Risk Costs and the Choice of Market Return Index

Abstract

Six measures of returns are used to estimate the most market index for southeast Kansas farms. Results suggest that localized indices are more appropriate than state indices for use as the market index. The appropriate index was used to estimate systematic and nonsystematic risk and risk costs for farm planning. Estimated risks depend on the choice of market index, whereas risk costs depend on the index choice and the risk aversion level. Rankings of enterprises change when risk costs and risk aversion are considered. More risk-averse specialized farmers are not completely compensated for risk. Farm income variability is a problem farm businesses deal with each year. Farm diversification is one method that can be used to reduce income risk. However, it is difficult for farmers to understand and plan for risk because of the various sources of risk and because farmers often do not understand the riskreturn tradeoffs based upon correlations, means, standard deviations, and risk-aversion coefficients. Meanvariance techniques used to derive efficient diversification strategies usually do not consider an individual enterprise's contribution to the risk of the farm. In order for a farmer to make decisions more wisely, improved information about risk associated with individual farm enterprises is necessary. Including risk cost information in enterprise budgets will allow farmers to begin to see some of the risk-return tradeoffs that occur when comparing alternative enterprises. Considering risk costs may change the preferred ordering of enterprises. The objective of this study is to determine the levels of systematic and nonsystematic risk and corresponding costs for a selection of farm enterprises in southeast Kansas using enterprise budgets from actual farm data. In addition, this article considers whether the results will differ using alternative definitions of the market portfolio. Nonsystematic risk is reduced as a farm diversifies, while systematic risk is not. If a farm is fully diversified, nonsystematic risk is zero. A risk cost can be estimated from systematic and nonsystematic risks of an enterprise and can be subtracted from the budgeted returns. By estimating the risk costs of different enterprises, farm managers can use this risk information in the selection of efficient portfolios. The single index model (SIM) has been used in finance and agriculture to simplify the information needs of mathematical programming models (Sharpe; Collins and Barry; Turvey, Driver, and Baker). It provides estimates of risk that represent the variance-covariance structure of enterprise returns. Several studies have used the SIM either to provide risk information and derive optimal enterprise combinations or to determine the risk costs (Collins and Barry; Turvey and Driver; Turvey, Driver, and Baker; Gempesaw et al.; Sharpe and Baker). The problem of market index choice has been considered ex post in the finance literature (Frankfurter). Frankfurter found that on an ex post basis, some index measures performed as well as others. However, Frankfurter argued that better efforts should be made to determine the appropriate market index. Several SIM applications in agriculture have used state enterprise extension budgets and various measures of the market index. Collins and Barry used deflated averages of enterprises to form the market index. Turvey, Driver, and Baker chose nominal averages of individual enterprises for the market index. Gempesaw et al. used deflated detrended averages of individual enterprises for the market index. Sharpe and Baker chose real Indiana net farm income and a rate of return on assets as possible indices. Thus, their indices