We use novel monthly security-level data on U.S. household portfolio holdings, flows, and returns to analyze asset demand across an extensive range of asset classes, including both public and private assets. Our dataset covers a broad range of households across the wealth distribution, notably including 439 billionaires. This ensures representation of ultra-high-net-worth (UHNW) households that are typically not well covered in survey data. With these data, we study the portfolio rebalancing behavior of households and ask whether (and, if so, which) households play an important stabilizing role in financial markets. Our findings reveal a stark contrast: less affluent households sell U.S. equities amid market downturns, while UHNW households buy and contribute to stabilizing markets. This behavior is more pronounced among households who rebalance their portfolios more frequently. However, the sensitivity of flows to returns is generally quite small and as the trades of different wealth groups partly offset each other, the aggregate household sector plays a limited role to absorb financial fluctuations. To understand the contrasting trading behavior across households, we show that a household’s flows to U.S. equities are negatively correlated with its “active returns” (the difference between an investor’s return and the market return). However, the flows to U.S. equities of less affluent households are also positively correlated with broad market returns – perhaps due to shifts in risk aversion, sentiment, or perceived macroeconomic risk – leading this group of households to act pro-cyclically. Across all asset classes, three factors with intuitive economic interpretations explain 81% of all variation in portfolio rebalancing. Those factors bet on the long-term equity premium, the credit premium, and the premium on municipal bonds. In sum, our framework paints a quantitative picture of U.S. households’ assets and rebalancing marked by a great deal of insensitivity and inertia throughout the distribution, even for UHNW households. These new facts are useful for the calibration of macro-finance models with heterogeneous households and multiple risky asset classes.