A Backtest of the Dividend Growth Model, 1871-2010

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SimpleGift
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A Backtest of the Dividend Growth Model, 1871-2010

Post by SimpleGift »

This post is to report on a backtest of the simplified Dividend Growth Model for predicting forward 10-year stock returns for planning purposes (same as used by Mr. Bogle). The analysis was done by Research Affiliates in 2012, using Shiller data from 1871 to 2010 — and I reproduced their results in the chart below. Their simple forecast model is:
  • Image

    Their Method: The 140 years of Shiller data between 1871 and 2010 were divided into 14 discrete, non-overlapping decades. The dividend yield at the beginning of each decade was added to the real earnings-per-share growth rate over the entire 140-year period (1.7%) — then compared with the real realized stock returns for each decade.

    Their Results: On the chart below, the expected returns for each decade (x-axis) are plotted against the actual real returns (y-axis). The overall fit to the trend line was R^2 = 0.28. However, there are two obvious outliers — the 1910s during World War I (when returns were way below forecast) and the 1990s Tech Bubble (when returns were way above forecast). Without these two unusual outliers, R^2 = 0.62.
IN SUM: The simplified Dividend Growth Model appears to have some predictive power for the next decade's real equity market returns, with the proviso that the results can be quite imprecise — and unusual events can happen (a couple of times a century, it seems) that will entirely negate the forecast. Each investor can decide for themselves about the usefulness of this simple model for their own financial planning.

Image
Source: Analysis from Research Affiliates, based on Shiller data
Last edited by SimpleGift on Mon Oct 27, 2014 4:58 pm, edited 3 times in total.
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by SimpleGift »

Just to add that most of us passive investors have portfolios containing both stocks AND bonds — and since future bond returns can be very reliably predicted based on their current yields (R^2 = 0.92, chart below), this will improve the precision of an investor's overall portfolio return forecast.

Image
Source: Wade Pfau et al.

For more on forecasting overall portfolio returns, see Expected Return — (this is the same article by Research Affiliates linked to in the original post above).
Last edited by SimpleGift on Mon Oct 27, 2014 10:17 pm, edited 1 time in total.
FinancialDave
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by FinancialDave »

Going back 140 years is a little beyond my confidence that we are comparing apples to apples, just because of how much corporate dividend policies have changed in the last 100 years.

How much would the curves change if you only went back 60 years?

Also, I can't tell from the charts what this is indicating for the next 10 years.

fd
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by mjb »

An R squared of 0.2799 is pretty poor. I would want to see greater than 0.6 to make any conclusion
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by thenextguy »

mjb wrote:An R squared of 0.2799 is pretty poor. I would want to see greater than 0.6 to make any conclusion
Easy! Throw away the two outliers! :D
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by larryswedroe »

IMO the critics are totally off base on this issue, failing to understand that the higher the r-squared the less risk there would be and the ERP would be TINY!!!!!
The fact that we cannot forecast returns with high degree of accuracy is simply a function of the fact that the future is unknowable and we are dealing with uncertainty, not even risk which we know the odds.
Now the fact that you have positive correlations and likely statistically significant means that there is valuable information in valuations.
The research shows that CAPE 10 and current valuations both explain about 40% of the future returns, that is valuable information that one ignores at their peril IMO.
Valuations clearly matter a great deal or you would not have 40% explanatory power, and just be thankful it isn't very high or equity returns would be very low
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by siamond »

FinancialDave wrote:Going back 140 years is a little beyond my confidence that we are comparing apples to apples, just because of how much corporate dividend policies have changed in the last 100 years. How much would the curves change if you only went back 60 years?
mjb wrote:An R squared of 0.2799 is pretty poor. I would want to see greater than 0.6 to make any conclusion
The devil is in the details with this kind of math, but in my own reconstruction of such 'expected (real) fundamental returns' math, I get an R2 of 0.35 (starting in 1881). Now things do improve quite a lot if you ignore the hectic end of the 19th century, and even better if you went back only 80 years back (to a surprisingly high R2 around 0.7). Personally, I don't think it's wise to ignore the 1929 crisis, so I'd rather look at the past ~100 years, and then I get a more paltry R2 of 0.4.

When adding a speculative correction factor, things do improve, but this isn't what SimpleGift wanted to discuss... Note that expected fundamental returns are relatively smooth, and have little provision to take in account the occasional speculative craziness, so it's no wonder that the 20s put a big wrench in the R2...

