It is standard in economics to assume that assets are normal goods and demand is downward sloping in price. This view has its theoretical foundation in the classic single period model of Arrow with one risky asset and one risk free asset, where both are assumed to be held long, and preferences exhibit decreasing absolute risk aversion and increasing relative risk aversion. However when short selling is allowed, we show that the risk free asset can not only fail to be a normal good but can in fact be a Giffen good even for widely popular members of the hyperbolic absolute risk aversion (HARA) class of utility functions. Distinct regions in the price-income space are identified in which the risk free asset exhibits normal, inferior and Giffen behavior. An Example is provided in which for non-HARA preferences Giffen behavior occurs over multiple ranges of income.