Technically the markets have a slight upward trend, so their up-day probability is only slightly higher than 50%.

So we rearrange our likelihood distributions accordingly, and better understand our recent outcome taking this behavior into account (e.g., using the variance of a compounded Bernoulli distribution). We initially stated that having two up days out of the first seven trading days is a 28% probability, but in the illustration below we can see how our new Bayesian likelihood levels look. It shows that we are instead closer to being in a slight down-streak period, characterized by up-day probabilities closer to 40% (less than a fair 50% chance of an up-day).

In other words we are more likely to be tilted in a slight down-streak (about 39% likelihood of being in a 40% up-day probability phase) vs. being tilted in a slight up-streak (about 9% likelihood of being in a 60% up-day probability phase).

Whether we consider the 6% fair chance to see our YTD results from about a 60% up-day probability (as in the prior chart), or a 9% chance to see it from with Bayesian conditions (as in the chart below), both probabilities are too low to fit with any interpretation that 2014's YTD performance is just a continuation of last year's upward fast ride.


Recall that we said that there was a 16% chance of seeing the Dow Jones Industrials drop on five out of seven trading days, if we first assumed that each up-day probability was 50%. But per the chart above, if we see these five down days (out of seven trading days), we can see that we are more likely in a period that is not characterized with a daily 50/50 chance of going up or down.

So instead of a 30% likelihood for a down day in a case where we have a 50% up-day probability, we instead suggest that 2014's YTD performance shows a 39% likelihood of being in a down streak, with only about a 40% probability of being up on any given day.

This article represents the opinion of a contributor and not necessarily that of TheStreet or its editorial staff.

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