Yield Rank's  Instablog

Series Part 4: Back to the future.

In parts 1-3 of this series I established some of the key principals to my analysis:

1. Comparing dividend growth stocks of different yields and growth rates is non-obvious
2. Solution: Compare dividend growth stocks to bonds
3. Separate risk analysis and cash-flow analysis into two separate steps. This article focuses on the second

The final element before we look at real data is the topic of future dividend yield. Since dividend yield is defined as the ratio of the dividend to the price of a stock, any future assumption of the dividend yield means an assumption of the future price of the stock.

When comparing any two assets, the one with the lower starting yield must eventually grow its dividend to surpass the higher yielding one, or it can never provide more total cash return, as discussed in Zeno's paradox in part 2. As previously pointed out, when comparing two assets you must re-invest the excess yield of the one with higher cash flow in a given year to be fair. When re-investing dividend yields the amount of new stock that can be purchased depends on the yield at the time the future growing dividend is paid.

After analyzing various scenarios using real historical data as well as different idealized scenarios, I have come to the firm conclusion one should not use the future stock price in any calculation. It distorts the result to the point of not being useful. Using a pure analysis also leads to better investment decisions.

I will summarize the reasons why I reject any use of future stock price (and therefore future dividend yield) in any financial cash-flow valuation analysis for DG stocks:

1. It is circular reasoning
2. Historical data shows large fluctuations in dividend yield independent of growth rate
3. Dividend yields of all stocks are often re-priced as a group
4. Back testing shows this model produces better returns with lower volatility

Instead, the only future values I use are the interest rates on bonds. There are a number of reasons for this choice, but the main one is that it is better that bond interest rates are a better choice than future stock prices and yields, for the reasons outlined above. I should point out that no attempt at models for valuation of growing dividend yields has been proposed that does not use some type of future interest or discount rate. The reason for that is self-evident: Long interest rates are non-zero (for now) and inflation is non-zero, and a growing dividend necessarily derives much of its value in the future. A dollar today is not worth the same as a dollar in the future. If you need a certain amount of income and are not concerned about interest rates, you can instead substitute your estimate for the rate of inflation. Any interest rate, inflation rate, or discount rate will do.

You are probably wondering what I think I have solved, substituting one hard problem (valuing future growing dividends) with another (forecasting interest rates). My solution is deceptively simple: Use the currently available long-term bond rate. Since equity has infinite term, the longer the better. At least 20 years, but 30 or even 40 may be better. There are several reasons for my choice, but chief among them is that it is an "available rate". When valuing a DG stock, look at it as a real practical choice: At this point in time (today), get a quote on the stock and a quote on a suitable bond. Make your projection and judgment on the growth rate for the stock, and the credit quality of the bond. Then calculate based on "assume everything goes as planned" - i.e. the stock and bond perform exactly as projected. This is the concept of "separate risk and valuation" explained in part 3. You can build in provisions for bond defaults and dividend cuts to your portfolio after the calculation is complete.

So far I have assumed a constant interest rate in my work. The main reason is that it is available: You can in practice buy a zero coupon long bond that will have a constant compounded rate to maturity. Floating rate or inflation-indexed bonds often carry such a low current yield that most often the DG stock has a higher start yield and is very unlikely to underperform such a bond. I also ran calculations on different interest rate changing scenarios and the answers I get depend more on the starting interest rate at the time of the choice and the rate in the next few years, rather than the rate in year 10 or 20. Thus a constant rate is a reasonable assumption. This makes sense since future dollars are worth less than current dollars. I also notice that bond rates do not fluctuate as much as dividend yields in the 1-5 year period after the choice. There are some other technical reasons as well why the answer does not vary much with constant rate or changing rate due to the re-investment.

In summary, the fourth principal is that future stock prices and yields should not enter into the calculation at all. The only inputs I use are:

1. Currently available long bond rate ask quote (20-40yr)
2. Currently available stock yield ask quote (dividend/price)
3. Projected compound annual dividend growth rate (method up to the investor)

Thus you can view the metric as a practical choice: Do you buy a certain long bond, or the dividend growth stock in question? If you are comparing two stocks to a bond, I have found that at some points in time you will buy either the first stock, or the second stock, or the bond. As all three assets re-price daily, that answer will change over time. More on how to use that information will be explained in a later section.

