## Reconciling the Fama-French 5 factor model and the Discount Dividend Model

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BenS
Posts: 11
Joined: Sat Jun 25, 2022 2:02 pm

### Reconciling the Fama-French 5 factor model and the Discount Dividend Model

Dear Bogleheads,

I am attempting to really understand the relatively recent FF 5 model as compared to the 90's 3 factor model, and how both of these fit into the context of the dividend discount model. This forum has proven to have such a wealth of information, I thought it might be a good place to check.

To recap, the dividend discount model including fundamental and speculative terms is well approximated by R_total = R_dividend + R_growth + R_PE_Expansion. The more recent FF 5 model suggests that virtually all returns can be decomposed into 6 independent contribution sources:

R_total - R_f = beta_mkt * (R_mkt - R_f) + beta_smb * SMB + beta_HML * HML + beta_RMW * RMW + beta_CMA * CMA,

where the five betas are the amount of exposure to each risk factor, and R_f is the risk free rate. For a total market fund such as VTI, for example, I can write R_mkt = R_dividend + R_growth + R_PE_Expansion, since all betas except beta_mkt are zero. Over the last decade R_PE_Expansion has been large and not showing signs of mean version since the GFC.

Can a similar DDM decomposition be applied to SMB, HML, RMW, CMA? Has someone already done this? If so, what are the R's like?

Second line of questioning: With the inception of the new model, I also appreciate that:

(i) SMB has been generally small, and many experts question if it even exists/how relevant it is. Similarly,
(ii) the newly introduced RMW factor seems to have been adding a significant contribution to returns going back to the 90's, and
(iii) CMA and HML are very highly correlated ~.0.8 correlation coefficient.

Given these facts, all things being equal, it seems to me that if one expects the FF 5 factor model to describe returns going forward, then beta_mkt, beta_RMW, and beta_HML/CMA would be the only three factors worth pursuing in a portfolio. Am I missing something here? Also, with the existence of more ETFS passively and actively pursuing the RMW factor will it get arbitraged away?

I look forward to any thoughts or guidance which you can offer.

Cheers,

Ben
rkhusky
Posts: 13107
Joined: Thu Aug 18, 2011 8:09 pm

### Re: Reconciling the Fama-French 5 factor model and the Discount Dividend Model

BenS wrote: Thu Aug 04, 2022 10:13 pm Dear Bogleheads,

I am attempting to really understand the relatively recent FF 5 model as compared to the 90's 3 factor model, ...
For this portion, I recently calculated the following (PV=portfoliovisualizer.com):
rkhusky wrote: Wed Aug 03, 2022 8:35 am Below are some R^2 values from PV for different portfolios using different factor models. The portfolios are large growth (VIGRX), large value (VIVAX), small growth (VISGX), and small value (VISVX). Time period is Jun 1998 - Jun 2022, which is constrained by the lifetimes of VISGX and VISVX. Monthly returns. FF Research Factors.

R^2 for CAPM, 3-factor, 4-factor, 5-factor:
VIGRX: 92.4%, 96.1%, 96.2%, 96.6%
VIVAX: 86.5%, 95.1%, 95.8%, 95.1%
VISGX: 79.1%, 92.3%, 92.8%, 92.9%
VISVX: 76.8%, 93.8%, 94.2%, 95.2%
I would be interested in a tool (like PV) where one could choose the factors to include in the factor model and compute R^2 values for the model applied to various portfolios. For example, one could then choose Market, CMA, and RMW, and see how that model works.

You should be able to create your own factors around dividends, by separating stocks into high dividend payers and low dividend payers, high dividend growth and low dividend growth, high PE expansion and low PE expansion. You can try using 2 bins or 3 bins. Then compute the difference in returns between the two groups and compute the regression ala Fama/French.
JoMoney
Posts: 13927
Joined: Tue Jul 23, 2013 5:31 am

### Re: Reconciling the Fama-French 5 factor model and the Discount Dividend Model

The Fama-French "factors" are "risk factors" they theorize that these measure priced "risk" in an efficient market model.
If you believe the market is efficiently pricing "risk premiums" then trying to discount the cash flows via DDM is irrelevant for an individual, the market has already efficiently priced that commensurate to the risk, so investing to your risk preference as measured by the modeled risk factors is the only relevant thing to look at (if you believe the model.)
"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks." - Benjamin Graham
dbr
Posts: 41904
Joined: Sun Mar 04, 2007 9:50 am

### Re: Reconciling the Fama-French 5 factor model and the Discount Dividend Model

I am a pure amateur at this so the following could be pure baloney.

1. The dividend discount model attempts to reflect processes that actually occur in the market. The inclusion of a speculative component amounts to a fudge factor. One might question whether that model has any explanatory or predictive power at all. Someone would have to comment on that.