Oh, and I got results very similar to Wade Pfau on the bonds side (counting in nominal returns).
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by SimpleGift »

larryswedroe wrote:The research shows that CAPE 10 and current valuations both explain about 40% of the future returns, that is valuable information that one ignores at their peril IMO.
Backtest of CAPE Earnings Yield
Matching the methodology of Research Affiliates in the OP, I ran a backtest using the CAPE earnings yield (inverse of the price-earnings ratio) at the beginning of each decade to see how well it forecast actual real returns over each decade. The fit to the trend line was R^2 = 0.38 (chart below), a slight improvement over the R^2 = 0.28 for the Dividend Growth Model. When the two outliers are removed from the CAPE plot below, R^2 = 0.65.

Image
(Note: Only 13 decades can be plotted since 1871, due to CAPE's 10-year trailing earnings.)
Source: Shiller Database

Backtest of Average of Dividend Growth & CAPE Earnings Yield
Going further, I obtained somewhat better backtest results by using a simple average of the Dividend Growth Model and CAPE earnings yield at the start of each decade — the fit to the trend line improved to R^2 = 0.40, and with the two outliers removed, R^2 = 0.75.

Image
(Note: Only 13 decades can be plotted since 1871, due to CAPE's 10-year trailing earnings.)
Source: Shiller Database
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by backpacker »

Simplegift wrote:The dividend yield at the beginning of each decade was added to the real earnings-per-share growth rate over the entire 140-year period (1.7%).
Nice work SimpleGift! This is really interesting.

The problem: Using the historic average 140-year growth rate as the projected growth rate in effect gives your hypothetical historical investor a crystal ball. How would I, for example, go about figuring out the average growth rate for the US economy between now and 2150?

The fix: Use a rolling projected growth rate. For each year (or month if you're using the monthly data), calculate the projected growth rate as the historic growth rate up until that year. That way, your model will be only using data that real investors could have known at the time.

I suspect the reliability of the model will drop without building in information about future growth rates.
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by backpacker »

larryswedroe wrote:IMO the critics are totally off base on this issue, failing to understand that the higher the r-squared the less risk there would be and the ERP would be TINY!!!!!
From the fact that the R2 couldn't be high, it doesn't follow that the low R2 is alright. It could be that we just don't have any useful way of predicting future returns.

That the R2 is even .4 also looks like a historical fluke. Dimson, Marsh, and Sunstein look at the international reliability of D10 (trailing ten-year dividends) at predicting returns. They used D10 instead of PE10 because the international data is better and the two are highly correlated. They found that the reliability in the US was a best case scenario. In many countries, the R2 was in fact slightly negative. That is, returns had a tendency to be the opposite of what D10 predicted.

I don't see the point of predicting future returns. Formulate a plan that has lots of margin for error. Then stick with it. If your plan fails with long-term real equity returns of 2%, your plan does not have enough margin for error.
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by larryswedroe »

backpacker

The fact that you have an rsquared as high as 40 means that there is valuable information there. It's not like it's 0 or .1
It's really as simple as that

As to D10 as I have said the really isn't as much logic to Gordon Model (except it does great job of explaining returns ex post) because simple economic theory is dividend policy doesn't matter. The best models the research makes clear are valuations. Damodaran has excellent paper on subject for those interested

As to no value, there is simply no logical way to determine an AA without having expected returns. In fact without them there is no reason to invest in stocks period. And there is no way to determine the need to take risk. Finally we do know that valuations matter a great deal, not just a little bit. As you go down in E/P the next 10 years returns increase monotonically. Clearly showing there is valuable information in valuations, What we don't know is how risk premiums will change, as those are time varying.

Not being able to forecast "accurately" doesn't mean there isn't value in current valuations nor in the exercise, one just has to be humble about the predictions, and understanding that there is a wide dispersion of potential outcomes

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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by SimpleGift »

FinancialDave wrote:How much would the curves change if you only went back 60 years?
We'd only have 6 independent data points over the 60 years, which is quite limited. However, you can see the historical relationship between expected returns and realized returns in the chart below. Generally, expected returns from the dividend model (in green) tend to be relatively stable, while the CAPE earnings yield (in blue) responds to the extremes of valuation — for example, in 1921 when CAPE was at 5! The average of these two methods (not shown) appears to capture some of the best from both.

