Volatility drag: why volatility costs you return

In depth8 min read · 4 sources

Volatility drag describes a simple but often overlooked effect: if you experience +50% followed by −50%, you have not broken even but lost 25%. The more returns fluctuate, the further actual growth (the geometric mean) falls below the average of the individual returns (the arithmetic mean). Rule of thumb: the gap is about half the variance.

Two averages, two questions

The arithmetic mean is the simple average of the annual returns. It answers the question: what return should you expect for a single, random year? The geometric mean is the constant annual return that leads to the same final wealth, i.e. the CAGR. It answers the question: how fast has wealth actually grown?

The reason: gains and losses are applied to different amounts. The 50% loss hits wealth that has previously grown by 50%, and it eats up more than the gain. The larger the swings, the larger the effect: with ±10%, 99% is still left after two years; with ±50%, only 75%.

The rule of thumb: half the variance

The formula is an approximation that works well for small returns and normally distributed log returns. At 20% volatility, the drag is 0.2² / 2 = 2 percentage points; at 40%, it is already 8 percentage points. So it grows quadratically: double the volatility, four times the drag.

The table shows how strongly the drag grows with volatility. The values follow directly from the rule of thumb:

For bonds the effect is negligible, for broad equity portfolios it is noticeable, and for individual stocks, commodities or cryptocurrencies it is considerable. The “typical investment” column is only a rough guide; actual volatility depends on the period.

The diversification return

Something remarkable follows from the rule of thumb: a diversified portfolio can grow faster than any of its holdings. Diversification lowers volatility without lowering the arithmetic mean, and so it also lowers the volatility drag. Booth and Fama (1992) call the difference between the geometric growth of the portfolio and the weighted growth of the individual holdings the diversification return.

Willenbrock (2011) stresses this point: the return only arises if the portfolio is regularly reset to its target weights, i.e. winners are sold and losers are bought. Without rebalancing, the weights drift toward the better-performing investment, and the portfolio becomes less diversified over time. The stochastic portfolio theory of Fernholz and Shay (1982) describes the same mechanism in general terms: the growth rate of a portfolio exceeds the weighted average of its holdings' growth rates by an amount that arises from diversification.

For advanced readers: leverage, Kelly and log returns

Leveraged ETFs and daily resetting

Leveraged ETFs reset their leverage every day. In volatile markets without a trend, they therefore lose money even when the index ends up unchanged:

The Kelly criterion

With leverage f on an investment with excess return μ − r and volatility σ, wealth grows at approximately r + f × (μ − r) − f² × σ² / 2. The second term is the volatility drag of the leveraged portfolio. Growth is greatest at f* = (μ − r) / σ², the Kelly criterion; beyond that, the drag eats up more than the additional return brings in.

Log returns

If you work with logarithmic returns ln(1 + r), the arithmetic mean of the log returns is exactly the logarithm of geometric growth. The rule of thumb is then exact if log returns are normally distributed: the expected value of the simple return is half the variance above that of the log return. Samuelson (1971), however, warned against regarding maximizing the geometric mean as optimal for every investor and every horizon.

Mean and median of final wealth

Volatility drag also explains why forecasts of final wealth can differ so much depending on which metric is quoted. The average final wealth across many possible paths grows at the arithmetic mean. The typical final wealth (the median, exceeded by half of the paths) grows at the geometric mean.

The longer the horizon and the higher the volatility, the further the mean and median diverge. If you extrapolate with the arithmetic mean over decades, you therefore overestimate what a typical investor ends up with. Monte Carlo simulations show this directly: their median is below the value that an extrapolation with the average return gives.

What this means for investors

• Reading forecasts: when a study quotes an expected return, it usually means the arithmetic mean. For wealth growth over decades, the geometric mean is what counts, typically one to two percentage points less for equities.
• Volatility is not just a feeling: with the same average return, the calmer investment grows faster. This explains part of the low-volatility anomaly.
• Rebalancing pays off with uncorrelated investments: the diversification return is greatest when the investments have similarly high expected returns, fluctuate strongly and have low correlation.
• Be careful with leverage: leverage multiplies the arithmetic return linearly, but the drag quadratically.

An example of the last point: a portfolio with 15% volatility and a 7% average return grows by about 5.9% according to the rule of thumb. With double leverage financed at an interest rate of 2%, the average return rises to 12% and volatility to 30%, but growth only rises to about 12% − 4.5% = 7.5%. So the leverage brings a good one and a half percentage points instead of the hoped-for five, and with drawdowns twice as deep.

Limits of the rule of thumb

• Only an approximation: with very large fluctuations, skewness and fat tails, the actual geometric mean deviates from the formula.
• The diversification return is not a free lunch: it assumes that the investments have similar expected returns. If you mix a high-return investment with a low-return one, the portfolio may still grow more slowly than the stronger one alone.
• Costs: frequent rebalancing causes trading costs and taxes that reduce the return.

How Portfolio Lab calculates it

In the Backtest, the CAGR is the geometric mean: final wealth without inflows and outflows, expressed as a constant annual return over the years covered. Volatility is the standard deviation of period returns, annualized with √12 or √252. The Monte Carlo simulation shows the historical average return as an arithmetic mean (monthly mean × 12); your own return assumptions are also meant as arithmetic means. With a 7% return and 15% volatility, the simulated paths therefore grow at a median of only around 6% a year, i.e. roughly one percentage point less, as the rule of thumb 7% − 0.15² / 2 = 5.88% suggests. More on this in the metrics methodology.

This article explains a method; it is not investment or tax advice. Worked examples are simplified and rounded. All terms in the glossary.