· 5 min read
Here is an investment: in year one it gains 50%, in year two it loses 50%. Its average annual return is (50% − 50%) ÷ 2 = 0%. Start with €100 and you end with €100 × 1.5 × 0.5 = €75. You lost a quarter of your money on an investment whose average return was zero.
The average yearly return is 0% the whole time; the money still shrinks by a quarter every two years.
That gap between the average return and what you actually earn is called volatility drag, and it affects every investment whose returns go up and down.
Arithmetic vs geometric return
The arithmetic mean adds up the yearly returns and divides by the number of years. It is the number most often quoted. The geometric mean, or compounded annual growth rate, is the constant yearly return that would have turned your starting amount into your final amount. It is the one that decides your wealth.
The two are equal only when returns never vary. As soon as they do, the geometric return is lower, because a loss needs a bigger gain to recover: after −50%, you need +100% just to get back to where you were.
How big is the drag?
A good rule of thumb: geometric return ≈ arithmetic return − (σ² ÷ 2), where σ is the volatility, the standard deviation of yearly returns, and σ² is σ × σ. At 20% volatility: 0.20 × 0.20 = 0.04, halved = 0.02, so the drag is 2 percentage points a year.
| Volatility (σ) | Drag (σ² ÷ 2) | Typical of |
|---|---|---|
| 10% | 0.5% a year | a balanced stock/bond mix |
| 15% | 1.1% a year | a broad global stock index |
| 20% | 2.0% a year | a single country or sector |
| 30% | 4.5% a year | a single stock |
σ² ÷ 2: doubling the volatility quadruples the drag.
So a stock market with a 7% average yearly return and 15% volatility compounds at only about 5.9% a year. Over 30 years, that difference alone is the gap between multiplying your money by about 7.6 and by about 5.5.
7% average yearly return, 15% volatility. The shaded wedge is what volatility drag takes over 30 years.
What this means for you
- Check which return you are being shown. Long-run "average returns" in marketing are often arithmetic. Plan with the compounded one.
- Lower volatility is worth something on its own. Two portfolios with the same average return do not end with the same wealth; the steadier one ends higher. This is one reason diversification helps: it cuts volatility more than it cuts the average return.
- Concentrated bets carry a hidden cost. A single stock with 30% volatility needs an average return about 3.4 percentage points higher than a broad index with 15% volatility just to compound as fast (4.5% − 1.1% of drag).
- Leverage multiplies the drag. Doubling exposure doubles volatility and quadruples σ².
The Compound Growth calculator shows the +50%/−50% example and lets you set your own average return and volatility to see the gap open up over time. To see how mixing assets that do not move together lowers volatility, and with it the drag, build an efficient frontier in the Portfolio Diversification calculator.
Run it with your own numbers
The figures above are one illustration. These calculators take yours: free, no sign-up, nothing you type leaves your browser.
Worked examples use round, illustrative numbers in today's money with real (after-inflation) rates. They are not advice for your situation; see the terms and the methodology.