Image
FinancialDave wrote:Also, I can't tell from the charts what this is indicating for the next 10 years.
It's not on the charts, but we can easily calculate it, first using the Dividend Growth Model:
  • Current Dividends (2%) + Real Earnings Growth Rate (1.7%) = Expected Real Return (3.7%).
Then we can check this estimate against the earnings yield: The current CAPE is 25, so the CAPE earnings yield is now 4% (1/25). If we average the dividend growth estimate and the CAPE earnings yield, we get an annual expected real return for stocks of about 3.85% for the decade ahead — so say 4% real for planning purposes.
Last edited by SimpleGift on Tue Oct 28, 2014 12:25 am, edited 1 time in total.
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by hornet96 »

larryswedroe wrote:The fact that you have an rsquared as high as 40 means that there is valuable information there. It's not like it's 0 or .1
It's really as simple as that
I'm not sure it's really as simple as that. What are the f-test results on this regression analysis? What about a Dickey-Fuller type test? The point being that we don't really know whether we are dealing with a normal distribution of returns, or whether we have non-stationarity (random walk). The R2 of 0.4 may actually be meaningless in terms of predictive power, and we don't realize it.

With that said, your point about the equity risk premium disappearing if the R2 was higher is an interesting one that I hadn't thought of before. Basically, I think you are saying that if the model had a better "fit," more investors would pile into whatever factors the model is currently calling for, which would drive up those equity prices and result in a lower earnings yield. Then again, if that happened, wouldn't the model then fall apart? In other words, it would seem to result in a kind of paradoxical loop where (say) the PE10 indicates that stocks are undervalued, investors immediately pile in, then the PE10 immediately indicates stocks are overvalued, investors immediately sell everything.....and so on.
Simplegift wrote:Their Results: On the chart below, the expected returns for each decade (x-axis) are plotted against the actual real returns (y-axis). The overall fit to the trend line was R^2 = 0.28. However, there are two obvious outliers — the 1910s during World War I (when returns were way below forecast) and the 1990s Tech Bubble (when returns were way above forecast). Without these two unusual outliers, R^2 = 0.62.
Improving the R2 after removing "anomalies" and trying to extract predictive value from it is otherwise known as data mining. To me, it's also an indication that there have been "regime changes" that renders the model as questionable (at best) for forecasting future returns. What can the model tell us about future regime changes? Nothing, of course.

All of this (and more) just reminds me of how difficult (impossible) it really is to predict anything about the future. At best, our statistical models can attempt to explain what has already happened, and the models of our financial markets do a fairly poor job of even doing that.
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by larryswedroe »

hornet
I suggest you read the literature on this stuff. Damodaran has the best paper I believe.
As to higher r-squared. Let's say model was perfect predictor. Then there would be no risks in stocks at all. IF there is no risk, you knew the return ahead of time, then stock prices would be bid up to the same prices as safe bonds whose returns we know in advance.

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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by hornet96 »

larryswedroe wrote:hornet
I suggest you read the literature on this stuff. Damodaran has the best paper I believe.
As to higher r-squared. Let's say model was perfect predictor. Then there would be no risks in stocks at all. IF there is no risk, you knew the return ahead of time, then stock prices would be bid up to the same prices as safe bonds whose returns we know in advance.

Larry
I would be glad to read the Damodaran paper once earnings season (and my reporting duties) conclude. :beer
I assume it was published in the Financial Analyst Journal (CFA publication) or some other similar publication? Perhaps it addresses my questions posed above....

I still think there is something more to explore regarding what would happen if the model was a perfect predictor of equity returns (perhaps this is something that Damodaran explores?). I agree with you in the sense that such a model would essentially be impossible to achieve, as equity prices are fundamentally based on expected company earnings (which are not a stated annual rate, unlike safe bonds). If earnings were known with certainty in advance, we wouldn't be talking about a capitalist system any longer (and hence, such a perfect model would break down and be meaningless, eliminating the equity risk premium as you note).
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by bhsince87 »

Looks like good work. Kudos to you! I would only change one word:

"IN SUM: The simplified Dividend Growth Model appears to have HAD some predictive power for the next decade's real equity market returns...."
Time is what we want most, but what we use worst. William Penn
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by grayfox »

Simplegift wrote:This post is to report on a backtest of the simplified Dividend Growth Model for predicting forward 10-year stock returns for planning purposes (same as used by Mr. Bogle). The analysis was done by Research Affiliates in 2012, using Shiller data from 1871 to 2010 — and I reproduced their results in the chart below. Their simple forecast model is:
  • Image

    ...

    Image
Thanks for posting this, it is very timely for me.

Just yesterday, I was looking at pretty much this exact question. But instead of backtesting, I was looking at the Dividend Discount Model DDM from a purely theoretical viewpoint. To cut to the chase, I concluded that the DDM was useful for understanding how price, dividend, growth rate and expected return are all tied together. But the DDM makes a poor forecasting model of anything that an investor might be interested in because we don't know anything reliably.

