Out of the Market and Meaningless Stats

The stock market had a field day last Thursday (7/12/2007). The Dow rose 284 points, its biggest point gain in nearly five years. It reminded me of the stats about the risk of being out of the market. It goes like if you missed the best X days in Y years in the stock market, your return would’ve been cut in half or something like that. Let me tell you those stats are meaningless.

There’s a chart like this in a recent issue of Schwab’s On Investing magazine (sorry, no online link):

It said the S&P 500 Index returned on average 8.4% a year between July 1, 1997 and June 30, 2006. Based on an average of 252 trading days a year, if someone missed the best 10 trading days in those 10 years, the return would’ve been only 3.4% a year. In dollars, 8.4% a year means $10,000 invested in 1997 would turn into $22,402 in June 2006, for a cumulative gain of 124%. If one missed the best 10 days, $10,000 in 1997 would only turn into $13,970 in 2006, or only a 40% cumulative gain. If someone missed the best 40 days, the return would’ve become -6.4%, which means $10,000 in 1997 would turn into $5,161, for a cumulative loss of 48%. Hmm … 124% gain or 40% gain, perhaps even a 48% loss, night and day, huh? Unbelievable.

These striking stats are used as arguments against market timing because they illustrate the risk of being out the market. Market timing means investing in the market when the conditions are considered favorable and getting out of the market when the conditions are considered as unfavorable. There are various schemes of market timing. Some are based on seasonality, some on chart shapes, some on valuation metrics. It is argued that if someone is out of the market for even a short period of time, 10 days or 40 days in the example above, and if they happen to be out on the wrong days (best X days in Y years), the long term return would suffer, a lot.

Although I haven’t double checked the statistics myself, I don’t doubt their accuracy. The stats are technically true however this piece of information is meaningless. Why? Let’s see what the stats really say. Being out of the market on the 10 best days in 10 years means that

  1. Someone is out of the market for 10 and only 10 days out of 2,520 trading days in 10 years; AND
  2. Those 10 days happen to be the best 10 days in 10 years.

If someone is going to be out of the market for 10 days, how likely is it that he/she will cherrypick 10 random days which in hindsight happen to be the best 10 days in 10 years? Very unlikely. How unlikely though? A math exercise will tell us.

The math formula for our calculation is called combination. We are calculating the number of ways you can choose 10 days from 2,520 trading days in 10 years. There is only one possible way those 10 days happen to be the 10 best days.

C(2520, 10) = 2520 * 2519 * 2518 * … * 2511 / 10! = 2.796E+27

You will need a scientific calculator for this. The ! symbol means factorial. If you use Excel, enter this formula and you will get the same result.

=COMBIN(2520,10) = 2.796E+27

The symbol E here represents scientific E notation. That’s 2.796 * 1027, or 2,796 followed by 24 zeros. A billion is 109. What we have here is that this unlucky market timer has one in 2.8 billion, billion, billion chance for missing the best 10 days in 10 years. In other words, IMPOSSIBLE. What about missing the best 40 days? Don’t even go there.

What’s the point of zeroing in on this impossible event? I don’t know. Shock and awe, perhaps. Nobody should care what happens if the chance of it happening is one in 2.8 billion billion billion. If some other one in 2.8 billion billion billion event happens to me, I will be a million times richer than Bill Gates and Warren Buffett combined. The meaningless stats don’t support effectively what they are supposed to prove. The really meaningful stats are those for the average or median impact to one’s long term return if someone is out of the market for 10 random days, or 10 random consecutive days, not the 10 best days. I’ve never seen stats for those scenarios. Perhaps because they don’t support what they are trying to tell you. My guess is that the average impact of being out of the market for 10 random days or 10 random consecutive days in 10 years is practically zero.

