Geometric mean
The average that compounds correctly over time. For a series of returns it is the right summary; the arithmetic mean always overstates once returns vary.
Where you will meet it
Geometric mean appears in 4 learning outcomes on the CFA syllabus. A few of them:
- Work out an equity's price return and its total return
“Over several periods the returns are linked by compounding, multiplying (1 + r) for each period and subtracting one, not by adding them, and an annualised figure is the geometric mean of those period returns.”
- Explain what measures of central tendency show
“For returns compounded over time, the geometric mean is the correct summary; the arithmetic mean overstates realised performance whenever returns vary.”
- Set out how the main asset classes have performed historically in terms of risk and return
“The geometric mean, which is what an investor compounds, falls below the arithmetic mean by more the more volatile the asset.”
- Set out how an equity risk premium can be estimated from past data or from forward-looking inputs
“Historical estimates average past excess returns; the choice of arithmetic or geometric mean, the period and the benchmark all change the answer, and survivorship bias tends to push it up.”
Practise it
Practise geometric mean until it is automatic: questions that explain every wrong option.
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