With R^2 =0.2799, backtesting confirms what I had concluded from purely theoretical considerations. With so few data points, you can run random numbers and easily get R^2 = .20 or .30

:idea: The DDM is very useful for understanding the relationship among price, dividend, growth and expected return. Providing accurate forecasts, not so much.
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by richard »

backpacker wrote:<>The problem: Using the historic average 140-year growth rate as the projected growth rate in effect gives your hypothetical historical investor a crystal ball. How would I, for example, go about figuring out the average growth rate for the US economy between now and 2150?<>
This is a major problem and essentially invalidates the posted backtest.

Being able to accurately predict the growth rate is key to the dividend growth model. Investors in, for example, 1950 don't know what the growth rate for the next 60 years will be. Using the average over the entire period means (including the next 60 years), in essence, tells them what the future will bring. I'm surprised the resulting R^2 is so low.

Ignoring outliers is just silly. It's the same as saying that all of my predictions are accurate, if you ignore the predictions that are inaccurate or, perhaps more on point, my investments always go up, if you ignore the years in which they go down.
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by richard »

larryswedroe wrote:<>As to no value, there is simply no logical way to determine an AA without having expected returns. In fact without them there is no reason to invest in stocks period. And there is no way to determine the need to take risk.<>
You could start at 50/50, then adjust based on risk aversion and needed returns.

How much to save? I did a poll here some time ago and most people used a fixed percentage of income, such as 15%. You could adjust over time.

How to know when you have enough? When you can live on a 4% (perhaps 3%) withdrawal rate. Looking at how close you are to your goal and your planned retirement date can be used to adjust savings rate and perhaps AA.

The real question is how well this simplistic model works compared to something more sophisticated. I'd bet most people do something like this and somehow manage to survive.

Damodaran's papers are http://people.stern.nyu.edu/adamodar/Ne ... apers.html Were you refering to Equity Risk Premiums (ERP): Determinants, Estimation and Implications at http://papers.ssrn.com/sol3/papers.cfm? ... id=2238064 ?
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by grayfox »

With so few data points, you can run random numbers and easily get R^2 = .20 or .30

To see if I was talking through my hat, I generated two sets of 14 random numbers and looked at the correlation. Anyone can duplicate this exactly.

Code: Select all

> set.seed(1234)
> for (i in 1:10) {
+ cat(cor(100 * rnorm(14, mean=0.06, sd=0.02), 100 * rnorm(14, mean=0.06, sd=0.08)), sep="\n")
+ }
0.1547621
0.1298075
-0.0539934
0.1588261
-0.05893308
0.2866594
-0.436904
0.3525912
-0.1364081
-0.2804018
In just 10 cases I see four of them have magnitude greater than 0.2799.
So 0.2799 for 14 points is not that impressive.
Maybe someone knows how to test the null hypothesis the result is purely random.

Is there a difference between correlation and regression R^2 ? They must be similar. They both go from -1 to +1 and show the strength and direction of a linear relationship.

Now I am not saying that the return has _nothing_ to do with the valuation like starting dividend yield. Just that it is quite weak.
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by larryswedroe »

Richard
Even in your example how do you know how much to adjust based on what return you need if you don't estimate returns? Impossible. You have to know how much to adjust.
And I would add not 4% as that is too high today for a 65 year old because yields are lower and valuations higher. 3% is the new 4%, at best since you have virtually no real return on bonds.That's another example of not using historical data
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by richard »

larryswedroe wrote:Richard
Even in your example how do you know how much to adjust based on what return you need if you don't estimate returns? Impossible. You have to know how much to adjust.
And I would add not 4% as that is too high today for a 65 year old because yields are lower and valuations higher. 3% is the new 4%, at best since you have virtually no real return on bonds.That's another example of not using historical data
Larry
You guess how much to adjust. For a related concept, see Taylor's posts on how much to withdraw. For example, "We simply withdrew what we needed and kept an eye on our portfolio balance. Most years our balance went up and we spent the money on vacations, luxuries and charity. When our balance went down we tightened our belt and economized."

Many people use simple rules of thumb, such as save 15%, have a target based on planned spending and 3% or 4% withdrawal rate, and adjust as they go based on perception of whether they're on track. I'm not clear how one can run empirical tests on this, but I haven't seen any empirical tests based on valuations, MCS, etc. Unexpected changes in income, planned spending, etc. introduce a large degree of uncertainty into the process, likely enough to make the difference between rules of thumb and more formal models not as large as might be imagined.

