Modern Dividend Theory Explained Part 2: Risk And Diversification

Includes: HAS
by: David Van Knapp

<< Return to Part 1

Back in March, I published "Modern Dividend Theory Explained." It was an initial effort to construct a framework for an income theory that could stand beside Modern Portfolio Theory (MPT). My main goal was and remains to provide a theoretical framework for MDT (Modern Dividend Theory). At some point, MDT might be widened out to Modern Income Theory (MIT), but for the moment I am just focusing on dividends from stocks.

Before I discuss risk and diversification, I want to come closer to constructing a brief definition of MDT.

Definitions of Modern Portfolio Theory and Modern Dividend Theory

MPT is defined by Investopedia like this:

A theory on how risk-averse investors can construct portfolios to optimize or maximize expected [total] return based on a given level of market risk, emphasizing that risk is an inherent part of higher reward.

One of the important things to notice about that definition is that it focuses on portfolio construction. Harry Markowitz's paper "Portfolio Selection" (Journal of Finance, March, 1952, link) is often cited as the source of Modern Portfolio Theory. Markowitz, now 84, stated recently that the words " 'portfolio selection' … are the two most important words I ever wrote." (The New York Times, May 20, 2012.). The Times article went on to state, "Rational investors ought to assemble rigorously diversified portfolios of stocks and bonds with a mix of risk and return optimized for their own needs and beliefs [emphasis added].

Here's my first crack at what a definition of Modern Dividend Theory might look like in a brief Investopedia presentation.

A theory on how risk-aware investors can construct portfolios to optimize the portfolios' dividend returns from stocks for their own needs and beliefs.

I made four significant changes from MPT to MDT in constructing the basic definition.

  • Changed "risk-averse" to "risk-aware." My thinking is that "risk averse" seems to presuppose what an investor's goals are, which goes against what Markowitz says he was trying to do. While MPT certainly deals with risk concepts, as I will do below for MDT, I do not see MPT as exclusively for risk-averse investors. Rather I see it as explaining relationships between risk and potential returns and creating a framework for maximizing returns given a particular level of risk (the so-called Efficient Frontier, illustrated below). Its concepts can be used by investors with high risk tolerance as well as by risk-averse investors. Similarly, MDT can be used by a broad swath of stock investors.
  • Deleted "emphasizing that risk is an inherent part of higher reward." As will be discussed below, risk in MDT carries a different connotation than risk in MPT.
  • Deleted "market risk." As soon as you talk about the market, you are talking about price changes. Dividends are not correlated to price changes. Indeed dividends often rise while prices are falling. The market does not determine dividends, so reference to the market in the definition of MDT seems unnecessary or even misleading.
  • Limited returns to dividend returns. I know that many investors whose primary goal is total return use dividend growth concepts and methods in their investing. However, at this early stage, I thought it best to emphasize dividend returns over total returns. Later on, the definition may be broadened to cover total-return investors.

Now let's turn to the main subject of this article, which is risk and diversification. Before we get going, I wish to acknowledge that this topic came into much better focus for me as the result of a recent article by Dividend Growth Machine, "Dividend Growth Investing: The Role of Diversification," published on May 9. Not only was the article very helpful, but so were comments and discussions beneath it, especially involving commenters Rodger Luebke, chowder, richjoy, Robert Alan Schwartz, and ro-jo, as well as the author himself.

An Overview of Risk

A general definition of "risk" straight out of a Google search yields this:

A situation involving exposure to danger. To expose someone or something to danger, harm, or loss.

Going back to Investopedia for a definition specifically targeted at financial subjects, we find this, which I have edited for conciseness:

The chance that an investment's actual return will be different than expected. Risk includes the possibility of losing some or all of the original investment ... A high standard deviation indicates a high degree of risk ... The greater the amount of risk that an investor is willing to take on, the greater the potential return. The reason for this is that investors need to be compensated for taking on additional risk.

You may note something subtle going on here: The Investopedia definition of financial risk presumes that the MPT concepts about risk-namely that risk and reward are correlated-are inherently correct. So they use MPT's concepts about risk to define "risk" itself. To my eyes, this is an illustration of how MPT has so permeated modern investment thinking that it is hard for anyone to think outside that box. They don't even know they are in the box. From his paper in 1952 to the present day, Markowitz equates volatility with risk.

