Cautiousness, Skewness Preference, and the Demand for Options

In this article we establish cautiousness as a new downside risk aversion measure, using a portfolio problem with a risk-free bond, a stock, and an option. We show that, an investor has higher cautiousness (i) if and only if she is always more likely to buy the option; and (ii) if and only if she always demands more options per share. As an option’s payoff is a convex function, increasing positions in the option increases the convexity of a portfolio, which leads to an increase in skewness. Thus the results in this article establish the link between cautiousness and skewness preference.