My sense is most people here use (or plan to use) 4%, which I agree is too high. 3% would be better for the reasons you cite. Personally, I'm under 2%, but that may be too cautious.
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by swaption »

grayfox wrote:Just yesterday, I was looking at pretty much this exact question. But instead of backtesting, I was looking at the Dividend Discount Model DDM from a purely theoretical viewpoint. To cut to the chase, I concluded that the DDM was useful for understanding how price, dividend, growth rate and expected return are all tied together. But the DDM makes a poor forecasting model of anything that an investor might be interested in because we don't know anything reliably.
Yes, this is the way I see it. Not sure why we need to be on this never ending quest to explain the unexplainable, in this case 10 year forward returns. In some way in the process tainting the wonderfully elegant DDM, which almost by definition cannot be wrong. In my mind the only concensus that there seems to be in terms of these types of forecasts is to offer some rough parameters around expectations. For instance right now, the DDM or any number of other metrics would convey expecations of relatively low expected returns.
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by larryswedroe »

Richard, so you think that guessing without any basis for that is better than making an informed estimate? Is that what you are really saying?
I'd add that a simple rule like 3% is fine ONCE you are there for it will likely work for most AAs (though perhaps not the most extremes)
But that isn't helpful at all until you get there as you need to estimate the rate of return you need to earn to hit "the number" and then what AA you need to achieve that return
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by SimpleGift »

swaption wrote:In my mind the only concensus that there seems to be in terms of these types of forecasts is to offer some rough parameters around expectations. For instance right now, the DDM or any number of other metrics would convey expectations of relatively low expected returns.
You've expressed it beautifully, swaption. "Rough parameters around expectations" is what these simplified forecast models are useful for, in my view, and not necessarily an exact number that is the holy grail. Also, by looking at exogenous factors (CAPE market valuations, global investment and saving rates, projected GDP growth around the world, etc.), one can put these forecast numbers into context to see if they sound reasonable or perhaps need to be adjusted up or down a bit. It's as much art as science.

And as you say, the simple forecast models (and most of the exogenous factors that I'm seeing today) point to expected asset returns going forward that are much lower than the historical averages.
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by siamond »

grayfox wrote:Is there a difference between correlation and regression R^2 ? They must be similar. They both go from -1 to +1 and show the strength and direction of a linear relationship.
For sure. R2 is correlation to the power of two. Simple as that. In Excel, I use the CORREL function, then multiply it by itself.

To provide a reference, Wikipedia says:
Similarly, in linear least squares regression with an estimated intercept term, R2 equals the square of the Pearson correlation coefficient between the observed and modeled (predicted) data values of the dependent variable.
grayfox wrote:In just 10 cases I see four of them have magnitude greater than 0.2799.
So 0.2799 for 14 points is not that impressive.
Well, at least in my own Excel sheet, I often have higher R2 numbers, but no matter. Overly focusing on R2 might be missing a bit the point of what I believe SimpleGift is saying. Take a very jaggy trajectory (plenty of those in finance!). Take a linear regression series of such jaggy trajectory. The correlation (or R2) between the jaggy line and the linear regression will be very poor. And yet, the linear regression does provide a lot of interesting information... Sure, expected fundamental returns are not a straight line over time, but they are quite smooth compared to the hectic reality of what happens for real, one of SimpleGift's charts shows that clearly, it's much more a smoothed expected trajectory than an exact prediction. So the R2 ain't that great, notably in times of speculative turbulence. And yet, the information remains meaningful, and valuable to some. At least, I think so... And Jack Bogle himself seems to be a believer! :wink:
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by SimpleGift »

backpacker wrote:The problem: Using the historic average 140-year growth rate as the projected growth rate in effect gives your hypothetical historical investor a crystal ball. How would I, for example, go about figuring out the average growth rate for the US economy between now and 2150?
No doubt the exact earnings growth rate is unknown in the future. However, assuming continued growth in GDP and in GDP-per-capita (an assumption that one almost has to make to invest in stocks to begin with), the long term growth of earnings-per-share should follow. In fact, this is what the historical record has shown (chart below).

We can quibble about whether the real earnings growth rate will be, say 1.5% or 1.7% in the future, but we can agree that it most likely will be positive over the long-term (barring global catastrophe) — and, in the end, the difference of a few tens of a percent will not be that significant to the rough estimates of expected return that these simplified forecast models produce.

Image
Source: Research Affiliates
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by richard »

Larry, I'm asking if there is any evidence that projecting returns with an accuracy of +/- 8% improves on starting out with some arbitrary model (e.g., save 15% of income) and adjusting based on whether you're on track.

Is there any empirical work at all in this area (not evidence regarding the accuracy of models, evidence regarding planning techniques and how they play out)?

"It is obvious that" does not count as evidence :D
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by grayfox »

siamond wrote:
grayfox wrote:Is there a difference between correlation and regression R^2 ? They must be similar. They both go from -1 to +1 and show the strength and direction of a linear relationship.
For sure. R2 is correlation to the power of two. Simple as that. In Excel, I use the CORREL function, then multiply it by itself.

