I did a little test to see if the past 5-year growth rate correlates with the "future" 5-year growth rate. Since I don't have access to the future data, I will use the earnings data from the past 10 years split into two parts. I have a list of stocks whose earnings I have looked at over the past few years. This is not a random sample by any means but should not be terribly biased. If there is any bias it might be that I typically look for companies with consistent results which might bias things in the direction of positive correlation.
Here is the list of tickers. There are 157 stocks. All have been pruned to have at least 9 years of data.
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For each of these I calculate the 5-year (annualized) growth rate of earnings in the most recent five year period (years 5 to 9) and in the more distant 5-year period (years 0-5). The growth rate is calculated by using all of the points and fitting an exponential curve to these points. I throw away growth rates greater than 50% or less than -50% to avoid have large numbers skew the averages.
Here are the results:
The mean annualized growth rate in the first 5-year period is M1=11.9% and the standard deviation is S1=15.2%.
The mean annualized growth rate in the second 5-year period is M2=13.9% and the standard deviation is S2=13.9%.
The Pearson correlation coefficient R is -0.0329.
R = 1/(N-1) * Sum_i (G1_i-M1)/S1 * (G2_i-M2)/S2
So there is a small (and probably negligible) NEGATIVE correlation. Thus, there is no evidence at all that the 5-year growth rate is useful in predicting the growth rate of the next five years.
This study does not claim to be conclusive by any means but it shows that if there is such correlation, it is not very strong.
See scatter plot below of the growth rates plotted versus one another. No correlation is apparent.