Mark Hulbert wrote recently for Market Watch on the Dow's sustained run and its statistical significance.  He argues correctly that, given the historical rarity of probabilistically equivalent runs, few conclusions can be drawn with much certainty.  I decided to loosen the analysis up to a few other metrics in order to better evaluate the Dow's past performance and typical behavior.

    First, I've taken the Dow's adjusted close and, for every day since 1928, given the number 1 to days on which the index rose, and the number 0 to days on which the index was unchanged or fell.  Though some may question lumping unchanged and fall together, interest accumulates daily, and long margin outweighs short margin, so I think unchanged counts more as loss.

    First, you find that the Dow has had more up days than down, as a quick look at the 79 year chart will hint.  To be precise though, there have been 9,472 down/unchanged days and 10,260 up days, for a ratio of 1.08 up days to every down.  Fascinatingly, if you treat this as an annual interest growth factor before inflation, you get the following calculation: Initial Dow Index  * (Ratio of Up-to-Down Days - Average Rate of Inflation)^Time = Current Dow Index, where the initial adjusted Dow index is 240.01, the average rate of inflation is about 3%, and time is 78.6 years.  Remember that this analysis does not take into account the magnitude of change at all - a 0.01 point gain is the same as a 200 point gain in an indicator variable's eyes. 

    Next, I take the moving average of this indicator variable time series.  The moving average at each day now represents the percentage of the last N days that were up, and 1 minus this number represents the percentage of down and unchanged days. 

    First off, a 200-session moving average of the Dow's entire history.  I've labeled some of the maximums to give you the exact date and percentage for comparison.  You'll also probably want to click the thumbnail image to see the detail.  Note that there have been a considerable number of times the Dow has approached and even passed 60% here.

    Next is the 50-session moving average.  Since this is so noisy, I've restricted the graph from 1990 to last Thursday.  Again, I've labeled maximums with dates and values, as well as a minimum in this case, and again, you'll probably want to click through the image to see the details.

     Next, I took the 25-session moving average.  This was too noisy to show any reasonable interval, so I've instead generated a histogram.

    Currently the Dow is running up at 88% of the last 25 days.  This distribution has a mean of 51.97%, with a standard deviation of 10.29%, meaning that we're currently at mean plus three-and-a-half standard deviations.  This of course ignores the skew and kurtosis of the distribution, but as they seem slight enough that this measure is still meaningful.  Above 3.5 sigma, you'd expect about 0.02% of the distribution, and given that the Dow has had 19,733 sessions, you'd expect to see between 4 and 5 such sessions.  Currently, we have had 3 sessions at or above , so in some technically incorrect sense, we've actually had fewer sessions than we should have.

    For comparison, here is the same distribution of the 200 session average.  In this case, however, we're only running at 60% near mean plus two standard deviations.

    At last, I've taken these moving averages of percentages and calculated their actual correlation to the return over a following N sessions.  In this case, I've taken the symmetric case where the number of sessions for the moving average is equal to the number of sessions for the following return.  As the table summarizes, it looks like there is a reasonably positive correlation between the percentage of days up and the return. 

    So all in all, based on this analysis, it seems as if the Dow is still in uncertain territory.  Though it's a frightening height for the 25-session average, the 200 average is still well below 5% of all sessions.  Furthermore, given the positive weakness of the correlation, it's near impossible to statistically predict the Dow's next move with much accuracy, and, given the end of earnings season, there's definitely dynamics to be played out in the coming sessions that are not typically present in the market.

    All that said, I personally have position in the DXD, a double-inverse Dow tracker.  Though I don't subscribe to terribly bearish sentiments right now, it's cheap as far as market insurance policies go, and requires a lot less effort than managing your own puts.  As is usual with these things, only time will tell which camp was right.