Lies, Damn Lies, And Statistics

From About the only certainty in the stock market is that, over the long haul, overperformance turns into underperformance and vice versa. Is there a pattern to this movement? Let’s apply some simple regression analysis to the question.

Here’s a chart of the S&P Composite stretching back to 1871. The chart shows real (inflation-adjusted) monthly averages of daily closes. We’re using a semi-log scale to equalise vertical distances for the same percentage change regardless of the index price range. The regression trendline drawn through the data clarifies the secular pattern of variance from the trend — those multi-year periods when the market trades above and below trend.

The Bearish View
The peak in 2000 marked an unprecedented 160% overshooting of the trend — double the overshoot in 1929. The index had been above trend for 17 years. It dipped about 6% below trend briefly in March, but at the end of August it had risen 22.6% above trend. The major troughs brought declines in excess of 50% below the trend. If the S&P 500 were sitting squarely on the regression, it would be hovering around 825. If the index should decline over the next year or two to a level comparable to previous major bottoms, it would fall to the vicinity of 400.

The Bullish Alternative
A critical factor for the reliability of a regression analysis of stock prices over many decades is the accuracy of the inflation adjustment. The Bureau of labour Statistics (BLS) has been actively tracking inflation since 1919 and has estimated inflation rates back to 1913 using data on food prices. In 1982, however, the BLS began incorporating changes to the Consumer Price Index (CPI), which is used to calculate inflation. These changes have resulted in much lower “official” inflation rates than would have been the case if the method of calculation had remained consistent.

At his website, Economist John Williams publishes an “Alternate CPI” employing the earlier BLS method. Here is a chart that illustrates the significant difference between these two calculation methods.

Now, let’s take another look at the S&P Composite, this time adjusted for inflation since 1982 using Williams’ Shadow Government Statistics. The change is astonishing. The adjustments to post-1982 data alter the slope of the regression that impacts the variance from the trend across the entire time frame, dramatically so in the last two decades. With this adjustment, the S&P 500 has been below trend since 2002. The current bear market low saw the monthly average index price drop to 56% below the trend, which puts us in the territory of those secular market troughs. The current price is about 42% below trend.

So the question is . . .
Are you bearish or bullish about the market? Or for us data drudges, which is more reliable: the Bureau of labour Statistics or

My opinion is that the optimum method for calculating consumer prices is somewhere between the revised BLS method and the historic method preserved by Williams. But for a long-term regression analysis, consistency is essential, which may lend some credibility to the alternate CPI chart as an indication of the current index price relative to previous troughs.

We generally avoid predictions at, but a future trough somewhere between the bearish and bullish view seems a reasonable expectation.

Check back next month for another update.

See more excellent charts and analysis at >

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