In this three-part blog post, I started by articulating the case that dividends are a special form of return because they can be predicted more accurately than price appreciation. Research supports this. In addition, I provided links to research from the finance literature that explains why estimation risk, the uncertainty in prediction, is so important. The high number of responses to this first piece raised a number of follow-on topics that I started to explore in Part 2.

Even after the first two parts, there was still a lot of debate over some basic questions. Part 1 has 530 comments and Part 2 has 238. Much of the commentary is a back-and-forth argument.

In this post, Part 3, I am returning to the primary issue raised in Part 1. Dividends matter because they are the component of return that can best be predicted. For some reason, that point seems to have gotten lost or perhaps not fully understood by many readers. So, I am going to try to explain this point in more detail.

## The Four-Factor View of the World

In the "total return" world view, dividends provide no forward guidance in selecting investments. As advisor and columnist Larry Swedroe recently asserted in comments to one of my posts on dividend investing: "It's not that dividends are good or bad - they don't matter - it's the other factors that do." When Mr. Swedroe refers to the "factors that matter," he is working from the paradigm of Eugene Fama and Ken French in which the returns from a portfolio are explained via four explanatory variables:

1) Market risk, as measured by beta

2) Small cap tilt

3) Value tilt

4) Momentum

The assumption that the return from a portfolio can best be explained by these factors is called the "four-factor model." Market risk is straightforward. Higher beta means more market risk and a portfolio with more market risk is expected to earn higher returns than the market portfolio (an S&P 500 or total market index). Fama and French also showed that a portfolio loaded with smaller firms than the market portfolio has historically provided additional return. Similarly, a portfolio in which the average price-to-book and price-to-earnings values of the holdings are lower than that of market portfolio has historically delivered higher returns than the market portfolio. In a later addition to the model, it has been found that a portfolio of stocks that have recently outperformed is somewhat predictive of future out-performance (the momentum factor).

When Mr. Swedroe and other advocates of the four-factor world view say that dividends don't matter, what they mean is that adding dividend yield as an additional factor in this model does not improve the explanatory power of the model. This is, however, not a conclusion that is really supported by the data. The dividend yield of a portfolio is closely related to its value tilt. Higher-yielding portfolios also tend to have a substantial value tilt. The fact that adding dividend yield to a statistical model that already includes a value factor does not add explanatory value is not shocking. The value factor should encompass high dividend stocks as well as stocks that have simply been beaten down and have low P/E values or low P/B. Value portfolios also capture some of the additional returns provided by low-beta stocks that are inconsistent with the four-factor model. In other words, the "value" factor includes a range of properties of stocks that have historically been predictive of higher returns. This does not, however, mean that this factor somehow renders the properties that it encompasses meaningless in and of themselves. In other words, the four-factor model is a great model but that does not mean that it is a perfect model or that the model somehow explains away that important properties of stocks that it captures.

It is also important to really grasp that the four-factor model does not tell us anything about estimation risk of the various components of returns that are rolled up into the "value" factor. And this, I assert, is very important.

## Another Way to Decompose Returns

Rather than breaking returns up into performance factors as in the four-factor model, we might start an analysis of returns by looking at more of a simple mathematical breakdown of the components of returns in terms of their most basic expression. A research paper from Research Affiliates from 2012 provides the following chart:

This paper makes the straightforward point that total return of equities is the sum of:

1) Changes in the P/E ratio

2) Inflation

3) Increases in the Earnings-Per-Share (EPS growth)

4) Dividend yield

The chart above shows the average contribution of these factors to total return, as well as their standard deviation. The higher the standard deviation, the more volatile that component of returns is. Note that dividends have historically exhibited a very low standard deviation and a large contribution to total return. The lower volatility of dividends demonstrates that the dividend component of return tends to be very persistent through time.

This is a form of the so-called Gordon equation. The beauty of this approach is that it is so straightforward. The way that you get real return (return net of inflation) from a portfolio of stocks is from dividends, price gains relative to earnings, or earnings growth. This is essentially inarguable. If this is not clear, please read William Bernstein's essays on this. John Bogle also espouses this way of looking at returns.

