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Planet Economics vs Planet Earth
I've been involved in a back and forth in the comments section of this article:
seekingalpha.com/article/199672thefutu...
It is my contention that in the real world you cannot estimate a return by adding dividend yield to dividend growth. In the comments to the article, in response to a comment in which a formula was produced, I explained that the formula doesn't work in the real world. More details of the formula can be found here. Mathematically the infinite series can be rewritten as:
The assumptions are that r > g , that r and g are both constant, and that g is less than economic growth. If you're wondering about the third assumption it is there because if you have a perpetuity growth number that exceeds economic growth you are saying that the asset being valued will eventually become the entire economy. The value that the series converges to (right hand side of the arrow) can be used to derive the formula cited in the article comments.
However this series converges very slowly for typical values of r and g. The smaller the difference between r and g, i.e. the smaller the dividend yield, the slower the convergence. What this means is that for typical investment horizons the formula that is derived by summing all terms to infinity is nothing like what you get in practice  and after all it is the real world that we live in  i.e. it doesn't even constitute a good approximation.
Here is a plot to show you what I mean. A 3D plot of real rate of return vs number of years. The orange surface is what you get using the simplified textbook formula and the green surface shows the real world. We can see that in the real world the surfaces are not very close to each other (understatement) due to the infinite series converging very slowly. The calculations where made using a real dividend growth of 1.3% which is the number cited by one of the adherents to this model in the comment stream. I note that no error estimate accompanied this number.
Here is a video to get a better idea of the gap between real world and textbook:
www.screencast.com/t/MWZlM2U0YzQt
As a result of the textbook situation bearing no resemblance to the real world, I maintain that the use of the formula to calculate a rate of return is a crock, useless, a waste of time, and so on.

For those interested, for an expansion over a finite number of years ( y years) the formula is:
which means that the theoretical relationship between rate of return, dividend yield, and dividend growth, is actually:
Disclosure: not relevant
Interpreting Economic Data
In the figure below I have some underlying L shaped data and below it the MOM and YOY changes in the data.
The shaded region marked "A" is where those pundits inclined to bullishness would typically be pointing to the MOM or YOY data as indicating a recovery. Yet when an economy has been in decline, the first signs of MOM or YOY upturns simply indicate a lessening of worseness as we clearly see in the underlying data. It is mathematically impossible for underlying data to "bottom out" without this "V" shape in the MOM and YOY data. Even when the "V" shape in the MOM and YOY data is complete (region marked "B") this is still not indicating a recovery, it merely indicates a bottoming of the underlying data has been reached.
An example of this type of data, complete with erroneous conclusions, can be found here:
In the next example there is some underlying data which recovers after a downturn. Region "A" is the same as in the previous chart: i.e. less worse underlying data producing "V" shaped MOM and YOY data.
In the region where the underlying data is actually recovering (not highlighted but evident in the chart) we see positive numbers in the MOM and YOY data. As the underlying data approaches a full recovery, region "C", the MOM and YOY data begins to decline. The decline in the MOM and YOY data is not bad news, it just means the rate of change in the data is decreasing as the underlying recovers to the reach the values prior to the decline. Mathematically the chart must exhibit this shape.
An example of this type of data can be found here (Note that I've been unable to find the original article that is referenced in this link). The article contains this chart which plots 3 sets of difference data:
The reason I chose this chart is that commentary seemed to be rather concerned about the downward trend in the lines. The change in the leading indicator and the change in the coincident indicator in the chart indicate that the underlying leading and coincident indicators suffered a drop but have now nearly recovered to the values prior to the drop. The declines, with values remaining positive, are not bad news, they are a mathematical artifact of the type of chart being used. The third line in the plot is some kind of diffusion index which seems to be substantially more volatile than the other two lines. There is no "underlying" for diffusion indices. They are difference data to begin with, and rescaled so that 50 is analogous to zero on MOM and YOY charts. This index has headed below 50. Despite the lack of an underlying set of data, diffusion indices should be interpreted in the same way as MOM and/or YOY difference charts. A fall below zero in coming months for the two difference indicator lines would indicate a downturn. How you react to a fall below 50 for the diffusion index depends on what is known about that index. Given the data displayed in the chart, this "lurch" below 50 could simply be another example of the wild volatility of this index. Certainly more information is needed before drawing any conclusions.
At some point, maybe not for quite some time the way this "recovery" is shaping, lots of MOM and YOY economic data we see will start to exhibit this "region C". What's the bet that this is accompanied by some hand wringing and concerns from pundits. When those concerns eventuate they will be just as unfounded as the exuberance we see about the "V" shaped signals in current and recent data.
What I hope readers take out of this is that "V" shapes in difference charts, i.e. charts showing MOM or YOY data, that occur following a period of decline, don't necessarily equate to a recovery in the underlying data. If the "V" is in the negative half of the chart, or below 50 in diffusion indexes, then it simply corresponds to a period of decreasing worseness. It is best to consider both MOM or YOY difference charts sidebyside with their underlying data before drawing conclusions.
Disclosure: no positions
Derivatives and Differences of Time Series
If you were to take the derivative or difference (MOM or YOY) if it you'd end up with something like this:
This curve/data appears to be declining and may cause alarm ...but is that what it is saying? No. It is saying that the underlying time series has recovered.
I'll add more to this post when I get time (it was hastily prepared to comment on this article: seekingalpha.com/article/193626ischina...). In the meantime this article fleshes out some further thoughts on caution when interpreting difference time series.
seekingalpha.com/article/190348debunkin...
Disclosure: no positions