Definition
A time-average return is the geometric mean per-period return realized by an investment held continuously over many periods, equivalent to the time-average growth rate of the invested capital.
Why it matters
The time-average return is the figure that describes what compounding actually produces for an investor staying with one investment over a long horizon. Under the multiplicative dynamics that govern most financial assets, it is lower than the arithmetic average of the period returns, by an amount that grows with the variance of those returns. The gap between the two is sometimes called volatility drag, and it is the structural reason why advertised average returns can systematically overstate what a long-horizon investor experiences.
How it works
The time-average return is constructed by observing the period-by-period returns realized on a single invested position and computing the per-period rate that, compounded over the period count, reproduces the total realized growth. Equivalently, it is the geometric mean of the gross period returns minus one. The construction requires only one position and a long enough observation window; it does not require a population of parallel investments. Under multiplicative dynamics, the time-average return is mathematically less than the arithmetic mean of the same period returns whenever those returns vary — the gap is approximately one-half the variance of the period returns and is what is meant by volatility drag.
In practice
For an individual evaluating long-horizon investment outcomes, the time-average return is the figure that describes their own experience holding a single position through time. The simplest illustration is a position that gains 50% in one period and loses 50% in the next — the arithmetic mean of the two period returns is zero, but the time-average return is approximately negative 13.4% per period, because the compounded value is 0.5 × 1.5 × 1.0 = 0.75 after two periods. The same effect compresses the realized returns of any volatile asset relative to the simple average of its period returns, in a way that is structural rather than incidental. Asking whether a published average return is an arithmetic mean of period returns or a geometric (time-average) figure is the practical move that surfaces which one is being cited.
In the Longevity Standard Framework
Time-average return is the foundational formulation in ergodicity economics of the per-period growth rate that compounding actually produces for a single position over time, which under multiplicative dynamics is less than the ensemble-average return because of volatility drag. The Longevity Standard framework also uses the vocabulary in an applied actuarial-pooling context, where the focal observable is the surviving pool member's per-period income outcome and the relevant ordering can differ because mortality credits enter the survivor's path that do not enter the ensemble of all entrants.
Related terms
- Ensemble-average return
- Time average
- Ergodicity
- Geometric mean
- Volatility Drag
- Multiplicative dynamics
- Pooling multiplier
- Mortality credit