Unexpectedly Intriguing!
February 5, 2009

Forecasting the Road AheadHow well can our Price Dividend Growth Ratio, the ratio of the year-over-year growth rate of stock prices to the year-over-year growth rate of dividends per share, predict when the stock market will hit a bottom?

That's the question we're tackling today, as we first hinted over at Econbrowser that January 2009 may well represent the bottom of the current decline in stock prices, at least as measured by the average of each month's daily closing prices for the S&P 500.

Previously, we indicated that this particular measure was a particularly good indicator of both market distress and recessions in the U.S., but we had only presented data spanning the modern era of the the stock market, since January 1952, and limited it to just coincide with the largest spikes in the value of the ratio coinciding with recessions.

Today, we're expanding our frontier to include all our trailing year data for the S&P 500, covering some 1,645 datapoints spanning each rolling one-year period since January 1871. The chart below reveals our calculated value for the Price Dividend Growth Ratio from January 1872 through January 2009:

S&P 500 Trailing Year Price Dividend Growth Ratio, January 1871 through January 2009

Note: We've arbitrarily capped the extreme values of the Price Dividend Growth Ratio in the chart above at +125 for positive values and at -125 for negative values. These very large spikes coincide with periods in which the denominator of the trailing year compound annualized growth rate of the S&P 500's dividends per share was equal to zero, which would otherwise result in a spike of infinite value.

We next counted up all the spikes in the Price Dividend Growth Ratio, broadly defined as the absolute value for a given month being greater than the absolute value of the ratio for both the month preceding the spike in value and the month following the spike in value. We used a similar broad definition of a market bottom, in this case counting every occurrence of a month whose average monthly S&P 500 index value was lower than that for the months both preceding the trough and following the trough.

Overall, we counted some 322 spikes in the absolute value of the Price Dividend Growth Ratio and 323 troughs in the average monthly index value of the S&P 500.

We next identified the number of times that a spike in the Price-Dividend Growth Ratio coincided exactly with a trough in the value of the S&P 500. For good measure, we also found the number of times that such a spike occurred within one month of a market trough, as well as the number of times that such a spike occurred within two months of a market trough. Our results are presented in the table below:

Coincidence of Price Dividend Growth Rate Spikes with Market Troughs
Data Item Number of Occurrences Percentage of Total
Total Number of Spikes 322 100.0%
Number of Spikes Exactly Coinciding with Trough 78 24.2%
Number of Spikes Within One Month of Trough 192 59.6%
Number of Spikes Within Two Months of Trough 257 79.8%

In basing our prediction that January 2009 will in fact mark the bottom of the current decline of the stock market, we do so by noting that this month very likely coincides with the trailing year compound growth rate of the S&P 500's dividends per share's crossing the zero line from a positive to a negative value. By mathematical definition, this will produce a spike in the Price Dividend growth ratio, which as we've shown above, represents a 24.2% probability that January 2009 will in fact mark the bottom of the market.

What can we say? We like those odds! And in the worst case, it would mean that there's a 60% chance that we're within one month of the trough and an 80% chance that we're within two months. Speaking of which, here's our chart showing the rebounds of stock prices following some of the worst bear markets in U.S. history.

Update 6 February 2009: We should have thought of this yesterday, but if we subtract out the 24.2% of the troughs occurring in the same month as a Price-Dividend Growth Ratio spike from the 59.6% of stock price troughs occurring within one month of a spike, and noting that it can't be December 2008 because stock prices were higher then than in January 2009, we find that the odds that February 2009 will mark the bottom of the current decline stock market to be 35.4%.

We like those odds more!

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