Vine-Copula Based Models for Farmland Portfolio Management

U.S. farmland has achieved total returns of 10%-13% over the past decade with volatility of only 4%-5% (NCREIF Farmland Index). In addition, farmland returns have had low or negative correlation with traditional asset classes. These characteristics make farmland an attractive asset class for investors. Farmland, as a real asset, can also provide a hedge against inflation because farmland returns exhibit positive correlation with inflation. Over the past decade, annual U.S. farmland total return exceeds U.S. inflation rate by 3.55% (NCREIF Farmland Index and Consumer Price Index - Urban). With growing global demand for agricultural commodities and limited land to expand capacity, some investors expect that farmland will continue to generate superior returns for the foreseeable future. Efficient risk management and portfolio management are critical to create optimal risk/return profile for all investments. An essential issue in portfolio risk management is how marginal time series and the correlation structure of a large number of asset returns are treated. Most previous studies on farmland portfolio analysis were performed under the Capital Asset Pricing Model (CAPM) framework (Barry, 1980; Hennings, Sherrick, and Barry, 2005; Noland, Norvell, Paulson, and Schnitkey, 2011). The linear correlation assumption implied by the CAPM, however, is not adequate to capture complex correlation structure such as tail dependence and asymmetry that potentially exist among farmland asset returns. In addition, the normality assumption of the CAMP for asset returns has proven to be inappropriate in agriculture (Just and Weninger, 1999). Copula modeling is a suitable alternative. Margins and dependence can be separated by the copula function. The choice of marginal distribution is arbitrary and various copula types exhibiting flexible and complex correlation structures are available. Chen, Wilson, Larsen, and Dahl (2014) used the Gaussian copula to model joint distribution of agricultural asset returns to account for non-normal margins. However, the Gaussian copula can only capture symmetric correlation structure and allows no tail-dependence. Besides, the Gaussian copula, restrictions exist for most other multivariate copulas (Student’s t copula, Archimedean copulas, etc.). This inflexibility issue can be overcome by the pair-copula modeling proposed by Joe (1996). In particular, the regular vine (R-vines) representation of pair-wise copulas specifies arbitrary bivariate copulas as building blocks and hence can model any possible correlation structure. This study applies vine copulas to model farmland asset returns. We focus on annual state-level cropland returns for 30 major U.S. agricultural producing states. Average annual cropland returns on eight multi-state regions that the 30 states belong to and the average returns on the United States are included as well. This 39-dimensional data set covers the period spanning from 1998 to 2015. Following Brechmann and Czado (2013), ARMA-GARCH models with appropriate error distribution are fitted to each return. R-vine copulas are then used to model the correlation structure of standardized residuals obtained from the marginal GARCH models. Given the high dimensionality of the vine copula modeling, a Regular Vine Market Sector (RVMS) model (Brechmann and Czado, 2013) is applied to specify the R-vine structures and estimate the parameters. By grouping states by multi-state regions, this model mitigates the curse of dimensionality and facilitates interpretation of the correlation structure. The vine-copula based model used in this study loosens the restrictive normality and linearity assumptions under the classical CAPM framework, and allows for complex and flexible correlation structure such as tail-dependence. We compare this model to relevant benchmark models using the Gaussian and t copulas. The results show that the vine-copula based model provides a better a fit as indicated by modeling-fitting criteria. We show that, farmland portfolio management can benefit in terms of forecasting tail risk (Value-at-Risk) and constructing optimal portfolio more accurately for both passive and active portfolio management. We also use the vine-copula based model to identify and separate market, regional, and idiosyncratic risk for different risk measures. Our results show that the model provides an approach to precisely assessing and allocating risk of the farmland portfolio under the modern risk management framework. The vine-copula based model used in this study can serve as an initiative for more elaborate models for farmland portfolio management. One direction for future research would be to explore dynamic vine-copula structures to take into account the dynamics of correlations among farmland asset returns for forward-looking portfolio management. Another direction could be the consideration of estimation risk to account for the uncertainty of correlation parameters in the vine-copula model.