Using Bogle's terminology, there are two fundamental elements of return and one speculative element. Dividends and earnings growth are fundamental - they reflect what is really happening. The speculative element of return is increases or decreases in the P/E ratio. An increase in the P/E ratio means that investors are willing to pay more for a dollar of earnings based on some projection about the future. They are betting that future investors will be willing to pay more for this dollar of earnings than they did or they are betting on some type of future growth that will boost earnings.

Earnings growth may be a fundamental measure of stock investments, but it is notoriously hard to forecast. For this reason, there is a high level of estimation risk in this component of returns. Likewise, P/E expansion is volatile and thus will also be hard to forecast over any given time period.

Now, here is the crucially important point. If value stocks generate higher returns and these higher returns are not due to dividends, the excess return must come from either earnings growth or P/E expansion. These two latter variables are historically very volatile and thus must be quite hard to predict.

## Introducing Estimation Risk

What is ignored in all of the discussion of factor models such as the Fama-French formulation and its variants is that investors do not simply get to sample from history. Investors need to make predictions about expected returns in the future. These implicit predictions have considerable uncertainty. In what is one of the most important papers that I am aware of in finance in recent years, *Are Stocks Really Less Volatile in the Long Run*, Lubos Pastor and Robert Stambaugh introduced the issue of estimation risk into the asset allocation debate. This paper has garnered awards and considerable recognition in academic finance, but its implications have been somewhat slow to catch on.

The Pastor and Stambaugh (P&S) paper makes the following common sense point. While it is true that the last hundred-plus years have been very good for stock investors, investors over this period did not know this ahead of time and it was not at all clear that the average return of equities would be so attractive relative to the volatility:

*Uncertainty about the expected return contributes to the investor's overall uncertainty about what the upcoming realized returns will be. Predictive variance includes that uncertainty, while true variance excludes it. Expected return is notoriously hard to estimate. Uncertainty about current expected return and about how expected return will change in the future is the key element of our story. This uncertainty plays an increasingly important role as the investment horizon grows, as long as investors believe that expected return is "persistent," i.e., likely to take similar values across adjacent periods.*

This is an incredibly deep point that is often ignored in discussions about how we come up with expected returns and risks for various asset classes or asset tilts for portfolios. The four-factor model is great, but there is considerable uncertainty as to how each factor tilt will contribute to return as well as with regard to the equity risk premium itself. This parameter uncertainty is part and parcel of the challenge of coming up with expected returns for a portfolio. This uncertainty, the authors demonstrate, is the problem with simply looking at historical returns from equities and concluding that a stock-heavy portfolio is invariably a good thing. This source of uncertainty is also what makes dividends a "special" component of returns.

## Estimation Risk and Dividends

Once we introduce the issue of uncertainty in estimating expected return, there is a rational reason for investors to prefer dividends over other forms of return. The forward-looking estimation risk for this component of return is lower. The fact that the four-factor model or other regression models show that value is a more powerful explanatory factor than dividends in an historical analysis does not bear at all on the issue of estimation risk. In the real world, investors must come up with estimated returns on a forward-going basis.

The data suggests that investors pay a price for the reduction in estimation risk. Dividend-based selection of stocks has historically slightly under-performed a broader value strategy. This does not mean that dividend investing is irrational. The error in the standard "value vs. dividend" comparison is that assumes that estimation risks don't matter. If you knew the future expected return for each asset class with certainty, you could dramatically out-perform real-life investors. The problem is that we simply don't know the future equity risk premium with certainty, nor do we know the value premium with certainty. There can be little debate that we have considerably greater certainty in estimating the dividend component of return than either the EPS growth piece or the P/E expansion piece.

What is intriguing here is that most income investors implicitly grasp this attractive feature of dividends even if they are unaware of the research into estimation risk. For those who want a higher level of accuracy in their estimates of future return, dividends are very attractive.

The lengthy debates will continue, with experts on both sides. While there will continue to be plenty of people who contend that dividends provide no meaningful benefit beyond their contribution to total return, even long-term advocates of market efficiency and index funds such as John Bogle and Burton Malkiel believe that dividends are an especially attractive form of return. Explicitly introducing the idea of estimation risk can reconcile the apparent dilemma.

**Additional disclosure:** I am long many dividend stocks

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