I did a Google search for images on the term "risk-reward curve" and got over 170,000 responses. Most of the top responses seemed to convey the general idea that potential reward goes up with the amount of risk assumed. I selected this image (also from Investopedia) to illustrate the conventional thinking about risk vs. reward.

This diagram illustrates the "Efficient Frontier" that is a hallmark of MPT. I have great respect for the work that has gone into MPT over the years, from its original development to the present day. But MPT is really limited by its presumptions and conclusions (I have difficulty telling sometimes what has been presumed and what has been derived): "Return" = total return, "risk" = standard deviation, and so on. MPT leaves no room for thinking outside that box. From within the box, more risk = more (potential) return, less risk = less (potential) return, and that's that. My view is that this is not always true, and that therefore the risk-reward curve is incorrect, at least insofar as one would apply it to dividend growth investing.

The Fallacy of Equating Higher Risk with Higher Return

The shape of that curve, showing that returns go up as risk goes up, has bugged me for a long time. There appears to be an obvious flaw in MPT's identifying higher returns as only available if you take on more risk. It might be called the Graham-Buffett flaw. Graham, as we all know, posited that higher returns are available if you reduce risk in your investment selections. Indeed that is how you improve your chances of producing higher returns, by reducing the probability (risk) of downside moves and increasing the probability of upside moves.

In the 1973 edition of The Intelligent Investor, Graham wrote on pp. 60-61,

… the idea of risk is often extended to apply to a possible decline in the price of a security, even though the decline may be of a cyclical and temporary nature and even though the holder is unlikely to be forced to sell at such times ... But we believe that what is here involved is not a true risk in the useful sense of the term ... [T]he bona-fide investor does not lose money merely because the market price of his holdings declines; hence the fact that a decline may occur does not mean that he is running a true risk of loss ... [W]e apply the concept of risk … to a loss of value which is … realized through actual sale … or, more frequently perhaps, is the result of the payment of an excessive price in relation to the intrinsic worth of the security [emphasis added].

The "excessive price," of course, we call overvaluation, or paying more for a stock than it is intrinsically worth. In a nearby footnote, Graham said this:

In current mathematical approaches to investment decisions, it has become standard practice to define "risk" in terms of average price variations or "volatility." … We find this use of the word "risk" more harmful than useful for sound investment decisions-because it places too much emphasis on market fluctuations.

In other words, Graham's concept of risk was in sharp disagreement with MPT's definition of risk. He recognized the price distortions often introduced by Mr. Market, and he advised against paying too much for a stock. Indeed, he advised paying only bargain prices, giving yourself a "margin of safety" in case your projections are off. These principles have since become basic tenets of value investing.

Here is InvestorWord's definition of valuation:

The process of calculating the fair market value of a stock by using predetermined formulas that factor in various … indicators. Stock valuation can be calculated using a number of different methods.

There are dozens if not thousands of ways to value a stock. Many are based on various flavors of net present value calculations, while others revolve around comparing common valuation ratios (such as price-to-earnings, price-to-sales, and price-to book value) to historical market averages or to the stock's own historical values. The outcome is variously called fair value, intrinsic value, true value, and the like. It is commonly thought that the stock's actual price, which rarely sits exactly at its intrinsic value, will over time revert toward its fair value if it gets too far out of line with it.

Around Seeking Alpha, the idea that higher returns can be associated with lower risk has been illustrated over and over by Chuck Carnevale with his familiar graphs. Here is an example:

(Click to enlarge)

The orange line represents Hasbro's (NASDAQ:HAS) "earnings justified" value according to Chuck's methodology for computing fair value. The black line represents Hasbro's actual price. As you can see, the price wanders back and forth through the orange line, spending some time above it (overvalued) and some time below it (undervalued). As illustrated by Hasbro's actual price, when it has been overvalued its price has tended to drop over time, and when it has been undervalued its price has tended to rise. So it has been when the stock has been undervalued (or less risky) that its chances of increased return have been highest. This is the exact opposite of what MPT says.

What Is Risk to a Dividend Growth Investor?

