The article introduces new ways to measure investment performance using arithmetic means of rates of return weighted by market values. This method helps evaluate how well a fund or portfolio is doing, as well as how effective a fund manager is. It shows that the Internal Rate of Return (IRR) is a weighted average of rates of return based on different values, which can affect the overall performance measurement. The manager's Arithmetic Internal Rate of Return (AIRR) is found to be the true equivalent of the cumulative Time Weighted Rate of Return (TWRR), while the period TWRR gives a different ranking. This approach can be adapted to handle different benchmark rates and addresses the challenge of estimating values when they are not readily available.