Volatility Drag Makes Smooth Returns Compound Faster

$10,000 up 50% is $15,000. Down 30% from there is $10,500. The average of those two years is a gain of 10%, which sounds healthy, and the account is up 5% over the pair, which works out to less than 2.5% a year. The gap between those figures is volatility drag.

Same average, different money

Take $10,000 and run it through three two-year paths, each with a simple average return of 10% a year. The only thing that differs is how far each year strays from that average.

Path	Year 1	Year 2	Average	Ending balance
Steady	+10%	+10%	10%	$12,100
Choppy	+30%	-10%	10%	$11,700
Wild	+50%	-30%	10%	$10,500

The last line is the one that surprises people. A path of +20% then -20% averages exactly zero, and it loses 4%. Losses and gains are percentages of different balances. The gain is measured on $10,000, the loss on $12,000, so the loss takes more dollars than the gain added.

Run it the other way and the asymmetry is plainer still. A 20% fall needs a 25% gain to get back to even. A 50% fall needs 100%.

Hold the average fixed, and the more the returns swing around it, the less money is left at the end, because every loss lands on a balance that the gain before it had just inflated.

The rough rule for the size of the drag

A standard approximation links the two figures. The compound return is roughly the average return minus half the variance of the returns, where variance is the average of each year’s squared distance from the mean. It is an approximation. It drifts as the swings get bigger.

Close for the choppy path. Off by almost half a point for the wild one. Use the rule to see the shape of the problem, and compound the actual returns when the answer matters. The volatility drag estimator does that for any sequence you type in.

The rule does say something useful even when it is off. Drag grows with the square of the swings. Double the distance from the mean and the drag roughly quadruples, which is why the choppy path loses a modest amount against the steady one and the wild path loses most of its gain.

The strongest objection: the volatile path may earn more

Nobody is offered two paths with identical averages. The volatile investment usually promises a higher average, and that is the reason to hold it.

Answer: compare compound figures, because an account balance is a compound figure. Take a fourth path of +60% then -30%. Its average is 15% a year, well above the steady path’s 10%. It ends at $10,000 x 1.60 x 0.70 = $11,200, which is $900 short of the steady path. The higher average bought a lower balance.

So the question to ask of any volatile holding is whether its average beats the steady alternative by more than half its variance. Sometimes it does. Often the pitch quotes the average.

Look for the other number. An annualized return over several years, the figure a fund fact sheet usually prints next to the calendar-year returns, is a compound figure: it is the steady yearly rate that would have produced the same ending balance, so it already has the drag baked in. Put the calendar-year returns in a column, take their simple average, and compare it with the annualized figure for the same period; the gap between the two is roughly what the swings cost, and a wide gap on a fund you are about to buy for its headline average tells you most of what you need to know.

Where the drag can be clawed back

Drag bites hardest on a single position, or on a portfolio that moves as one lump. Mix holdings that swing at different times and rebalance between them, and part of the drag comes back.

Two hypothetical funds each follow the wild path, one in the opposite order to the other. Fund A goes +50% then -30%. Fund B goes -30% then +50%. Held alone, each turns $10,000 into $10,500. Split $10,000 evenly between them and rebalance to 50/50 at the end of the first year, and each year the portfolio earns half of +50% plus half of -30%, which is +10%, and the two years together give $12,100, the steady path’s result from two wild ingredients.

Real holdings never cancel that neatly. The direction is right, though, and it is the case for rebalancing that the mise en place for money course builds on. The flip side is concentration: a portfolio dominated by a few names swings like those names, which is the point made in your index fund has a concentration problem too.

Smooth compounds faster, unless the average is much higher

For one position or one undiversified portfolio, a smoother path with the same average ends with more money. A volatile holding earns its place only if its extra average return clears the drag its swings create. Check that sum before you buy the swings.