Multiple arbitrage, or roll-up, is the strategy of acquiring small companies at low valuation multiples and selling the combined, larger group at a higher multiple that bigger businesses command. The value is created by the difference in multiples between small and large, not necessarily by improving the underlying operations.
Multiple arbitrage is distinct from multiple expansion, which reflects a re-rating of the same business, and it is structural rather than performance-driven. Because a sophisticated buyer understands the mechanic, they will price it accordingly — crediting the arbitrage to strategy and structure, not to operating skill. Conflating the two overstates how much of a return came from running the business better.