Probably not. I mean let’s settle down here and assume that no dividend streak could go on forever. Even if a company were to perpetually stay in business, some adverse event out of their control, is sure to happen. Something that throws their profitability so off-kilter that it is in their best interest to freeze, reduce or even suspend the dividend. There are companies that have been around in one form or another for over a hundred years. Even a few hundred years. Suppose for a moment, there is a publicly traded company who has increased their dividend every year for 50 years. What would be a realistic expectation of how many more years they could keep the streak alive? If you knew nothing about the company’s past and absolutely zero insight into the future, what would your best guess be? Might it be another 50 years?
That seems as good a guess as any. After all, if a company just raised their dividend for the 50th year in a row, it says they’re capable of a 50-year streak. Who better to go another 50 years? It would seem a bit ridiculous to make that same guess if they were just coming off a 5-year streak. It might even seem equally ludicrous to suggest that they’re only good for another 5 years. Have I convinced you that, barring any other information, going another 50 years is the best, most realistic estimate one could make?
The Lindy Effect
Such a guess would in fact be consistent with a phenomenon called the Lindy Effect. It basically states that ‘the future life expectancy of some non-perishable things, like a technology or an idea, is proportional to their current age’. Obviously, this doesn’t apply to a human being. We shouldn’t expect an 80-yr old, to live another 80 years. But it isn’t a stretch to suggest that well-managed businesses could persist and exhibit such an effect. The story of how this idea became known as the Lindy Effect is an odd one and worth a read, but the mathematical justification for it is a bit more appealing to me. On the same wiki page in the link above, there is a very nice example in lay terms provided by Nassim Nicholas Taleb, perhaps best known for writing The Black Swan: The Impact of the Highly Improbable.
If a book has been in print for forty years, I can expect it to be in print for another forty years. But, and that is the main difference, if it survives another decade, then it will be expected to be in print another fifty years. This, simply, as a rule, tells you why things that have been around for a long time are not “aging” like persons, but “aging” in reverse. Every year that passes without extinction doubles the additional life expectancy. This is an indicator of some robustness. The robustness of an item is proportional to its life!
Arabica or Robusta?
In coffee you want Arabica. Maybe if you’re having espresso, you’ll come to appreciate at least a little Robusta in a blend (like only the Italians can pull off), but never in a single origin roast. But people, in a stock? Robustness! This is what we want to invest our money in. We want robust companies. A Dividend King has exhibited a certain ability to weather recessions, setbacks, increased competition, etc. They are robust.
Now, when I chose ‘Building a Portfolio for the Ages’ for a tagline, I had multiple meanings for ‘ages’ in mind. On the one hand, I thought it would be entirely possible to build a portfolio that could stand the test of time. It would consist of great companies, one would buy and hold, ideally, forever. But also, I thought such a portfolio would be appropriate for all ages. You could be a kid looking to routinely save half of your lawn cutting money or a retiree who is looking to deposit a nest egg into some strong income stocks. Fifty more years of increasing dividends suits everybody just fine. And such lofty expectations can only reasonably be applied to robust, shareholder-friendly businesses who’ve already established they have what it takes.
Until now I have been dancing around what you’re really interested in Dear Reader. And the wiki page for the Lindy Effect doesn’t go into all the detail you’re thirsty for. You’re really interested in the mathematical development of this. The nitty gritty.
Vilfredo Federico Damaso Pareto
Vilfedo Federico Damaso Pareto, born Wilfried Fritz Pareto on July 15, 1848, at some point in adulthood looked like this:
The hair, the beard, the intensity of his eyes. These are not even the most impressive things about him. You can read all about him, but let me ask? Have you ever heard of the 80/20 rule? It is also referred to as the Pareto Principle. It comes from his study of how wealth was distributed among a population. 80% of the wealth was controlled by 20% of the population. [I think wealth in our day, in the USA at least, has become much more skewed, but the 80/20 rule does seem to come up in other areas of life.]
Apparently, some things in this world can best be modeled using the Pareto distribution, which is technically a whole family of distributions, named after that handsome gentleman, above. The probability density function has a couple of parameters in it and one can play around with legitimate choices for those parameters and see how they change the distribution.
Where Pareto Meets Lindy
The probability density function is defined as
I have to simplify. Otherwise, I get cranky. The (necessarily) positive constant, xm, is the smallest value x can take, since there is zero probability of x being any lower than that. Now, if a stock pays a dividend and aims to start a streak, well then, we have to have at least 1 annual increase. Thus, for us, the smallest dividend streak is technically ‘1’. So, let’s say xm=1.
Folks, we need to pick a value for the shape parameter, α. I backed into the appropriate value so you wouldn’t have to waste precious time. Let α=2. It’s the blue curve in the chart above.
Assume X represents the total, final length of a dividend increase streak in years just after it comes to an end and likewise, that x0 is the streak so far to date. Then X-x0 is the years remaining in this streak. And if we believe a company’s dividend streak is to behave like only Vilfredo Pareto could imagine, then the expression E[X-x0|X>x0] is the expected value of the number of years remaining in a dividend streak given the streak is already x0 years long.
Obviously that expression is equal to x0. I kid. I used to enjoy when mathematics texts referred to something I couldn’t see right off the bat as obvious. But yes, E[X-x0|X>x0] = x0. Read as ‘we expect the number of years remaining in a dividend streak to be equal to the number of years already achieved’. This is my rudimentary work-up and, holy cow, my ability to integrate is nearly gone.
