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Planet Economics vs Planet Earth

Subtitle: Using only dividend data to calculate estimated returns

I've been involved in a back and forth in the comments section of this article:

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 re-written 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.

Click to enlarge

Here is a video to get a better idea of the gap between real world and textbook:

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