If you want to know where stock prices are going to go next, you need to know three things:

1. What stock prices are today.
2. What the expectations are for the amount of dividends that will be paid out in future quarters today.
3. How far into the future investors are focusing when they make their investment decisions today.

If you know those three things, you have a decent shot at being able to predict the future trajectory of stock prices, assuming that no unusual amounts of speculative noise are at work in the stock market.

The first two are not hard to figure out. You can easily look up stock prices and also the values of the dividend futures contracts that will give you an indication of what dividends that investors reasonably expect will be paid out in future quarters. You can even uses contemporary news reports to identify how far forward in time investors are focusing their attention.

But the holy grail of being able to tell exactly where stock prices are going to go in advance of their getting there is being able to tell in advance when investors are going to suddenly shift their forward-looking focus from one point of time in the future to another. The occurrence of those kinds of events are quintessentially random in nature, and when they happen, they are often associated with sudden and very large movements in stock prices. Instead of just pacing along a garden variety random walk, they suddenly erupt into a full Lévy flight, or as we've come to understand them, a quantum random walk.

When they happen, they are a sight to behold. Last Friday's Brexit event provided an excellent case study for such an event, where investors appear to have shifted their attention from the distant time horizon of somewhere between 2017-Q1 and 2017-Q2 to the much nearer term future of 2016-Q4, with U.S. stock prices following along accordingly.

In the animated image above, we're showing the trajectory of the S&P 500 in the period from 7 April 2016 through 24 June 2016, with respect to the alternate levels it might be based upon the historic value of stock prices and the expectations for dividends in future quarters. [If you're reading this article on a site that republishes our RSS news feed and the animation doesn't play, you may want to click through to our site to see the original animation. For it to play, you will need to use a modern web browser with JavaScript enabled].

Every time you see the lines move in this animation, you're seeing the effect of the changing expectations for the future. When you see a sudden shift in the value of stock prices, you're seeing the effects of investors changing their time horizon in making their current day investment decisions in response to the random onset of market moving news events.

The Brexit event isn't the only dramatic example of this factor that directly drives the volatility of stock prices at work that we can present. It was also clearly apparent 10 months earlier, during China's August 2015 stock market meltdown - here's our animation of that event.

Not uncoincidentally, the Brexit event represents the most the U.S. stock market has declined in a single day since the China event 10 months earlier. And in truth, the reason it wasn't bigger is because there is less of a difference in the expectations for future dividends between the respective future quarters that investors shifted their attention from and the future quarters they shifted their focus toward.

Update 27 June 2016, 6:00 PM EDT: And now, investors are looking more intently at the defacto current quarter of 2016-Q3....

Having already mentioned market moving news events, here are the headlines that caught our attention in Week 4 of June 2016 - the week when the Brexit vote caused investors to reel in their forward-looking attention to a less distant point of time in the future.

Monday, 20 June 2016

• Oil up 3 percent as Brexit chances dim; gasoline surges too
• Wall Street ends higher as Britain seen staying in EU

Tuesday, 21 June 2016

• Fed cautious on rates due to Brexit, U.S. hiring slowdown: Yellen
• Wall St. ticks up on economy bets; Brexit fear ebbs

Wednesday, 22 June 2016

• Fed's Powell says 'ready for whatever happens' in Brexit vote
• Healthcare stocks boost Wall Street
• Wall Street flat, all eyes on Brexit vote - the S&P 500 closed lower by 3.45 points. Last week, Reuters had the headline "Wall Street falls as Brexit vote becomes major fear, which saw the S&P 500 fall by 3.74. We had some more to say on this topic in a Thursday post last week, which we updated on Friday morning after the big news broke, before U.S. markets opened....

Thursday, 23 June 2016

• U.S. jobless claims, factory data point to firming economy
• Wall St. rallies on bets Britain will stay in the EU

Friday, 24 June 2016

• Traders weight chance of Fed cutting U.S. rates after Brexit - later saw the following related headlines: Fed says ready to provide dollar liquidity after British vote, then U.S. jobs, UK vote prompted rate-hike delay for Fed's George: MNI, and also Brexit vote means Fed stays put. The current consensus is that the Fed won't act to hike short term U.S. interest rates until December 2016 (2016-Q4) at the earliest, which matches what we see in our animated 2016-Q2 chart above.
• Brexit vote triggers shock, silence but market chaos averted
• Meanwhile, in the U.S., Wall St. slumps as Brexit takes investors by surprise. - No, really?!
• Oil prices plunge 5 percent as Britain votes to leave EU

Events like last Friday's are why we make a point of keeping track of certain contemporary news stories.

Previously on Political Calculations

• Emerging Order in the Stock Market - 12 June 2008
• Acceleration, Amplification and Shifting Time - 10 December 2008
• The Math Behind How Stock Prices Work - 23 April 2009
• Playing the S&P 500's Wild Cards - 6 May 2013
• S&P 500: Odds Suggest Schrödinger's Cat Is Three Quarters Dead - 3 September 2013
• Completing a Quantum Shift in Future Expectations - 30 January 2014
• A Better Frame of Reference, Mean Reversion and the S&P 500 - 18 March 2014
• Taking the Fork in the S&P 500's Future - 1 August 2014
• Quantifying Stock Price Volatility - 13 July 2015
• Decoherent Expectations and the S&P 500 - 22 June 2015
• What We Do, Explained by Others - 6 July 2015
• Order Breaks Down in S&P 500, As Expected - 21 August 2015
• Quantum Random Walks and the S&P 500 - 31 August 2015