Does Last Year's Change in the S&P500 Help Predict This Year's Return? Are Down Years Followed by Rising Ones?

Last year's change in the S&P 500 versus the next 12 month change, January, 1946-May, 2007*, n = 724:
		Last 12 months' change:		Next 12 months' change:
Percentiles:	n	From:	To:
Min-10%	73	-41.4%	-12.7%	12.2%
10-25%	109	-12.7%	-2.5%	11.6%
25-50%	180	-2.5%	9.4%	8.7%
50-75%	181	9.4%	20.1%	7.0%
75-90%	109	20.1%	28.8%	9.7%
90-Max	72	28.8%	53.4%	9.1%
		Correlation:		-.073
All:	724		Average:	8.4%

*Technically, this is until May, 2006, the last data point with next-12-month S&P 500 return data.

It's clear that the market's performance last year is only weakly and inversely correlated with its performance the next year. Very poor periods are followed by slightly above average periods. In the 10% of cases when the market fell 12.7% or more, it was followed by an above average 12.2% rise. Drops of 2.5% to 12.7% were followed by 11.6% average rises. Above average years (in this case, the 50% of times the market rose 9.4% or more), were followed by below average years, but not compellingly so (7.0% for the 50th-75th percentile, or 1.4% below the average year).

What is curious is that the strongest years are followed by above average years, indicating the market does seem to have some momentum: In the 15% of times the market rose between 20.1% and 28.8%, the market rose an average of 9.7%. Even the top decile (28.8% gains or greater) were followed by above average gains of 9.1%

This is perhaps why the correlation is so weak (only -.073) but it is slightly negative. This is also reflected in the linear regression formula:^[1]

Next year's S&P 500 change = -.072 times last year's change plus 9.3%, R2 = .5%

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^[1] Linear regression is really only valid when the data fall into a certain pattern, including a fit into a straight line. The very low R2 of .005 (values of 1 or -1 would indicate a perfect fit to a straight line) indicates using linear regression on this data series could give misleading results.