When the SPX suffers a big first-day fall, how is the rest of the period affected?

So, 2016 got off to **a pretty horrid start** for stocks. The S&P 500 Index (SPX) was down over 2.5% on Monday before rallying back in the last half hour to end the day down 1.53%. Of course, not only was it the first day of the year, but it was also the first day of the quarter, the month, and the week.

Does the SPX's first-day performance mean anything at all? Is it some kind of omen? Obviously, it *shouldn't* mean anything. If any period can be predicted by its first trading day, then that would be quite an inefficiency in the stock market. However, this week I'll take a look at the numbers to see what has happened in the past.

**First Day of the Year:** To do the analysis, I went back to 1929 on the SPX. Then I simply looked at the first day of year and found how the rest of the year turned out (excluding that first day). I grouped the data by whether the first day was down by 1% or more (like this year), down by less than 1%, up by less than 1.25%, or up by more than 1.25%.

The table below shows that a big down day on the first day of the year has, in fact, been a bad omen for the rest of the year. When the SPX has fallen by at least 1% on the first day, the average return and percent positive for the rest of the year are much lower, compared to the other brackets. The standard deviation of returns is also much higher.

The sample sizes of the returns aren't big enough to make me think there's something to this, but it's something to note. The last year in which the SPX lost at least 1% on the first day of the year was 2008, when it was down 1.44%. The rest of the year, of course, was a disaster, with the index falling another 37.5%.

**First Day of the Quarter:** Well, the first day of the year data wasn't comforting; what about the first day of a quarter? Again, I looked at the first day of a quarter and found how the rest of the quarter did based on that day. The table below summarizes the results.

When the quarter starts with a drop of 1% or more, you again see some underperformance when it comes to average return -- but the median return is the highest, indicating some big negative returns. On the quarterly data, the rest-of-period percent positive and standard deviation when the first day is down big is more in line with typical results, unlike with the yearly data above.

**First Day of the Month:** The table below shows how the rest of the month does depending on the first day. Looking at the average return, it seems simple enough to say that if the first day is down, the rest of the month tends to underperform, and if the first day is up, it outperforms. However, it becomes more inconclusive when you consider the median and percent positive. The standard deviation of returns shows that, in the past, a big move on the first day indicated more volatility for the rest of the month.

**First Day of the Week:** Does the first day of the week say anything about the rest of the week? It's interesting that in this case, a big down day on the first day of the week has led to more gains for the rest of the week. A big down day of 1% or more on the first day of the week has seen the rest of the week average a gain of 0.49% and be positive 60% of the time. This is better than any of the other brackets.

**A Couple More Things:** Finally, as I was gathering this data, I found a couple more interesting things that aren't noted above. First, I have the standard deviations in the tables above, but for brevity I did not include the average positive and average negative. I found that in every single time frame above (yearly, quarterly, monthly, and weekly), when the first down day was down at least 1%, it led to the biggest average loss compared to any of the other brackets. Even in the weekly returns, where a big first down day led to the best returns on average, the average loss (that is, the average return when there is a loss) for the rest of the week was a loss of 2.35%.

The table below shows the average loss for the rest of the period in each of time frames discussed above. This would suggest the first day of the period being down big means an increased chance of a big loss.

Another thing I noticed which I found peculiar was that in the quarterly and monthly tables above you get roughly an equal number of first days going up by 1.25% or more as first days going down by 1% or more. Then, on the weekly table, you see only about half of the big up days compared to down days. I looked at historical data since 1929 and found that 8.3% of days saw the index gain at least 1.25%. However, the first day of a quarter gained that much 13.8% of the time. In other words, the first day of the quarter is 67% more likely to have a big up day (defined as a gain of at least 1.25%) as compared to any day.

Are there natural buyers on the first day of a quarter? I might look into that as the subject of a future article.