As Goes Yesterday?

Note: Please read the disclaimer. The author is not providing professional investing advice.

Shortly after finishing the previous research and article on the validity of the so-called January Rule (see As Goes January?), I was left with a similar question.

What, if anything, does the market’s performance yesterday say about what it will do today?

After all, just as some investors can be bullish on the rest of the year after an up January, it’s not uncommon to find oneself bullish on the market today after it closed up yesterday (and vice versa).

Well… Yahoo! Finance has all the historical data there for the picking. I thought I’d run a little simulation to see.

Now we know that, historically, the market has tended to go up. Therefore we can guess right off the bat that we’d be better off putting our money on the hypothesis that the market will rise today, regardless of what it did yesterday.

But does yesterday’s performance give us any further indication? Let’s compute 3 probabilities using the historical data.

1. The probability that the market closes even or higher than it opened on any given day, or

Prob(Close ≥ Open)

2. The probability that the market closes even or higher than it opened TODAY given that it closed higher than it opened YESTERDAY, or

Prob(Close ≥ Today | Close ≥ Open Yesterday)

3. The probability that the market closes even or higher than it opened TODAY given that it closed lower than it opened YESTERDAY, or

Prob(Close ≥ Open Today | Close < Open Yesterday)

Note: for “The Market”, I’m using the S&P 500 (Yahoo Ticker: ^GSPC).

Results depend upon what time frame one computes said statistics over. Here’s a graph showing the above 3 probabilities, computed over time frames spanning from the last 1 year to the last 40 years.

cond_prob_web.jpg

Let me first draw your attention to the black dashed line. That’s the probability that the market closes at the same or higher price that it opened, on any given day, regardless of what the market did yesterday.

No matter what time frame we simulate over (last 1 year to last 40 years), we would have always been better off assuming the market closed even or higher than it opened. Yes, on average it’s only slightly higher than 50/50, but still enough to give you 25 more wins than losses if you bet 1000 times.

What about the red and blue curves? They’re a bit more difficult to interpret.

If we look back 40 years… if the market closed down yesterday, there was only a 50/50 chance it would close even or up today.

Likewise, if the market closed up yesterday, we had roughly a 55/45 chance that the market would also close up today.

But oddly enough – examining the graph – a switch occured starting about 27 years ago.

Since then, the fact that the market closed down yesterday has been, more often than not, an indication that it will close up today!

And to be fair I should point out that as we follow the curves further to the left on the X-axis, we’re getting into territory where we have fewer and fewer samples in our set – meaning more uncertainty in the data.

So, what can you actually do with these 3 probabilities? Well I’m not really sure the conditional probabilities (#2 and #3) are useful given the switch-a-roo that happened 27 years ago.

But similar to our conclusion concerning the January Rule, probability #1 shows that, historically, regardless of what the market did yesterday, the smart money is on the market closing even or up today. 😉