Series Part 3: Risk & Reward - Keep 'em separated

This is the third in my series (on Dividend Growth Stock pricing. In my second Instablog I introduced the concepts of valuing DG (Dividend Growth) stocks compared to bonds and compared to each other.

The focus of my work has been on the pure cash flow analysis side of the question of valuation. I know that so many readers will quickly fill the comment space with alarmist comments of "how can you ignore risk, it is a key part of valuation". Please can you kindly settle down - I am not ignoring risk.

I have intentionally chosen to separate risk and credit analysis from the financial cash-flow analysis, particularly for DG (Dividend Growth) stocks. My reasoning is that millions of words are written on this board and elsewhere discussing the risk factors and prospects of the universe of DG stocks. I am not able to add to that more than a drop in the ocean on that front.

Instead I have chosen to address the following: Once you have done your analysis and concluded an estimate for the forward dividend growth rate of a stock, how can you financially value that compared to other similar or dissimilar assets? A key thing I have learned in investing over many years is to make sure you get enough reward. All rosy stock projections have risk, all bonds have risk, and life is risk. If you buy a handful of securities, especially if they are all stocks, some of the projections will not materialize. The ones that do materialize need to make up for the ones that do not.

In all discussions going forward I will take the DGR (Dividend Growth Rate) as a given. Look at the example used in Part 2 (link):

A) 2% yield, 15% dividend growth rate

B) 3% yield, 10% dividend growth rate

C) 4% yield bond, 4% coupon, 30 year maturity

Assume 15% DGR for A comes true, and it is exactly 15% for your lifetime. Was it better to buy the bond, or the stock? This I will address later. You may ask: How do we know the DGR is 15%? My answer: It does not matter. You can use any method you wish, whether forecast from an analyst, historical rates, projections, newsletters. I often use 10 yr. historical growth rates when looking at 50 year data, since that is all I have available as a forward projection for a point in time. Sometimes I blend it with 5 year and 2 year historical DGR rates. I might include a 2 or 5 year analyst forecast for a present day stock. In the end, you come up with a DGR number and I will calculate for you from a cash-flow perspective which is the best of the three based on current prices (yields).

An interesting note is that the 4% bond appears the easiest of the three to rate. After all, 4% is written into the contract. You know it will not be more than 4%. Of course, if the bond defaults it could be less, and then it depends on the recovery rate. If the bond defaults sooner it matters more than later since you have time to collect a lot of interest in the latter case to offset any principal loss. There are many factors to consider.

My separation of predictions and risk from valuation is analogous to bonds. One important reason for performing credit analysis on bonds is to be able to group them together to compare prices. You are essentially saying "this group of bonds has similar cash-flows, equity and business conditions" and then you can more easily compare their prices based on interest, calls and maturity. I pursue a similar strategy with bond-stock comparisons. If you do not like the number I used for a given DGR, give me another and I will re-run it.

The next question is what should we use as DGR for a stock? Should it be a conservative de-rated growth value that you believe the stock has a high likelihood to exceed? Should it be a mid-point consensus that has about 50% chance of being correct? Or should it be the best-case scenario? There is no right answer, and I can calculate for any value given. So far my thinking is you should tend towards something in the middle. Ask yourself this: If you take ten stocks with similar confidence level, as a group in twenty years they should achieve about 90% of the projected DGR. Those that overachieve can compensate for the laggards. Maybe you take all similar DGR projections and de-rate them by 10% so that you have a high likelihood, in the same region as the bond you are comparing to.

My work so far seems to indicate that historic rates should carry some weight, and that is for good reason. It appears that if a stock has a DGR of 10% over 10 years, it has a high likelihood of growing 10% in year 11. Also, companies that have a long history of dividend growth often recover even if they hit a tough patch. Even though I have used historical rates, I am not a proponent of any method. Pick the projection you like and run with it. But, project you must. My work says that over-paying can severely reduce returns, and you cannot calculate anything without a projection. At least use an historical rate if you do not have a better projection, it will tell you the relative valuation as the stock price moves day-to-day within a quarter.

In summary going forward in the next sections I will always separate risk and reward. Risk calculation will be left to others. I will focus on the relative rewards of various asset classes.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

Series Part 2: Oranges and Orangutans

This is the second in my series on dividend growth stock [DGI] pricing. In my first Instablog I introduced the question of how to price DG stocks.

