Measuring, modeling, and managing risk has always been an important task for researchers. Many of the traditional assumptions relied on in risk research, such as the assumption of normality and single period optimization, have proven too restrictive and alternative methods have been developed. The objective of this dissertation is to explore and apply these tools to analyze geographical diversification. The first step to analyze geographical diversification is to understand how different climate and spatial variables impact yields. Yield dependencies for wheat, cotton, and sorghum are estimated using linear correlation and copulas. The copulas provide an alternative to linear correlation. The results of the different dependency estimations indicate that there is a significant difference between the results. The next step is to analyze geographical diversification in a portfolio setting. Traditional portfolio optimization has assumed that risk and dependence are symmetric. Using a single period model, an asymmetric risk measure, conditional value at risk, and asymmetric dependence measure, copulas, are implemented into the portfolio optimization model. The efficient frontiers under both symmetric and asymmetric assumptions show that ignoring the asymmetric nature of the data could lead to optimal portfolio allocations that could underestimate the actual risk exposure. The implication of these results provides researchers with more motivation to move beyond the standard assumptions of linear correlation and normality. Building on the single period problem, a multi-period portfolio model is formulated using discrete stochastic programming. One key in formulating a discrete stochastic program is the representation of uncertainty. Scenario generation is a method to obtain a discrete set of outcomes for the random variables. A moment matching routine is developed to capture the first four moments of the variables and the multivariate relationship is modeled using copulas. The results show that the moment matching routine closely captures the higher moments of the data. The results also indicate that there are possible gains from geographical diversification. Wealth levels increased for all three regions when production is diversified over the different regions. The optimal land allocation was dependent upon the base acreage assumption
Measuring, modeling, and managing risk has always been an important task for researchers. Many of the traditional assumptions relied on in risk research, such as the assumption of normality and single period optimization, have proven too restrictive and alternative methods have been developed. The objective of this dissertation is to explore and apply these tools to analyze geographical diversification. The first step to analyze geographical diversification is to understand how different climate and spatial variables impact yields. Yield dependencies for wheat, cotton, and sorghum are estimated using linear correlation and copulas. The copulas provide an alternative to linear correlation. The results of the different dependency estimations indicate that there is a significant difference between the results.
The next step is to analyze geographical diversification in a portfolio setting. Traditional portfolio optimization has assumed that risk and dependence are symmetric. Using a single period model, an asymmetric risk measure, conditional value at risk, and asymmetric dependence measure, copulas, are implemented into the portfolio optimization model. The efficient frontiers under both symmetric and asymmetric assumptions show that ignoring the asymmetric nature of the data could lead to optimal portfolio allocations that could underestimate the actual risk exposure. The implication of these results provides researchers with more motivation to move beyond the standard assumptions of linear correlation and normality.
Building on the single period problem, a multi-period portfolio model is formulated using discrete stochastic programming. One key in formulating a discrete stochastic program is the representation of uncertainty. Scenario generation is a method to obtain a discrete set of outcomes for the random variables. A moment matching routine is developed to capture the first four moments of the variables and the multivariate relationship is modeled using copulas. The results show that the moment matching routine closely captures the higher moments of the data. The results also indicate that there are possible gains from geographical diversification. Wealth levels increased for all three regions when production is diversified over the different regions. The optimal land allocation was dependent upon the base acreage assumption