A Note on Indifference Curves in the Mean-Variance Model - Williams, Joseph T. (Journal of Financial and Quantitative Analysis, 1977)
The relationship between an investor's attitude toward risk and the shape of his preference functions has long been recognized in both the general portfolio problem and the mean-variance model. By contrast, the literature has largely ignored the connection between general measures of an investor's attitude toward risk and the shape of his mean-variance or mean-standard deviation indifference curves. Yet this relationship is significant. Through general measures of risk aversion, assumptions about an investor's behavior under uncertainty imply restrictions on indifference curves. Conversely, assumptions about indifference curves impose restrictions on an investor's behavior under uncertainty. The development of this relationship and its implications is the objective of this note.