discretereturn

Discrete return, also known as simple return or holding period return, is a basic measure of investment performance that expresses the percentage change in an asset's value over a period. For an asset with starting price P0 and ending price P1, the discrete return is r = (P1 − P0) / P0. If cash flows such as dividends or coupons are received during the period, the total discrete return becomes r = (P1 − P0 + CF) / P0, where CF represents net cash inflows.

Relation to other measures: The discrete return is contrasted with the continuously compounded (log) return, defined as r_log = ln(P1/P0). They are linked by 1 + r = exp(r_log). For small changes, r ≈ r_log, but the two diverge for larger moves.

Multi-period and annualized forms: Over consecutive periods, the overall discrete return is (1 + r1)(1 + r2)… − 1, reflecting compounding. To compare investments across different horizons, discrete returns are often annualized using the geometric mean: (1 + R)^(1/n) − 1, where n is the number of years.

Applications and limitations: Discrete return is commonly used in performance reporting and basic calculations, easily interpretable by investors, and can incorporate cash flows. However, it is not additive across time, so simple averages can be misleading; for time-series analysis, log returns are often preferred for additivity and statistical properties. When reporting performance, it is important to specify the time horizon and any cash flows or dividends included. See also log return, holding period return, and total return.