Inferior Good and Giffen Behavior for Investing and Borrowing

The standard assumption that asset demand increases in income and decreases in price has its origin in Arrow's classic model with one risky and one risk free asset, where both are held long, and preferences exhibit decreasing absolute and increasing relative risk aversion. However if one allows shorting of the risk free asset or decreasing relative risk aversion, the risk free asset can not only fail to be a normal good but can be a Giffen good. This behavior can occur even for members of the popular HARA utility family. More generally, Giffen behavior can occur over multiple income ranges.