Compounding
Growth in which each period's return is earned on the balance left by all the previous periods, so gains and losses multiply rather than add.
Final = Start × (1 + r₁)(1 + r₂)…(1 + rₙ)
Compounding means returns build on each other. A 10% gain on 10,000 makes 11,000; another 10% makes 12,100, not 12,000, because the second gain applies to the larger balance. Losses compound the same way, which is why recovering from a drawdown takes a larger percentage gain than the loss itself: a 20% loss needs a 25% gain to get back to even.
In code, an equity curve compounds daily returns with a cumulative product: start * (1 + returns).cumprod(). Adding the returns instead describes an account that withdraws every profit and tops up every loss each day.
Compounding also explains why volatility costs money. Two return series with the same average simple return end at different values if one swings more: the more volatile one compounds to less. Multi-year growth rates are usually quoted as compound annual rates for this reason.
On the desk
Starting with 10,000, a gain of 20% followed by a loss of 20% leaves 10,000 × 1.20 × 0.80 = 9,600. The average return is zero, but the account is down 4%.