The aggregate Lerner index is a popular composite measure of multi-product banks' market power, based on total assets as the single aggregate output factor. We show that the aggregate Lerner index only qualifies as a consistently aggregated Lerner index if three conditions hold. Under these conditions, the aggregate Lerner index reduces to a weighted-average of the product-specific Lerner indices. We test the three conditions for a sample of U.S. banks covering the years 2011-2017. All three conditions are rejected and we show that they may cause an economically relevant bias to the aggregate Lerner index, depending on the economic context. As a general solution, we propose using the always consistently aggregated weighted-average Lerner index whenever a composite Lerner index is needed.