Technical Notes for ‘Why Stock Prices Are More Stretched than You Think”

(Here’s the article that goes with this appendix.)

Calculating earnings trendlines

To calculate today’s P/E multiple using an earnings trendline, I based the trendline on forty years of earnings data beginning January 1973 and ending December 2012.

Similarly, trendlines for the last two bull market peaks are each based on forty calendar years ending in the December prior to the year in which the peak occurred.

For the other bull market peaks, forty years of earnings data wasn’t available as of the peak. Therefore, I used time periods beginning in January 1950 (the inception of the data) and ending once again in the December prior to the year in which the peak occurred.

Here’s a chart showing annualized earnings alongside the nine trendlines that I calculated:

stock valuation 5

As you may have noticed, I used exponential rather than linear trendlines.  With the exception of the periods ending between the mid-1960s and late 1970s, when the trendlines bent upwards, the slopes haven’t changed all that much.  It’s worth noting, though, that price-to-trend-earnings multiples for the “exception” periods are slightly lower than they would be if the trendlines for those periods had more typical slopes.

Calculating deviations from earnings trendlines

To calculate percentage deviations between actual earnings and the respective trendlines at each bull market peak, I used the highest earnings deviation from any of the three months prior to the peak. Here are the results:

stock valuation 6

And here’s a chart with earnings deviations on the horizontal axis and trailing four quarter P/E ratios on the vertical axis (to show how much of the market’s valuation was explained by earnings deviating from the long-term trend and how much was explained by traditional P/E multiples):

stock valuation 7

Calculating P/E multiples

For the historical P/E multiples above and in the main article, I used the highest multiple from any of the three months prior to the peak. I did this partly because earnings are updated quarterly and also because company guidance helps market participants anticipate major earnings events as they occur but before they’re reported.

“Today’s” P/E multiples are based on the S&P 500’s July close of 1685.73 to be consistent with the month-end data that I used for the historic bull market peaks.

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