To provide a reference, Wikipedia says:
Similarly, in linear least squares regression with an estimated intercept term, R2 equals the square of the Pearson correlation coefficient between the observed and modeled (predicted) data values of the dependent variable.
No wonder they call it R-Squared, because it R^2. :oops:

Probably no one cares, but just to close the loop on this question: how often two random set of 14 points will have R^2 > 0.2799

Code: Select all

> set.seed(1234)
> count <- 0
> n <- 10000
> for (i in 1:n) {
+     R <- cor( 100 * rnorm(14, mean=0.06, sd=0.02), 100 * rnorm(14, mean=0.06, sd=0.08) )
+     R2 <- R^2
+     if (abs(R2) > 0.2799) { count <- count + 1 }
+ }
> 100 * count/n
[1] 5.31
It looks like about 5% of the time.

Maybe about a 5% chance that the correlation is just random, so there his probably some explanation of returns in the model.
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by SimpleGift »

grayfox wrote:Probably no one cares, but just to close the loop on this question: how often two random set of 14 points will have R^2 > 0.2799

It looks like about 5% of the time.
Thanks, grayfox, that's good to know.

But don't forget that a simple average of the Dividend Growth Model and the CAPE earnings yield produced a better forecast, where R^2 = 0.40. And also that forecasts of expected bond returns based on current yields are R^2 = 0.90. So for a 50% stock/50% bond portfolio:
  • (50% x 0.40) + (50% x 0.90) = 0.65, as an R^2 for the entire portfolio.
That's not too bad a level of precision for forecasting one's overall portfolio returns.
Last edited by SimpleGift on Tue Oct 28, 2014 1:34 pm, edited 1 time in total.
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by larryswedroe »

Richard
All I know is that the research shows that if you look at all the typical suspects everyone finds that CAPE is about best and current valuation is very close
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by staythecourse »

Simplegift wrote:was added to the real earnings-per-share growth rate over the entire 140-year period (1.7%)
As mentioned already by several posters this alone defeats the purpose of the whole analysis.

Simplegift... Has anyone done the same using info. that might have been available at that time of calculation for 10 year future return? Maybe using the starting dividend yield and last 10 years of EPS growth to see how predictive it was? Maybe doing that analysis with rolling 10 year returns will give more sample size as well.
I would love to see if that R2 is any different.

In the end I don't see trying to predict future stock returns any different then going to a psychic down the street and looking at their crystal ball. There just is not enough predictive power after DECADES of folks trying to show there is any difference then just asking a psychic.

The interesting thing is with the some of the charts above going back to late 1800's to current there has only been 2 or so decades stocks have NOT given a real return of at least 4%. That is pretty darn good!!

Good luck.
"The stock market [fluctuation], therefore, is noise. A giant distraction from the business of investing.” | -Jack Bogle
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by staythecourse »

I do want to remind folks that Vanguard's paper did show R2 >0.8 when you focused on just the extremes of P/E ratios. Somehow I thought that the R2 was>0.8 if one had P/E <10 or >25. Anything in between did not mean much. That info. is possibly useful to implement in one's IPS.

Good luck.
"The stock market [fluctuation], therefore, is noise. A giant distraction from the business of investing.” | -Jack Bogle
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by Clearly_Irrational »

All the models suck, but they're still better than just throwing darts. Normally the two questions you want to answer are "Am I saving enough" and "How much can I spend". Putting some sort of boundaries around those numbers is helpful in getting you at least in the right ballpark. Generally the models won't tell you if your plan is good, but they will tell you if your plan is stupid. Personally I prefer to start with a non-stupid plan but YMMV.
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by Clearly_Irrational »

staythecourse wrote:I do want to remind folks that Vanguard's paper did show R2 >0.8 when you focused on just the extremes of P/E ratios. Somehow I thought that the R2 was>0.8 if one had P/E <10 or >25. Anything in between did not mean much. That info. is possibly useful to implement in one's IPS.
That's one of the ways I use the information, as a market irrationality indicator.
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by SimpleGift »

staythecourse wrote:Simplegift... Has anyone done the same using info. that might have been available at that time of calculation for 10 year future return? Maybe using the starting dividend yield and last 10 years of EPS growth to see how predictive it was? Maybe doing that analysis with rolling 10 year returns will give more sample size as well.
I would love to see if that R2 is any different.
I'm not aware of any such analysis. The problem is that, while GDP growth and GDP-per-capita growth rates have been relatively stable over long periods, the earnings-per-share growth rates are more noisy (see the growth chart just upthread). That's why the model uses the long-term average earnings growth rate (1.7% or thereabouts) — because the 10-year (or even 20-year) growth rates are just too variable. I can't see how using them would add precision to the model.
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by siamond »

