Monday, July 21, 2008

Growth and reversion to the mean

Here is an update of the previous post on whether a high 5-year growth rate predicts the next 5-year growth rate. The answer is still No but now with more statistical significance.

I have collected more data. Now I am using every stock on the NYSE, NASDAQ and AMEX.

I require that there is 10 years of data and that in each 5-year period, there is at most one year with earnings data not available or earnings that are negative. If earnings are negative (or unavailable) that one year, I ignore it and fit the growth rate to the remaining four data points. So there is a slight bias towards higher growth rates but this bias is the same in both periods so this should not cause any correlation. Growth rates above 50% or less than -50% are discarded. The results are insensitive to increasing this number 50% to 80%.

There are 2206 stocks that meet these requirements. Here is the result. (Click for higher resolution)

The top panel just shows the last 5-year growth rate versus the growth rate 5-years previously. As before there appears to be little if any correlation. The red dashed lines show the median growth for each period which is 10.5% for the last five years and 7.1% the five years before that. This higher growth in the latest period is probably real and is expected since the period 1998 to 2002, the internet bubble, went from a boom period to a recessionary one and the last five years 2003-2008 included the recovery and housing bubble. It looks like we are now going into another recessionary period due to the housing bust. The Pearson's correlation coefficient is -0.0953. This slight negative correlation is explained below.

The lower panel is even more informative. The stocks are sorted by the growth rate in the previous period and divided into 19 percentile groups. That is, each group has equal number of stocks and has similar previous 5-year growth rate. For each group, I calculate the median of the previous 5-year growth rates and the corresponding median of the last 5-year growth rates. These two median growth rates are plotted versus one another with error bars indicating the error due to having a finite sample. Clearly, there is no indication that the median growth rate in the next period has anything to do with the median growth rate in the previous one. The blue line shows the y=x relation that would be expected if the best predictor of future growth rate was the past growth rate. Clearly this is NOT a good fit to the data. The red horizontal line just shows the median growth rate in the last 5-year period. This fits the data points quite well. This would indicate that the hypothesis that "Future growth rates are independent of past growth rates" is consistent with the data. There is one deviant point which has the lowest growth rate in the previous period and in fact the highest growth rate in the more recent period. I haven't yet looked into this in detail but these may be highly cyclical companies such as oil, energy etc. This point probably is the cause of the slightly negative Pearson's correlation coefficient.

Overall, this study points toward mean reversion. Companies that are growing at higher or lower than average rates will most likely revert to average growth rates in the future.

The application to investing also seems to support the "value investing" method rather than the "growth method" at least in their simplest incarnations. That is, stocks that have grown rapidly and (usually) sport a high valuation on earning probably will not grow any faster than the stocks that have grown only slowly or even had negative growth. So paying a higher valuation for "growth stocks" does not appear to be logical. I will investigate this in more detail in future posts.