Define gains, losses and the return period
For observations r₁ through rₙ, let P = sum(max(rᵢ, 0)) and L = sum(max(-rᵢ, 0)). The net sum N = sum(rᵢ) = P - L. Gain-to-pain ratio = N/L when L > 0. Each observation has equal weight; zero returns add nothing to either sum. Using decimals or percentage points gives the same ratio if the scale is consistent.
- For monthly account returns without external cash flows, r = month-end equity / previous month-end equity - 1. Include the chosen treatment of open positions and costs in both valuations.
- Use consecutive, non-overlapping periods. Keep genuine zero-return months, resolve missing observations, and adjust deposits or withdrawals before treating equity changes as investment returns.
- If you choose trade-level dollar P&L instead, label the result as a trade-P&L GPR. Changing trade sizes means trade percentages and dollar outcomes need not produce the same ratio.
- Report the dates, frequency, number of observations, positive sum, loss sum and fee convention. The word net means positive observations minus negative observations here; it does not automatically prove that brokerage costs were included.