2. Factor models appear to me to be data mining of relationships that might occur in happenstance data. That does not mean they are not real. The explanatory power is high by definition. Whether there is predictive power would have to be discussed on the merits. Correlations can persist and correlations that are actually causes should persist. Understand that there are rationales for certain factors to reflect a real process. I don't know enough to talk about that.

I do have a hard time with the identification of factors with risk. It is easy enough to say that by risk we simply mean that which is correlated with return, or, mathematically, are terms that in a regression increase the explanatory power for expected return. In what way the identified factors are actually risk is above my pay grade. Remember in speaking of risk one must identify the "X" in "risk of X."

I have no idea how to relate the DDM to factors, but the idea that each factor should be able to be expressed broken down by a DDM model as the process for it would seem plausible.

I doubt this is that helpful but it is my take.

I would think that the accomplished academics in investment and finance would have a tutorial on this somewhere, but maybe it is so elementary that doing such a thing seems unnecessary. I know in my field, physics, a lot of what is done in first courses is present how one formulates knowledge in the field. It's terrible to talk about something without the basics for how one talks about that thing in hand.
yog
Posts: 563
Joined: Wed Jan 15, 2020 12:57 pm

### Re: Reconciling the Fama-French 5 factor model and the Discount Dividend Model

There are a few factor-based strategies that incorporate return of shareholder capital into the the rest of the factors.

OSAM is one who applies factor themes to their strategies as outlined here, and I've put in the key graphic for reference:
https://osam.com/Philosophy-and-Process

The last theme includes buybacks as well as dividends as part of total shareholder yield. They go into depth on the history of shareholder yield in this article:
https://www.osam.com/Commentary/the-fac ... lder-yield
nedsaid
Posts: 16451
Joined: Fri Nov 23, 2012 12:33 pm

### Re: Reconciling the Fama-French 5 factor model and the Discount Dividend Model

Higher dividends are related to both Value and Low Volatility. That is as much as I can help you at this time.
A fool and his money are good for business.
Logan Roy
Posts: 267
Joined: Sun May 29, 2022 10:15 am

### Re: Reconciling the Fama-French 5 factor model and the Discount Dividend Model

BenS wrote: Thu Aug 04, 2022 10:13 pm Second line of questioning: With the inception of the new model, I also appreciate that:

(i) SMB has been generally small, and many experts question if it even exists/how relevant it is. Similarly,
(ii) the newly introduced RMW factor seems to have been adding a significant contribution to returns going back to the 90's, and
(iii) CMA and HML are very highly correlated ~.0.8 correlation coefficient.

Given these facts, all things being equal, it seems to me that if one expects the FF 5 factor model to describe returns going forward, then beta_mkt, beta_RMW, and beta_HML/CMA would be the only three factors worth pursuing in a portfolio. Am I missing something here? Also, with the existence of more ETFS passively and actively pursuing the RMW factor will it get arbitraged away?
There's a good piece from Rob Arnott that I think elucidates this somewhat:

To Win with “Smart Beta” Ask If the Price Is Right
The high past performance of many of the increasingly popular factor tilt and so-called smart beta2 strategies came, in large measure, from rising valuations. These excess returns are an “alpha mirage” attributable to the strategies’ becoming more expensive relative to the market. Even the statistical significance of past performance was an illusion driven by rising relative valuation levels! Today, only the value category shows some degree of relative cheapness, precisely because its recent performance has been weak.

Product proliferation in factor investing and “smart beta” create two interconnected risks. First, few if any products will be introduced without having wonderful historical returns. In many cases, these returns are a consequence of rising valuations. Basically, in product creation our industry is data mining on past performance. This selection bias creates an illusion of high past alpha that often disappears when we subtract the effect of rising relative valuations. The alpha mirage creates implausible expectations for investors, who are disappointed when realized returns almost inevitably fall short, and they switch strategies, typically at a substantial cost.
https://www.researchaffiliates.com/publ ... e_is_right

So Asness poured a lot of cold water on SMB (being a result of unreliable historic data, etc.), Arnott here (this was from 2016) made me question RMW. I think a big problem is that there are macroeconomic trends that exert a great influence on different kinds of businesses, and some of these macro cycles play out over very long periods (70-100 years). So when look at data only going back so far, we may just be seeing a small section of a curve of something more fundamental going on. And as we go further back, we run into these problems with the reliability of data, and markets being less efficient capital allocators.

So I'd really echo Bogle, in saying that the best way to increase market returns is to increase market exposure. And I think the best potential market inefficiency to concentrate on is reducing risk. Put these two together, and you get the basis for the endowment model, the medallion fund, bluecrest, risk parity and all weather, etc.