CAGR for a decline and the recovery needed afterward
Keep annualized change separate from the percentage needed to recover a loss.
Method
CAGR = (ending value ÷ starting value)^(1 ÷ years) − 1. Use positive endpoints and a positive duration. It describes a smooth equivalent growth rate between two points, not the actual path. Additional deposits or withdrawals break a simple performance interpretation; the calculator does not adjust for their timing.
Worked example
A value falls from 10,000 to 8,000 over two years. CAGR = √0.8 − 1 ≈ −10.56% per year. The total loss is 20%. Recovering from 8,000 to 10,000 requires 2,000 ÷ 8,000 = 25%, not 20%, because the base has changed.
What to check
Do not average yearly percentage changes and label the answer CAGR. Keep dates, cash flows and fees explicit. A negative historical rate does not predict the future. If a starting value is zero, the ratio-based formula is undefined rather than a very large valid return.