This paper undertakes a quantitative investigation of the effects of anticipated inflation on the distribution of household wealth and welfare. Consumer Finance Data on household financial wealth suggests that about a third of the US population holds all its financial assets in transaction accounts. The remaining two-third of the US population holds most of their financial assets outside transaction accounts. To account for this evidence, I introduce a portfolio choice in a standard incomplete markets model with heterogeneous agents. I calibrate the model economy to SCF 2010 US data and use this environment to study the distributive effects of changes in anticipated inflation. An increase in anticipated inflation leads households to reshuffle their portfolio towards real assets. This crowding-in of supply for real assets lowers equilibrium interest rates and thereby redistributes wealth from creditors to borrowers. Because borrowers have a higher marginal utility, this redistribution improves aggregate welfare. First, this paper shows that inflation acts not only a regressive consumption tax as in Erosa and Ventura (2002), but also as a progressive tax. Second, this paper shows that the welfare cost of inflation are even lower than the estimates computed by Lucas (2000) and Ireland (2009). Finally, this paper offers insights into why deflationary environments should be avoided.