Each missed day removes a multiplier on the whole balance, which is why ten days out of twenty years can take more than a third of the result.
Missing the best days costs far more than their number suggests, because each one multiplies everything that follows. On an illustrative 10,000 invested for 20 years at 8.0 per cent a year, sitting out only the ten best days, 0.20 per cent of the 5,040 trading days, cuts the result from 46,610 to 28,614, a loss of 38.6 per cent, and the annual return from 8.0 to 5.40 per cent. Missing the thirty best leaves 15,094.
Worked in full in Stock Market Investing for Beginners by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The "missing the best days" chart is one of the most quoted pictures in investing, usually drawn from a real index over a real period. The figures below are not market data. They use round, illustrative assumptions so that every step can be checked by hand, and so that the mechanism, which does not depend on the period chosen, is visible.
| Input | Value |
|---|---|
| Amount invested at the start | 10,000 |
| Holding period | 20 years |
| Trading days a year | 252 |
| Trading days in the period | 5,040 |
| Annual return of the index, dividends reinvested | 8.0% |
| Average gain of the 10 best days | 5.0% |
| Average gain of best days 11 to 20 | 3.5% |
| Average gain of best days 21 to 30 | 3.0% |
| Average loss of the 10 worst days | −5.5% |
Each day in a band is treated as gaining exactly the band average, which keeps the arithmetic checkable; with real, uneven daily gains the factor removed is slightly smaller for the same average. The investor who misses a day is assumed to be in cash that day and to earn nothing on it. At an illustrative 3.0 per cent cash rate, ten days out of the market earn about 0.12 per cent, which changes none of the conclusions.
Final value = start × (1 + annual return)years = 10,000 × 1.0820 = 46,610, a multiple of 4.66 and a gain of 36,610.
Excel: =10000*(1+8%)^20
Returns compound by multiplication, so the order of the days does not matter. The fully invested result already contains the ten best days as a factor of 1.0510 = 1.6289. Dividing it out gives the value of the same 20 years without them:
Final value without the 10 best days = 46,610 / 1.6289 = 28,614
Excel: =10000*1.08^20/1.05^10
Annual return = (final value / start)1/years − 1 = (28,614 / 10,000)1/20 − 1 = 5.40 per cent.
Excel: =(28614/10000)^(1/20)-1
| Days missed | Factor removed | Final value | Annual return | Lost vs fully invested |
|---|---|---|---|---|
| None | 1.0000 | 46,610 | 8.00% | 0.0% |
| Best 10 | 1.6289 | 28,614 | 5.40% | 38.6% |
| Best 20 | 2.2977 | 20,285 | 3.60% | 56.5% |
| Best 30 | 3.0879 | 15,094 | 2.08% | 67.6% |
Ten days out of 5,040 take 17,995 off the final value. Measured on the gain rather than the total, the investor who misses them keeps only 50.8 per cent of what the market paid. Missing thirty days, 0.60 per cent of the period, leaves 13.9 per cent of the gain, and an annual return of 2.08 per cent, below the illustrative cash rate.
The loss grows faster than the number of days missed because each removed day is a multiplier on the whole balance, not an addition to it. A 5.0 per cent day on a large balance late in the period is worth as much as a 5.0 per cent day early on: the percentage is the same, and so is the share of final wealth it carries.
| Average gain of the 10 best days | Final value | Annual return | Lost |
|---|---|---|---|
| 4.0% | 31,488 | 5.90% | 32.4% |
| 5.0% | 28,614 | 5.40% | 38.6% |
| 6.0% | 26,027 | 4.90% | 44.2% |
| Horizon | Fully invested | Missing 10 best | Annual return missing them | Lost |
|---|---|---|---|---|
| 10 years | 21,589 | 13,254 | 2.86% | 38.6% |
| 20 years | 46,610 | 28,614 | 5.40% | 38.6% |
| 30 years | 100,627 | 61,776 | 6.26% | 38.6% |
The second table holds a lesson that the usual chart hides. The share of final wealth lost, 38.6 per cent, is the same whatever the horizon: it is fixed by the factor removed, 1 − 1 / 1.6289. What changes is how that loss shows up in the annual return. Over 10 years it takes the return from 8.0 to 2.86 per cent; over 30 years only to 6.26 per cent. A chart quoted as "annual return" over a long period makes the damage look smaller than it is.
The worst days matter just as much in the other direction. Missing the ten worst days, at an average of −5.5 per cent, would turn 10,000 into 82,065, an annual return of 11.10 per cent. Missing both the ten best and the ten worst gives 50,381, or 8.42 per cent, slightly better than staying invested. Taken literally, the arithmetic says that a good enough market timer wins.
The reason that does not help in practice is that the largest rises and falls tend to arrive close together, in the same volatile weeks. The investor who sells after a run of bad days has usually already taken the worst of them and then sits out the rebound. That investor does not get the 50,381 line. He gets the 28,614 line: all the bad days, minus the best ones. That asymmetry, not the size of any single day, is what the chart is really about.
A second error is to compare the 5.40 per cent with the average daily return times the days in a year. Daily returns compound, and the gap between an average and a compound rate is the subject of why CAGR is lower than the average return. The same multiplication explains why a loss needs a larger gain to recover.
The compounding behind these figures, worked for regular monthly saving rather than a lump sum, is in the free workbook for this book.
Not in wealth. Missing ten best days of 5.0 per cent each removes a factor of 1.6289, so final wealth is 38.6 per cent lower whether the horizon is 10, 20 or 30 years. Only the annual return looks less damaged over long periods: on an illustrative 8.0 per cent market it falls to 2.86 per cent over 10 years but to 6.26 per cent over 30.
Then the arithmetic favours the timer: missing the ten best and the ten worst days in the illustration gives 50,381 against 46,610 fully invested. In practice the largest falls and rises arrive in the same volatile weeks, so an investor who sells after the falls usually keeps the bad days and misses the rebound, ending with 28,614 instead.
Take the fully invested final value and divide it by the product of one plus each missed day's return. With 10,000 at 8.0 per cent for 20 years and ten days of 5.0 per cent, =10000*1.08^20/1.05^10 gives 28,614. The annual return is then =(28614/10000)^(1/20)-1, or 5.40 per cent.
This article is one calculation from Stock Market Investing for Beginners. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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