The above discussion was about price risk. In a dividend or income context, risk is different if the income investor's primary focus is on the dividend stream. So now I will attempt a definition of risk as seen by a dividend investor who is primarily interested in reliable, growing dividends:

In Modern Dividend Theory, risk is the chance that a dividend portfolio's income return will be lower than expected.

In this definition, I have tried to accomplish the following:

  • Make the definition specific to the income investor.
  • Reinforce the notion that we are more interested in a portfolio's performance than in the performance of individual componenets of the portfolio.
  • Remove the presumption that the risk of major interest is risk to total return. A dividend investor may be far more interested in the ability of his or her portfolio to produce income than in its sheer size.

In my earlier article, I included a table comparing the tenets of MPT and MDT. I stated that there were significant differences, starting with the underlying goals themselves. I noted that I thought that this is why MPT and MDT proponents often have difficulty even talking to each other, because the goals and tenets are so different

I included a table comparing those goals and tenets. Here are the portions from that table regarding risk. (I use "dividend" broadly to refer to common dividends, preferred dividends, and distributions by such entities as MLPs and REITs.)


Modern Portfolio Theory

Modern Dividend Theory

Risk measured by

Volatility or standard deviation from the mean in total return.

Unexpected reductions in dividend stream.

Can there be negative return?

Yes. Actual value of portfolio may go up or down.

Not in dividend stream. There is no such thing as a negative dividend. However, value of underlying portfolio can go up or down.



Low risk is associated with low potential total returns; high risk is associated with high potential returns. Higher returns can only be achieved by assuming higher risk (i.e., higher volatility).

High and growing dividend streams can be achieved with relatively low risk. There is no consistent relationship between risk levels of total returns and risk levels of dividends. Indeed, dividends can rise while total returns are falling.

Upon re-looking at that table now, I think that it stands up to scrutiny. The main point is that dividends and price returns are uncoupled from each other. Look back at the graph of Hasbro. The blue dividend amount just continues to go up each year, no matter what the price line is doing. While the price risk (potential upside and downside) changes constantly, the dividend volatility is obviously far less.

Just a few days ago, another example of risk being decoupled from volatility turned up in Morningstar. They ran an interview with Morningstar analyst Shannon Zimmerman. This was the interview's title and subtitle: "When Less Risk Equals More Reward: Recent research suggests that lower-volatility stocks and funds tend to perform better over the course of many years." The video interview can be seen here. In it, Zimmerman states:

  • It does turn out to be the case that over the course of many decades -- and sort of building on some research that has been done into individual equities that are rolled up into portfolios -- it turns out that less risk, if you define risk as volatility, actually leads to more rewards.
  • It sort of flies in the face of what people believe, and it seems counterintuitive. Seemingly, the more risk you take on, the greater the potential reward ... But if you define risk as volatility -- and typically academic researchers are defining it in terms of standard deviation or beta -- if you look at risk through those lenses, it turns out that the lower beta, the lower standard deviation investments, tend to perform better over the course of many years.
  • [Talking here about funds] … [I]t turns out that investors use low-volatility funds better because they ... don't get the willies when the quarterly report comes, and they haven't gone ... down 15% ... in a flat market. The smoother a ride a fund can give a shareholder, the better they tend to use it.

In other words, investors are less likely to suffer panic attacks, and to sell in a panic, if their fund or stock is less volatile than others. So not only do low-volatility investments perform better over long time periods than other investments, but investors are more likely to stick around and actually benefit from that out-performance.

Can the Risk of Reduced Dividends be Quantified?

In MPT, risk is quantified by some measure of volatility, with the most common measures being standard deviation and beta.

I am not aware of an analogous mathematical measure of the risk that a dividend stream will be reduced. Clearly, it is a function of the stability and predictability of dividends themselves. For now, I do not have nor am I going to attempt to invent a mathematical function that describes the risk to dividends or to dividend growth. Common experience suggests that the risk to dividends is far lower than price risk, but I don't know how to quantify that.

The Role of Diversification

Even though the risk to dividends cannot be quantified, it is relatively easy to quantify the risk to the total dividend stream from a single stock in a portfolio. As with MPT, I believe that the value of MDT is in portfolio construction.

