Follow the money, not just the average
Start with £100. A 20% gain gives £120. A subsequent 20% loss takes away £24, leaving £96. The arithmetic average of +20% and −20% is zero, but the portfolio is down 4%.
Different questions need different averages
The arithmetic mean summarises an average period. The geometric mean describes the constant periodic rate that would reproduce compounded growth. Here it is √0.96 − 1, approximately −2.02% per period.
Check the assumptions
This illustration has no deposits, withdrawals, fees or taxes. It is not a forecast. When reading a return claim, ask which measure is used and which period it covers.
Continue with arithmetic returns, geometric returns and drawdown.
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