Simplegift wrote:
staythecourse wrote:Simplegift... Has anyone done the same using info. that might have been available at that time of calculation for 10 year future return? Maybe using the starting dividend yield and last 10 years of EPS growth to see how predictive it was? Maybe doing that analysis with rolling 10 year returns will give more sample size as well.
I would love to see if that R2 is any different.
I'm not aware of any such analysis. The problem is that, while GDP growth and GDP-per-capita growth rates have been relatively stable over long periods, the earnings-per-share growth rates are more noisy (see the growth chart just upthread). That's why the model uses the long-term average earnings growth rate (1.7% or thereabouts) — because the 10-year (or even 20-year) growth rates are just too variable. I can't see how using them would add precision to the model.
Agreed with SimpleGift that EPS growth is way too noisy to use past 10 or 20 years. But I also agree with staythecourse that one shouldn't use information not available at the time. My own model uses a rolling average of XX (I settled on 50) years of earnings growth till the year where the prediction is made. But I don't use EPS. I use E10 (actually E25), as was suggested in one article I read, and this does help improve the results a bit. Fact is earnings are wild and need to be seriously tamed for such forecast...

If you folks are interested, I can simplify my Excel sheet, just hone on the model SimpleGift described and post it. This isn't rocket science. Not today though... And I doubt this will change anybody's opinion. It's definitely a bit of dark arts for a pretty approximate result. Whether you deem it useful or not is a judgment call.
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by TimesAWastin »

How do the results correlate if you start offsetting the start point by a year? The decade from 1996-2005 may look very different than the decade from 1990-1999, for example.

Set 1 is 1871-1880,1881-1890,...
Set 2 is 1872-1881,1882-1891,...
And so on
Stock goes up, stock goes down. Stock goes up, stock goes down. -- Homer J. Simpson (paraphrased)
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by SimpleGift »

larryswedroe wrote:All I know is that the research shows that if you look at all the typical suspects everyone finds that CAPE is about best and current valuation is very close...
Agree that CAPE earnings yield is a useful metric for forecasting — but I'd point out that Antti Ilmanen (as you know, the fellow who literally wrote the book, Expected Returns) has been using an average of the CAPE earnings yield and the Dividend Growth Model in his recent writings. Here's what he wrote in the linked Economist article (my bold):
Antti Ilmanen wrote:The "60/40 expected real return" is the forward-looking long-run real return of a 60/40 U.S. stock/bond portfolio. Stocks' forward-looking real return is proxied by an average of two measures: (i) smoothed earnings yield, or the inverse of the Shiller P/E and (II) the sum of dividend yield and 1.5% (a proxy for long-run growth rate in earnings per share). Bonds' real yield is the difference of the 10-year Treasury yield and a measure of expected inflation over the next decade. Inflation expectations are proxied by an average of several survey forecasts; before these became available in 1978, statistical estimates are used.
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by larryswedroe »

simplegift
Note I pointed out that what Illmanen does is exactly what we do (:-))

My personal problem with the Gordon model is that you need to make adjustments to it because far fewer companies are paying dividends than ever before, and at least in theory that means earnings growth should be higher (M&M showed div policy should be irrelevant long ago).

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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by backpacker »

Simplegift wrote:
backpacker wrote:The problem: Using the historic average 140-year growth rate as the projected growth rate in effect gives your hypothetical historical investor a crystal ball. How would I, for example, go about figuring out the average growth rate for the US economy between now and 2150?
No doubt the exact earnings growth rate is unknown in the future. However, assuming continued growth in GDP and in GDP-per-capita (an assumption that one almost has to make to invest in stocks to begin with), the long term growth of earnings-per-share should follow.
You could be right. The point is that it's cheating to give a model information about future returns. Try running the regression using only rolling historic earnings growth to and see how well it works. It might work wonderfully. It might work terribly. Without checking the actual data, there's no way to know.
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by backpacker »

larryswedroe wrote: As to no value, there is simply no logical way to determine an AA without having expected returns. In fact without them there is no reason to invest in stocks period.
The alternative is using the international historic ERP. DMS estimate the historic premium to 10 year government bonds to be 3.5%. With current yields of 2.3%, that's 5.8% nominal. Knock off 2% for inflation and you get 3.8%. But investors shouldn't use 3.8% because that number comes with wide error bars. I use 2% (like Zvi Bode) to leave room for error. I don't see why we need anything else. If your plan doesn't work with a 2% ERP, save more money or plan to retire later.
larryswedroe wrote: The fact that you have an rsquared as high as 40 means that there is valuable information there. It's not like it's 0 or .1
The point about DMS is that a predictive tool that looks pretty good in one country can perform miserably out of sample. I've attached the chart for dramatic effect. Note that the R2 is pushing .5 in the US. Take that act out of sample, though, and it performs miserably. The burden is on the advocates of PE10 or any other predictive tool to show that it doesn't suffer a similar fate.

