How Should Returns to Long Term Investors be Measured?

Widely used databases report stock returns that are measured at the monthly horizon, while investors participate in the markets over multiple months. Most academic studies report conditional or unconditional arithmetic means of the monthly returns. We describe the odd trading strategy interpretation of the arithmetic mean return and clarify the trading strategy interpretations of alternative measures, including the geometric mean, the dollar-weighted mean, and modified internal rates of return. We also identify the corresponding long term (i.e., holding period) return interpretation for each measure, and clarify that some such measures (e.g., the compound dollar-weighted return) do not have an economic basis. We illustrate and contrast the measures in a broad sample of over 71,000 stocks