Does this mean it’s OK to time the market then? No, just the cited evidence doesn’t support the case. There are other valid reasons for not timing the market, but this 10 days out of 10 years thing isn’t one of them. At least one shouldn’t be too worried about being out of the market for a few days when they have a 401k rollover being moved from one place to another. Relax. It’s not a big deal as some make it out to be.

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  1. Ted Valentine says

    I think these statistics are useful to a point, and that point is don’t hold your money if you plan to invest it in the market.

    What if someone was holding cash in a MM waiting for the market, at or near all time highs, to go down before investing in a Roth IRA?

    Say they missed last Thursday. Will they ever get the opportunity to make that back? Maybe the more important question is when will that occur?

  2. Anonymous says

    Another slightly related query is “what is the return if someone avoided the 10 (40) worst days?” While the odds of that happening are similarly impossible, the tried and true scaremongering stats of the brokerage houses avoid answering the question about how market timing can reduce risks in some circumstances.

    I tend to look at it on somewhat of a 1:1 basis. If I miss the best day of performance but avoid the worst day of performance, will that make me happy? Stated differently, would I give up the biggest “up” day in return for avoiding the biggest “down” day? Absofreakinglutely.

  3. Harry Sit says

    I’m sure the return would be phenomenal if someone is able to avoid the 10 worst days in 10 years. But the chance for that is also one in 2.8 billion billion billion. Don’t even think about it. Nobody can do it.

    Because the stock market goes up over time, being out of the market usually means missing some average “up” days. I don’t think trying to predict the “down” days and jumping out is a useful strategy. If you have to be out because of an account transfer, I wouldn’t worry about it. But I also wouldn’t get out of the market intentionally.

  4. Harry Sit says

    Ted asked:

    Say they missed last Thursday. Will they ever get the opportunity to make that back? Maybe the more important question is when will that occur?

    Now we know the answer is yes and time for the wait is two weeks. Right now the Dow is trading at 13,472.84 down 312.23. That is below the 13,577.87 close on July 11, before the 284 points jump on July 12.

    All these just show that the market is volatile. Some days are up. Don’t get too excited. Some days are down. Don’t get too pessimistic. Ignore the noise.

  5. fivecentnickel.com says

    While you’re correct that this overstates the problem in that people won’t miss just the 10 best days of the market, you’re forgetting that the biggest days often come in the earliest stages of a recovery.

    For example, looking over the past 25 years, three of the 10 biggest days came in the week and a half following Black Monday, and two more of them occur in close succession at the very tail end of the dot bomb debacle. Thus, these days are concentrated into periods when people are especially likely to have bailed on the market and not gotten back in.

    Consider the scenario in which sometimes gets smacked on Black Monday, jumps out of the market to lick their wounds, and then immediately misses gains of 9.3%, 5.3% and 4.9%. They’ve now locked in a huge loss that they had little chance of avoiding in the first place, and they also missed out on a huge recovery.

    Calculating the probability that people will randomly miss the ten best days is a *huge* oversimplification, and it casts doubt on your entire argument.

  6. fivecentnickel.com says

    An additional point in response to anonymous… The deck is actually strongly stacked against missing the low days and being in on the high days. As I’ve already pointed out, the highest days typically come in the wake of (relatively) unforeseen negative events. The fraction of investors that sold out just before Black Monday is very small compared to the fraction that bailed amidst huge losses. Many were then out of the market for the biggest bounce. You can’t look at this in terms of pure random probability. You have to consider the correlation between down markets and up days, as well as the human tendency to bail during the former, missing out on the latter.

  7. Harry Sit says


    Thank you for your comments. If you think my calculation was a huge oversimplification, what do you think the realistic odds are for missing the 10 best days in 10 years and 25 years and how do you prove it?

    Please read my follow-up post: More On Missing the 10 Best Days.

  8. Nate says

    I agree with you that one shouldn’t let rollovers and administrative transfers worry investors simply because they don’t want to miss the best market days.

