+10% in year 1, then −10% in year 2. Some people say the two-year return is 0%. Obviously (?), it isn’t.
Arithmetic returns compound by multiplying growth factors, not by adding period returns. Logarithmic returns do add over time - but reading a sum of logs as a wealth return is a different mistake, and it gets worse on long, volatile series.
A compact decision rule:
Do:
One period, wealth change → arithmetic return
Across time → log returns (they add)
Wealth from a sum of logs → exp(sum) − 1
Don’t:
Sum arithmetic returns across periods
Take cumulative products of (1 + log return)
I put the worked examples and the long-series gap in the short slide deck below.
