Out of the Market and Meaningless Stats
July 16, 2007 by TFBThe 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 * 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.
Related Posts:
Related Posts:- Avoiding the Worst Days and Missing the Best Days
- Carnival of Personal Finance #110
- More On Missing The 10 Best Days
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?
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.
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.
I never seen any statistics what happens if you missed 10/40 worst days on market.
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.
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.
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.
Nickel,
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.