From the perspective of dividend return, the worst thing that can happen to a stock is that its dividend drops to zero. Should that happen, the impact on a portfolio's total dividend stream depends on what proportion of the total stream was represented by that dividend. If the portfolio contains X stocks, and (for simplicity) each contributes the same amount to the total dividend stream, then the risk to the total stream from the failure of one stock is 1/X. So if the portfolio contains:

  • 5 stocks, 1/X = 1/5 = 20%
  • 10 stocks, 1/X = 1/10 = 10%
  • 20 stocks, 1/X = 1/20 = 5%

And so on. I always resist using words like "properly" diversified, as I think it is up to each investor to decide what is comfortable for himself or herself. But obviously the "protection" afforded an income stream is enhanced the more stocks there are in the portfolio, presuming that each stock has an identical chance of damage to its dividend. That is a big presumption. I think that most dividend investors would agree that careful stock selection, due diligence, and attentive portfolio monitoring can reduce the chances of owning very many stocks that cut or eliminate their dividends.

So just as with MPT, MDT would postulate that investing in more than one stock brings the common benefit of diversification, namely a reduction in the riskiness of the portfolio. As we saw above, the rate of reduction in riskiness from each new stock goes down as the number of stocks in the portfolio rises. Also as emphasized earlier, the "proper" amount of diversification is really a function of each investor's tolerance for different magnitudes of reduction in the dividend stream. No one answer is right for everyone.


For me, the biggest benefit of writing this article has been to realize that optimizing a portfolio for price or total returns is different from protecting a portfolio's income stream from reduction. In the past, I have believed in and been comfortable with concentrated portfolios. As the saying goes, why purchase your 20th best idea rather than your best idea or 5th-best? But now I realize that concept is more associated with price maximization than protecting the reliability and growth of a portfolio's income stream.

If your main focus is on a reliable and growing dividend stream from a portfolio of dividend growth stocks, adding more stocks to the mix-up to some reasonable number-seems to have little downside, so long as you are adding high-quality stocks at good valuations. So going forward, I am going to increase the actual number of stocks in my dividend growth portfolios from 10-15 to 20-25. I will also probably reduce the maximum allowable position size from 20% (currently) to 15% or maybe less. I would expect to move in that direction gradually as opportunities present themselves. I will not buy a low-quality company or an overvalued one simply to become more diversified.

I still believe that some dividend growth stock ideas are better than others. There is a chance that in increasing the number of stocks in a dividend growth portfolio, you will at some point be adding stocks that have a higher chance of cutting their dividend than your "best" stocks. There must be some tipping point where adding the nth stock to your portfolio does not add any safety to the dividend stream, because that stock is more likely to cut its dividend than higher-quality stocks. That is why I am not moving my upper limit to, say 100 stocks. That would seem to go beyond the "reasonable number" referred to above.

The second big benefit for me was the reinforcement that low-beta stocks tend to deliver better total returns over time. While I focused here primarily on dividend returns, I also keep my eye on total returns, as do most investors. I am going to give serious consideration to adding beta as a scoring factor in the next edition of Top 40 Dividend Growth Stocks, with rating points being awarded for stocks with lower betas. I do believe that psychologically, stocks with muted price fluctuations are easier to hold onto during turbulent markets. In general, holding onto stocks in a dividend growth strategy is desirable, as market gyrations usually have little effect on dividend and dividend increases.

There was one final benefit, which was the reinforcement of formulating investing principles based on subjectivity-probabilistic beliefs-as well as objectivity. In Harry Markowitz's 1952 paper, he acknowledged that future returns cannot be known, but that an investor can be expected to have "probability beliefs." That is,

"… we would expect that the investor could tell us, for any two events (A and B), whether he personally considered A more likely than B, B more likely than A, or both equally likely ... We cannot expect the investor to be consistent in every detail. We can, however, expect his probability beliefs to be roughly consistent on important matters that have been carefully considered. We should also expect that he will base his actions upon these probability beliefs-even though they be in part subjective."

We all know that past performance is no guarantee of future results. But that said, most investors would probably agree that history provides clues to the future, and that a lot of the due diligence process consists of studying history. For dividend growth investors, that means studying and forming informed beliefs about what stocks are likely to do with their dividends.

Disclosure: I am long HAS.