The period under investigation ends in 1994 due to a slight change in data collection methodology by the National Agricultural Statistical Service of the United States Department of Agriculture in 1995.

6. In the framework of downside risk, the correlation among assets is not dependent on the MMR or target return (T) of the investor.

7. See Cheng (2001) and others for the derivation of a VAR bootstrap procedure.

8. The bootstrapped M-S portfolio compositions without farmland are not presented, but are used to compare the bootstrapped with and without farmland optimized portfolios.

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by William G. Hardin*

Ping Cheng**

* Mississippi State University, Mississippi State, MS 39762 or bhardin@cobilan.msstate.edu.

** Florida Atlantic University, Boca Raton, FL 33431 or pcheng@fau.edu.