Image
Last edited by backpacker on Tue Oct 28, 2014 11:33 pm, edited 1 time in total.
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by backpacker »

siamond wrote:[ Agreed with SimpleGift that EPS growth is way too noisy to use past 10 or 20 years. But I also agree with staythecourse that one shouldn't use information not available at the time. My own model uses a rolling average of XX (I settled on 50) years of earnings growth till the year where the prediction is made. But I don't use EPS. I use E10 (actually E25), as was suggested in one article I read, and this does help improve the results a bit. Fact is earnings are wild and need to be seriously tamed for such forecast...

If you folks are interested, I can simplify my Excel sheet, just hone on the model SimpleGift described and post it. This isn't rocket science. Not today though... And I doubt this will change anybody's opinion. It's definitely a bit of dark arts for a pretty approximate result. Whether you deem it useful or not is a judgment call.
This sounds like exactly the way to do things. Do post your results if you have time!
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by at »

If a highly profitable company does not pay dividends and instead choose to buy back its own stocks with all its profits (so earning growth is zero as well), the model predicts low returns for this company. Does that make sense to you?
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by SimpleGift »

backpacker wrote:Try running the regression using only rolling historic earnings growth to and see how well it works. It might work wonderfully. It might work terribly. Without checking the actual data, there's no way to know.
As discussed upthread, the historical earnings growth rates are just too variable, even over 30- or 40-year rolling periods to be of much use. Personally, I'm not motivated to do more analysis on this just for the sake of curiosity — but it sounds like siamond has some interest and I'd encourage him to post his results. For others who may want to explore further, the Shiller data can be found here.

What I can say for sure is, as investors today in 2014, we now have over 140 years of earnings growth history for the U.S. market that suggests a century-long earnings growth rate trend of around 1.5%-1.7% real. This is ultimately all that we need today (plus the current dividend yield) for an expected equity return forecast — which can then be averaged with the CAPE earnings yield for planning purposes.
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by larryswedroe »

simplegift
As I have pointed out while we have long term earnings growth IMO you need to make adjustment, assuming a higher growth rate. Today only about 30% of companies pay dividends and the total payout rate is way down. At least in theory that should produce faster earnings growth. FWIW, that probably moves the estimated earnings growth up to say 2%.
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by SimpleGift »

larryswedroe wrote:Today only about 30% of companies pay dividends and the total payout rate is way down. At least in theory that should produce faster earnings growth. FWIW, that probably moves the estimated earnings growth up to say 2%.
Sounds good. Rick Ferri has made this same point in a different way, suggesting that one should add about 0.3% to the current dividend yield as a "buyback yield." Also, Mebane Faber has been advocating this idea for several years. It all means the same for the return forecast:
  • Dividend Growth Model
    • Current Dividend………….……..2.0%
    • Buyback Yield………….…………0.3%
    • Real Earnings Growth Rate…….1.7%
    Expected Real Stock Return……..4.0%

    CAPE Earnings Yield (1/25)…….4.0%
It's fairly rare that both forecast models end up with exactly the same estimate! Thanks for all your help.
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by larryswedroe »

simple gift
Yes buybacks help but even without them more earnings retention should lead to faster earnings growth. More sure though with buybacks
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by TJSI »

We have been down this path before but I will try again. Adding a buyback yield to the Gordon formula produces a nonsense number. Buybacks are investments.

If buybacks are good in general, their effect will show up in an increased earnings or dividend growth rate. Their effect is already included in the formula for good or bad.
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Re: A Backtest of the Dividend Growth Model, 1871-2010

Post by SimpleGift »

TJSI wrote:If buybacks are good in general, their effect will show up in an increased earnings or dividend growth rate. Their effect is already included in the formula for good or bad.
The problem arises when we use a long-term earnings growth rate derived from 140 years of history and then also try make allowance for share buybacks and lower payouts, which are a recent phenomenon since 1982 (chart below). The recent trend for lower payouts and higher buybacks is not adequately reflected in either the 140-year earnings growth rate or the current dividend yield, as I understand it.

To compensate, some folks recommend bumping up the long-term earnings growth rate (from 1.7% to 2.0%), while others suggest adding a "buyback yield" of about 0.3% to the current dividend yield. Either way, the effect on the Dividend Growth Model is exactly the same.

Image
Source: Yardeni Research
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