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

- Someone is out of the market for 10 and only 10 days out of 2,520 trading days in 10 years; AND
- 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 * 10^{27}, or 2,796 followed by 24 zeros. A billion is 10^{9}. 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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