Semester of Graduation

Summer 2024

Department

Agricultural Economics and Agribusiness

Document Type

Thesis

Abstract

Abstract

This thesis investigates the statistical distribution functions fit for modeling the returns of farmland derivative stocks and financial market indexes. Farmland derivative stocks have garnered increased interest due to their potential use in portfolio diversification and risk management. Financial asset returns can be characterized by higher moment behavior in the underlying statistical distribution. This implies that in assessing the statistical distribution properties of risks, proper consideration must be given to the choice of functional form. The Generalized Lambda Distribution (GLD) is used due to its flexibility in model various distribution functions.

The dataset comprises daily and monthly log returns of two major farmland REITs (LAND and FPI) from 2014 to 2023. The GLD was fitted to the log return series using the Maximum Likelihood Estimation (MLE) parameter estimation method. Goodness-of-fit tests, including the Kolmogorov-Smirnov (KS) test and Q-Q plots, were employed to evaluate the performance of the GLD relative to the normal distribution. Measures of risks such as VaR and ES are analyzed.

A correlation analysis of daily and monthly log returns for farmland REITs and major financial market indexes reveals that financial market indexes exhibit high correlations with one another across both daily and monthly, as expected; in contrast, farmland REITs show a relatively low correlation with these indexes, indicating their diversification benefits. For example, the daily correlation between LAND and the S&P 500 is 0.42, and between FPI and the DOW 30 is 0.31.

The results indicate that the GLD distribution provides a superior fit to the empirical return data compared to the normal distribution using the Kolmogorov-Smirnov test (KS). The GLD's ability to model skewness and kurtosis more accurately accounts for the heavy tails and extreme values characteristic of farmland derivative returns. The study reveals that the choice of the investment horizon significantly influences the distributional properties of returns. Shorter investment horizons (e.g., daily returns) exhibit higher volatility and fat tails, while longer horizons tend to normality. The logistic distribution was identified as the dominant function for daily and monthly returns, followed by the Cauchy distribution, and this finding is consistent with existing literature (e.g., Levy and Duchin, 2004).

Risk assessments using the best-fit distributions are calculated using Value-at-Risk (VaR) and Expected Shortfall (ES) and compared to the normal distribution. The normal (Gaussian) measures of VaR and ES often underestimate extreme losses whereas the GLD-based VaR and ES provide more accurate risk estimates. Backtesting the VaR estimates with the Kupiec test confirms the robustness of the GLD in capturing the tail risk associated with farmland derivatives.

In conclusion, the Generalized Lambda Distribution was adequate to model financial returns of farmland REITs which have skewness and leptokurtic characteristics. The logistic distribution was found to dominate the findings, lending support to the continued use of the Mean-Variance approach in portfolio selection (as found in Levy and Duchin, 2004). The study also illustrates the accuracy issue in measuring risk using VaR and ES which is often cited in empirical research in a broader financial context (Corlu et al., 1016).

Date

7-28-2024

Committee Chair

Hector O. Zapata

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