I will now complicate things further. If you need to compare apples to oranges and you are having difficulty, the solution is often to compare them both to something else, say orangutans. Let us introduce C:

A) 2% yield, 15% dividend growth rate

B) 3% yield, 10% dividend growth rate

C) 4% yield bond, 4% coupon, 30 year maturity

Well that did not seem to help. The bond has no income growth rate, or so it appears at first. C has twice the start yield rate compared to A and even at 15% growth rate it will take a while for A to catch up with C. Or will it ever catch up? Let us explore this question.

A key concept is that if you are comparing two different securities, you must re-invest the excess yield of the higher yielding security by subtracting the at least the lower yield. In the above A vs. C example, you can debate about whether you should spend 100% of the dividend, or 100% reinvest it, or keep it in the bank at zero interest, or somewhere in the middle. But you cannot argue that the excess 2% yield (4% - 2%) of the bond must be re-invested.

Think of it another way: If you are willing and able to accept the lower rate of A and if you are making a choice between the two, then you have to also be willing to accept the same 2% rate from C. In practice you can game-play different scenarios such as re-investing all of A and C's yield, or none of A and the difference A-C, or some in-between amounts, or raise the amount not reinvested by inflation, and many other variants.

The key constant, which will later prove to be very important, is that you must re-invest at least A-C yield (4% - 2% = 2%) on the higher yielding security in the first year.

Now let us say we spend all of the dividend from the stock in year one, and the same portion from the bond's interest to keep things fair, and reinvest the excess interest from the bond into more bonds. It will take a number of years for the 2% yield of A to grow to 4%. However, the excess interest re-invested in more bonds will increase the total income of the bonds beyond 4%. It will take some more time for the stock to catch up, and again the bond will have increased. You might wonder: Will the stock income ever catch up?

This problem is analogous to a famous mathematical paradox known as "Zeno's paradox of Achilles and the tortoise". Sometimes also called the "tortoise and the hare". The paradox is explained like this: Give the tortoise a 100 ft. head start in a footrace, and let us say it runs half the speed of Achilles (similar to our bond and stock above). By the time Achilles runs 100 ft., the tortoise has run (or crawled?) another 50 ft. By the time Achilles gets to 150ft, the tortoise is now at 175 ft., and so on. Zeno hypothesized the tortoise will never be caught.

Of course we know from every day experience that in practice Achilles blows by leaving our intrepid tortoise in the dust. I will leave the mathematics aside, but it was later irrefutably proven mathematically that we can calculate precisely the distance at which Achilles will reach the tortoise, and there is a simple formula for that. Similarly, we can calculate at what point in time the dividend yield will pass the compounding bond precisely.

Note: Zeno is a little simpler than our example since there is no re-investment to consider in the footrace. In our case each year the amount of excess bond income reinvested will decline as the stock yield rises exponentially. This complicates Zeno's formula. But with the power of computers it can still be solved in a straightforward way.

As a side note, I will mention a little known fact that is most often overlooked in discussions of Dividend Growth Incoming investing. For purists that care only about the future dividend stream the future price of the stock is not relevant. (This is often termed Yield Over Cost or YOC). These investors are called "income-only" investors compared to "total return" investors who care about both income and future stock price. If there is enough of a gap between the start yield of a stock and bond, and if the dividend growth rate is low enough compared to the re-investment rate of the bond, the stock dividend income never catches up. If you are an "income-only" investor the bond will always be superior. This little detail is often overlooked, but once you know it you can see why it is important to gain a more accurate understanding of how to value these securities.

From this section you should now be able to see that valuing these various securities in purely financial terms is not as easy as it first appears. Particularly when the yields and growth rates are fairly close, it is not that easy to know by gut instinct which will have a higher income in the future. In fact our instincts might sometimes mislead us. Even a mathematical approach at first seems straightforward but it gets surprisingly complicated.

One of the chief advantages of bonds is that they are easier to compare to one another than growing dividend streams. This is due to the intentional design of the instrument. There are hundreds of books on valuing bonds compared to one another, and I will not reiterate those details. Suffice to say it is relatively easy to sort through thousands of bonds and pick the ones that have the best relative price on a given day. This is the reason why I picked bonds as my orangutan. All we need to do is come up with a method to rank two DG stocks compared to a given bond, and then we can also know which DG stock is better, and by how much. Bonds also have another advantage in that like orangutans they are real, if not easier to catch. It may turn out the bond is better than both stocks by some metric at a particular price point. In that case you can simply purchase the bond.

In the next part of the series I will explore risk and reward, followed by narrowing down some key concepts and assumptions.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.