Swedroe: Madness And Dividends

March 07, 2014

The Math Of Cash Dividends Vs. Homemade Dividends

To demonstrate the point that the two are equivalent, we’ll consider two companies that are identical in all respects but one: Company A pays a dividend and Company B does not.

To simplify the math, we’ll assume that the stocks of both companies trade at their book values (while stocks don’t always do that, the findings would be the same regardless).

The two companies have a beginning book value of $10. They both earn $2 a share. Company A pays a $1 dividend, while Company B pays none. An investor in A owns 10,000 shares and takes the $10,000 dividend to meet his spending requirements. At the end of year one, the book value of Company A will be $11 (beginning value of $10 + $2 earnings - $1 dividend). The investor will have an asset allocation of $110,000 in stock ($11 x 10,000 shares) and $10,000 in cash for a total of $120,000.

Now let’s look at the investor in Company B. Since the book value of B is now $12 ($10 beginning book value + $2 earnings), his asset allocation is $120,000 in stock and $0 in cash. He must sell shares to generate the $10,000 he needs to meet his spending needs. So he sells 833 shares and generates $9,996. With the sale, he now has just 9,167 shares. However, those shares are $12, so his asset allocation is $110,004 in stock and $9,996 in cash, virtually identical to that of the investor in Company A.

Another way to show the two are equivalent is to consider the investor in A, who, instead of spending the dividend, he reinvests it. With the stock now at $11, his $10,000 dividend allows him to purchase 909.09 shares. Thus, he now has 10,909.09 shares. With the stock at $11, his asset allocation is the same as the asset allocation of the investor in B; namely, $120,000 in stock.

It’s important to understand that Company B now has a somewhat higher expected growth in earnings because it has more capital to invest. The higher expected earnings offset the lesser number of shares owned, with the assumption being that the company will earn its cost of capital.

There’s one more issue that should help to clarify why dividend-based strategies are not optimal.

The Explanatory Power Of Dividends

For the past 20 years, the workhorse model in finance has been what is generally referred to as the Fama-French four-factor model—the four factors being beta, size, value and momentum. The model explains the vast majority—more than 90 percent—of the differences in returns of diversified portfolios.

If dividends played an important role in determining returns, then the four-factor model wouldn’t work as well as it does, since dividends are not one of the factors. If, in fact, dividends added explanatory power beyond those of these factors, we would have a factor model that included dividends as one of the factors. But we don’t.

The reason is that stocks with the same “loading,” or exposure, to the four factors have the same expected return regardless of their dividend policy. This has important implications because about 60 percent of U.S. stocks and about 40 percent of international stocks don’t pay dividends.

Thus, any screen that includes dividends results in portfolios that are far less diversified than they could be if dividends were not included in the portfolio design. Less diversified portfolios are less efficient because they have a higher potential dispersion of returns without any compensation in the form of higher expected returns, assuming, of course that the exposures to the factors are the same.

 


 

Larry Swedroe is director of Research for the BAM Alliance, which is part of St. Louis-based Buckingham Asset Management.

 

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