This Linear Regression Chart is Flashing Red

 30/6/2024.  Reversion to the Mean is an Actual Thing.  Check your Asset Allocation?  

Mean reversion is the theory that prices tend to return to their long run average, and that the more extreme a variation away from the average, the more likely it is they will revert.  In the case of long-term rising markets, a linear regression line (a ‘best fit’ straight line) can be used as the average.

In the charts linked to below, parallel lines are drawn at 2 standard deviations above and below the linear regression line giving a 4SD range.  In a normal distribution, less that 5% of data points would lie outside of these rails. 

Stock prices are not normally distributed of course, but the concept of a long-term trend has foundation, as global market capitalisation and stock prices tends to track growth of the global economy (naturally enough). 

The stock market is a forecasting machine, with prices instantaneously reflecting the opinion of thousands of market participants.  Noone ‘really knows’ what will happen next in the stock market of course, and result is that shorter term volatility is driven by emotion and sentiment, which from time to time is amplified by unexpected events.


Helpful Clues

Thus, a linear regression chart of a major stock index can give us helpful clues about how much prices are north or south of the long-term mean.  Awareness of these clues is not an attempt to time the market, but simply input to an investors decision making processes.  A key decision being the risk profile, i.e. to what degree are we prepared to accept volatility as the cost of long-term returns.  A common method of reflecting risk profile into a portfolio is choice of ratio between core equity and bonds.

In the same way that seasoned blackjack players will increase bet size when the deck is ‘tens rich’ (odds are more in their favour), investors might choose to be more aggressive when prices are in extreme drawdown.  

Similarly, after a major market run-up, if prices are significantly higher than the long-term mean, we might be more aware of a likely turn to the downside and check or adjust our bet (equity/bond ratio) accordingly.  (We don't leave the table.)


Coiled Spring

We can visualise extreme price movements as a spring being tightened.  The more tightly wound is the spring, the more likely it is that a financial news ‘surprise’ will trigger mean reversion, and the quicker it will be.  We also keep in mind that generally for major movements, prices often fall faster than they rise.


Examples of Helpful Clues

On 10th January 2019, the S&P500 was at 2596.  I posted the linear regression chart here: “S&P500 Ready for Huge Rebound Says Linear Regression Chart”.   By 27th December 2029, the index had was at 3240, a 25% rise.

On 27th December 2019, I posted “S&P500 Due for Correction, Says Linear Regression Chart”.  By 23rd March 2020, the index was at 2237, a 30% decline.  Of course, linear regression could not predict COVID, but note my comment above about news surprises more likely to trigger mean reversion at extremes.

On 27th January 2022, the S&P500 was 4451.  I posted “Markets are Reminding Us, No New Normal”, indicating a mean reversion downwards was likely.  By 12th October 2022, the S&P500 was 3577, a 20% decline. 

Updated Chart

I haven’t posted any linear regression charts subsequently, being overly absorbed in my research on benchmarking multi-asset portfolios, “Is Your Investment Manager Good Value”, which has been quite a rabbit hole.  (The downloadable paper is a terrific read.  In the old-fashioned sense of terrifying.)

But today, it’s time to post an updated linear regression chart.  Click image to enlarge.


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