Two retirees each start with €500,000 and take out €25,000 a year. Over ten years they earn exactly the same ten annual returns, just in a different order.
One ends with about €572,000. The other ends with about €337,000.
Same returns, same average, same withdrawals, and a €235,000 difference. This tutorial explains why, building on the asset allocation and time value of money articles.
Quick check. An index rises 10% one day and falls 10% the next. Where is it after two days?
Most people say "back where it started". It isn't. The answer is below.
Part 1: volatility drag
In the quick check, €100 becomes €110, then €99. Two moves of the same size leave you 1% down. Losses are taken from a bigger base than the gains were added to.
Over many periods this becomes volatility drag, which Richard Messmore called "variance drain" in 1995:
compound return ≈ average return − σ² ÷ 2
The drag grows with the square of volatility (σ):
| Annual volatility | Drag per year |
|---|---|
| 10% | ≈ 0.5 points |
| 20% | ≈ 2.0 points |
| 30% | ≈ 4.5 points |
| 60% | ≈ 18 points |
Double the volatility and you quadruple the drag. That is why a calm portfolio with a slightly lower average return can end up richer than a wild one with a higher average.
Part 2: sequence risk
Without withdrawals, order doesn't matter: multiplication is commutative. Both of our retirees would have about €810,000 if they withdrew nothing.
Withdrawals change everything. A loss early on hits a large balance, and the money you take out at the bottom is gone before the recovery comes.
| Ten annual returns (average 5.8%) | End balance after €25,000 a year |
|---|---|
| Best years first | ≈ €572,000 |
| Worst years first | ≈ €337,000 |
This is sequence-of-returns risk. It is why the years just before and after you start living off your money matter most, and part of why William Bengen's famous 4% rule was built from the worst historical sequences, not the average.
What helps:
- A cash buffer of one to two years of spending, so you don't sell assets after a crash.
- Lower volatility in the years around the switch from saving to spending.
- Flexible withdrawals: spend a little less after bad years.
Part 3: why daily leveraged funds decay
Leveraged ETFs promise 2× or 3× the daily return of an index. Over longer periods, volatility drag works against them twice as hard.
Take the index from the quick check: +10%, then −10%, repeated 20 times (40 days):
- Index: 1.10 × 0.90 = 0.99 per pair, so after 40 days it is down about 18%.
- 2× daily fund: 1.20 × 0.80 = 0.96 per pair, so after 40 days it is down about 56%.
The index lost 18%. The 2× fund lost more than three times as much, not twice. In choppy, sideways markets, daily-leveraged products bleed value even when the index ends near where it started. In strong, steady trends they can do better than 2×. They are built for short holding periods, not for buy and hold.
The principle
Volatility is not just discomfort. It is a cost, and it is paid in compound returns. Reduce it where you can, size volatile positions small, and protect the years when you start withdrawing.
Your checklist
- Estimate your portfolio's volatility and work out its drag: σ² ÷ 2.
- If you hold one very volatile asset, check how much of the total swing it causes.
- Planning to live off your portfolio within 5 years? Plan a cash buffer.
- If you hold a leveraged ETF, read how it rebalances (daily?) and how long you intend to hold it.
Answer to the quick check
Down 1%. €100 → €110 → €99.
Sources
- Messmore, T. (1995). Variance Drain. Journal of Portfolio Management, 21(4), 104–110. Link
- Bengen, W. P. (1994). Determining Withdrawal Rates Using Historical Data. Journal of Financial Planning, 7(4), 171–180. Link
Educational content, not financial advice. Nothing here recommends any product, including leveraged ETFs. Return sequences are illustrations. Investing carries the risk of loss.