Cautiousness in the small and in the large

We characterize cautiousness, a downside risk aversion measure, using a simple portfolio problem in which agents invest in a stock, a risk-free bond, and an option on the stock. We present two different characterizations by answering the following two questions respectively: who buys the option? who buys more options per share of the stock? Our characterizations use a strong notion of an increase in skewness defined by Van Zwet (1964)