Average Gain is a geometric average of the periods with a gain. It is calculated by compounding the returns for gain periods where rates of return are greater than or equal to 0 and then the monthly average is calculated.
Determine number of gain periods,
Average gain return,
If T1 > 0
Otherwise, AGR = N/A
Arithmetic average gain is defined as:
Annualized average gain return,
Annualized arithmetic average gain,
1 Considering the fact that we will compute these statistics for long period of time (10 years or more), and arithmetic average tends to overestimate the gain/loss, we will use geometric mean. Geometric mean is less affected by outliers, and if one believes that returns are reasonably approximated by a lognormal distribution, the geometric mean is also the median of the distribution.
2 Linking average gain return and average loss returns gets you to cumulative total return: (1+AGR)*(1+ALR)