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Wildebeest
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Wildebeest is a PhD MBA who invests primarily in resource stocks such as base metals, iron ore and coal.
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• ##### Planet Economics vs Planet Earth 4 comments
Apr 24, 2010 12:00 PM
Subtitle: Using only dividend data to calculate estimated returns

seekingalpha.com/article/199672-the-futu...

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.

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:

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• Very nice article and super graphics.

Another factor that you didn't mention is that the rates r and g are actually f(t). The use of current values (or estimated time averages) can lead to vast deviation from the real behavior of the function over time.
24 Apr 2010, 06:06 PM Reply Like
• Author’s reply » Yes agree John. There are lots of pitfalls to be aware of. r and g as f(t) is particularly relevant because these sorts of models that use constant growth in perpetuity require that growth be less than the greater economy otherwise the asset you value becomes the economy (in a mathematical sense over infinite time). That is important in the real world where company growth can be quite large over an investment horizon yet this formula, assuming people understand its origins, precludes you from using a big growth number -- well you're not precluded from using a big number but if you use a perpetuity growth number larger than economic growth you are effectively saying that the company will become the economy at some point.

Many other points that could be made but the bottom line is I think it is a bad way to calculate a rate of return.
24 Apr 2010, 06:24 PM Reply Like
• Econdoc
, contributor

Thanks for this but it is a strawman to quibble about the fallacy of a constant growth rate - surely it is true as there is no single growth rate that applies to all stocks. That is self evident but does not detract from the value of a simple and theoretically grounded rule of thumb to quickly determine an expected market based return.

Adding the two numbers as in the Gordon equation provides a quick reality check. Am I paying too much or am I getting a bargain on the market at this time. That's all this is supposed to be. But for most people - who would not be able to comprehend a DCF analysis or cost of capital or even get what a PE is it is a very accessible tool guide their investing and asset allocation decisions.

Using capitalization rates works very well in the real world as you say - if you have bought farmland or rental or commercial property you will know that this is the way it is done - in the real world.

Beest. You are very theoretical - that's nice but you need some scars on you to be credible. Take it from me. Sometimes you only need one point to draw a straight line. That is going to make someone like you feel very uncomfortable but that is the difference between an analyst and a businessman.

as always - you are welcome

E
1 May 2010, 06:31 PM Reply Like
• Author’s reply » As always you have no idea econodoc. If you'd read my comments to the article that prompted this article, it was *you* promoting a formula and me rejecting its use. i.e. you were the theory guy. This article was simply to show a mathematical justification for that rejection. There are also conceptual reason to reject the theory such as constant dividends and growth. ...but if you like it, and it works for you, knock yourself out.

Everyone should ideally be theoretical to the extent that they understand formulas -- even crackpot ones, understand the assumptions, can derive them etc. Being able to do the math doesn't mean you adhere to the theory. Quite the opposite actually.

The CAPM discussion, in which you also commented earlier today, is another example of a nice theory that is totally useless (here is the article link for anyone interested: seekingalpha.com/artic...).

you're welcome
1 May 2010, 07:16 PM Reply Like

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