We've previously written that the only time we really ever get excited about what's going on in the stock market is when it changes by 2% or more from the previous day's closing value.
That threshold is based on our statistical study of the volatility of stock prices, where we found that the percentage change of the S&P 500 from one trading day to the next fit pretty neatly inside a normal distribution, where:
- 78.8% of all day-to-day percentage changes were within 1 standard deviations of the mean, about 10.6% higher than what would typically be expected for a perfect normal distribution.
- 95.3% of all day-to-day percentage changes were within 2 standard deviations of the mean, almost right in line with what would typically be expected for a perfect normal distribution.
- 98.6% of all day-to-day percentage changes were within 3 standard deviations of the mean, about 1.1% less that what would typically be expected for a perfect normal distribution, but still pretty close.
For bell curve fans, all those numbers mean two things:
- Small changes in stock prices are much more likely to occur than would be the case if their variation were the result of purely random factors.
- Big changes in stock prices from one day to the next are pretty unusual events.
So that brings us to yesterday, 1 September 2015, where for most of the day, stock prices were about 2-2.5% below where they had previously closed, before they suddenly dipped to be 3.5% lower before recovering to close at 3% lower in the last 37 minutes of trading.
And that was really pretty uninteresting because that final closing value would be exactly what our model of how stock prices work forecast it would be provided investors were setting stock prices according to the expectations they have for the current quarter, 2015-Q3.
Now, here's the thing about how our model works. What you see in our model as day to day variation for the alternative trajectories that stock prices are likely to take when investors are focused on a particular future quarter is based upon historic stock price data. We then factor in the change in the growth rate of dividends per share for each indicated future quarter for which we have dividend futures data, which you see as the vertical separation between the various trajectories.
For our standard model, for each day's forecast value, we use the historic stock prices that were recorded 13 months earlier, 12 months earlier and 1 month earlier as our base reference points from which we project future stock prices.
But in our rebaselined model, which we use when the historic price data for our standard model contains too much volatility to provide the most accurate forecast possible, we substitute the historic stock prices from different points in time and adjust our calculations accordingly. In forecasting each day of 2015-Q3 since 28 June 2015, we've been using the historic stock prices from 25 months earlier, 24 months earlier and 1 month earlier.
So when we see that today's stock prices are largely matching our forecast changes, as we basically have for all but three of the last 26 trading days, what we're seeing is that stock prices are directly echoing the events of 25 months ago, 24 months ago and 1 month ago.
Here's the multi-million dollar question: Why is that? We would only reasonably expect stock prices to fall somewhere within the range of values we forecast, where the actual trajectory of stock prices should be continually cutting across our forecast trajectories and the echoes of historic noise they capture, not paralleling them. Especially with the record levels of volatility that the market has shown recently.
But it's not, which would mean that other factors are at work. Our best guess is that those factors are somehow tied to options contracts and investments with two-year long maturities and expiration dates, where the confluence of interactions between investments initiated 25 months ago, 24 months ago and 1 month ago is compelling stock prices today to follow the course it is. Throw in a three-day long quantum shift in focus on the part of investors, and we have our recipe for explaining why stock prices have behaved as they have.
Or rather, why our model of how stock prices work has surprisingly managed to work as well as it has in the current stock market climate.
Labels: chaos, forecasting, SP 500
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Closing values for previous trading day.
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