Volatility drag estimator

Average return and compound return

The average return adds up the period returns and divides by how many there are. The compound return is the single rate that, applied every period, turns the starting amount into the ending amount: multiply one plus each return together, take the root for the number of periods, and subtract one. The second figure is always the smaller of the two unless every period is identical, and the difference is volatility drag. It grows with the size of the swings. A quick estimate is half the variance of the returns, which the working shows beside the exact number, and the viewpoint that smooth returns compound faster argues what that means for choosing between two strategies with the same average.

A worked example on the defaults

$10,000 gains 30% and then loses 10%. The average of those two returns is 10%. The money went to $13,000, then lost $1,300, and ended at $11,700. Growing at a steady 10% twice would have given $12,100, $400 more. The rate that really turns $10,000 into $11,700 over two periods is 8.17%, so the drag is 1.83 percentage points a period. The matched case is harsher. Gain 20% and lose 20% and you finish 4% down, $9,600 from $10,000, on an average return of exactly zero. So a run of big up and down years can average a respectable figure while the account barely moves. The same arithmetic, seen from the bottom of a fall, is the reason a drawdown needs a larger gain than the loss to get back to where it started, as the losing streak calculator shows.

Where the numbers get quoted loosely

A fund's or a backtest's "average annual return" can mean either figure, and the difference is large for anything volatile. An annualized return over several years is the compound one. On a screener, the performance columns show the change over each window, and reading those columns means knowing that two stocks up the same amount over a year may have taken very different paths. In backtest output, look for the compound annual growth rate next to the average trade, and read the drawdown alongside both, as the lesson on reading backtest results explains. The estimator ignores fees, taxes and money added or withdrawn along the way, all of which change what you actually end up with.