Tools · Volatility drag
The average return is not the return.
What an investment compounds at is always below the average of its yearly returns, and the gap widens with volatility. Two assets with the same average and different volatility do not end in the same place. This estimates the size of that gap.
Calculator
This page is showing a worked example. The figures below are for an average return of 8.0% a year with 20.0% volatility. Enable JavaScript to enter your own; the table, curve and method on this page do not need it.
- Average return
- 8.0%
- the arithmetic mean
- Drag
- 2.00%
- percentage points a year
- Compound rate
- 6.00%
- what it grows at
The drag rises with the square of volatility, so it is negligible at low volatility and dominates at high volatility. Doubling volatility quadruples the cost.
Reference
The cost of volatility.
The third column applies the drag to an average return of 8.0%, so it shows what the same average compounds at under each level of volatility.
| Volatility | Drag, a year | Compound rate from 8% |
|---|---|---|
| 5% | 0.13% | 7.88% |
| 10% | 0.50% | 7.50% |
| 15% | 1.12% | 6.88% |
| 20% | 2.00% | 6.00% |
| 25% | 3.12% | 4.88% |
| 30% | 4.50% | 3.50% |
| 40% | 8.00% | 0.00% |
This is the arithmetic behind a familiar observation: a steadier series with a lower average can finish ahead of a wilder series with a higher one. It is also why volatility is treated as a cost rather than only as discomfort.
Method
Where the gap comes from.
An approximation and an exact demonstration. Both say the same thing.
The approximation
compound ≈ average − σ² ÷ 2
The gap is about half the variance. At 20.0% volatility that is 2.00% a year, so an average of 8.0% compounds at roughly 6.00%. The approximation is exact for continuously compounded returns and close for ordinary ones; it loses accuracy at very high volatility.
The exact case
+50%, then −50% → −25%
The average of +50% and −50% is zero. The actual result is 1.5 × 0.5 = 0.75, a loss of a quarter. Nothing is lost to costs or timing: the gap is created entirely by the fact that a percentage gain and a percentage loss are measured against different bases. The same asymmetry drives drawdown recovery.
Limits
What this estimate assumes.
- It is an approximation. The σ² ÷ 2 term is a second-order expansion. At volatilities above about 40% the higher terms stop being negligible and the true drag is larger than shown.
- Volatility is treated as constant. Real volatility moves, and it tends to be highest in exactly the periods that do the most damage.
- The average must be an arithmetic average. Feeding a compound rate into this calculator and subtracting the drag again is a double count.
- It says nothing about which volatility is worth accepting. Volatility has a cost; so does avoiding it. This estimates one of them.
This calculator is provided for general information only and is directed to wholesale and professional investors. It is not personal advice: it does not take into account the objectives, financial situation or needs of any person, and it is not an offer, invitation or recommendation to acquire any financial product. Investing involves risk, including the possible loss of capital. Past performance is not a reliable indicator of future performance.
Definitions
Terms on this page.
Each links to the glossary entry, which states the convention the term assumes as well as what it means.
- Volatility drag — the gap between the average and the compound return.
- Arithmetic mean return — the simple average of the periods.
- Annualised return — the compound rate that actually accrued.
- Volatility — the dispersion the drag is a function of.
Questions
Common questions.
What is volatility drag?
The gap between the average of a series of returns and the rate at which the series actually compounds. It is roughly half the variance each year, so about 0.5 percentage points at 10% volatility and 2.0 points at 20%. It is arithmetic, not a cost charged by anyone.
Why is my CAGR lower than my average return?
Because a compound rate is a geometric mean and an average return is an arithmetic mean, and the geometric mean of a set of positive numbers is never above the arithmetic mean. The more spread out the numbers, the wider the gap. The two are equal only if every return is identical.
Does this mean lower volatility is always better?
It means volatility has a measurable cost that a headline average return hides. Whether accepting it is worthwhile depends on what is gained in exchange, which this page does not attempt to judge.
How exact is the half-variance rule?
Very close at the volatilities most portfolios run at, and increasingly approximate above about 40% a year, where it understates the drag. For an exact figure, compound the actual series rather than estimating from a mean and a volatility — the risk ratio calculator does that.