    However, while I may agree with your conclusion, I don’t necessarily agree with your method of arriving there. Like you, I think that the “10 best days” argument is a farce. I agree, that it would take the single most unlucky investor in the world to only miss those 10 days and it’s statistically unlikely to happen. But on the other hand, there is plenty of evidence to support Nickel’s claim that the best days most often occur during “bad” periods. Thus missing those days are not purely “random chance”. An investor IS statistically more likely to miss an up day as compared to other randomly chosen days. There is ample evidence to show that the average investor tends to bail out of the market at the tail end of a recession (where a major “up” day is statistically more likely to occur).

    I’ll also point out that the Financial Planning Association tackled your argument in one of their past publications. In short, they agreed (like I do) that it was unfair to only look at the 10 best days. In turn, they looked at both the best and the worst days. They discovered that almost all “best” days occurred within 90 days of a “worst” day and that 50% of the time they were no more than 12 days apart. The take away lesson was that a market timer is likely to miss both best and worst, if they miss any at all.

    The FPA’s final conclusions: 1) missing the best days was devastating to a portfolio, but unlikely to happen. 2) missing the worst days was amazingly beneficial but equally unlikely. 3) missing both the best and the worst days resulted in performance almost identical to a buy and hold strategy EXCEPT the buy and hold required considerable less time, effort, research, and anxiety. Plus the timing strategy would entail transaction costs and (potentially) taxes that would result in a lower NET portfolio value.

    And I’d like to add that just because Nickel can’t (or hasn’t) offered a better solution doesn’t lend any additional credibility to your solution. Suppose, for example, that you made the claim that aspirin could cure all cancers. I don’t have to provide an alternative cure of my own to prove that your claim is false. There’s plenty of evidence that aspirin doesn’t cure cancer. If Nickel’s only contribution is to make people think more critically about your proposal, then I say it is still a worthwhile post and shouldn’t be dismissed simply because it doesn’t offer an alternative solution. I interpreted your response to be “if you can’t provide a better method, keep your mouth shut”. If I misinterpreted, I apologize in advance.

  9. Harry Sit says

    @Nate – I wrote this some time ago and I had to re-read it to see if I was disrespectful to any reader. I don’t see it. Nickel and I are friends now. I hope you read my followup post linked in the previous comment, which takes a closer look at the best up days near the market bottoms. My argument is that there is enough margin of error in the math. Even if you take into account people’s propensity to panic when the market is down and that best days are near market bottoms, and you up the odds by a factor of a billion, the odds are still lower than winning the powerball lottery. It doesn’t change the conclusion that these best 10 days stats are meaningless, which I think you agree.

  10. jmg says

    I like a few others agree with your conclusion that the 10 day stat is a little like cherry picking, but I believe your argument is based on a misunderstanding. Nobody is claiming that you can only miss 10 days and they have to be the best days for the stats to be correct. I’m sure we can all agree that someone who is habitually timing the market will more then likely be out for a whole lot more then 10 days. Every day that they are out of the market increases the odds that they will miss a substantial jump.

    Further, it is a wide known fact that most investors fail to follow the basic idea of buy low and sell high. It seems that most panic and sell when the market is low, and then buy when the market is high. Why would they do this? The most logical conclusion I have heard is that they have fallen victim to timing the market. They feel comfortable buying when the stock is doing well, but not comfortable with their position when the stock price is struggling. This creates a natural phenomenon in which investors trying to beat the market end up losing.. bad.

    To conclude, I would agree that the stats can be misleading, but I would not call them meaningless. I would compare them to analogies used to demonstrate points. Using them should fall under the same category as saying you can buy EVERY graduating high school student in the country a brand new Porsche for the next 4 years 14 times over to demonstrate how large our debt is. No one would do that, but yet it is still valid.

    As someone who has worked with the public I know first hand that the majority of people respond better to stories that they can visualize. In this manner these stats give people a tool to better inform people of SMART investing strategy in a way that they can easily understand and embrace.

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