JR writes in essence that minor discrepancies among multiple sources of data are on the same order of magnitude as the difference between multiplicative and additive calculations. So don't sweat it.
I'll decompose that because I disagree with two out of three parts:
1. Data sources will be inconsistent. While true, that's a problem that can be circumvented by using a single data source containing all the necessary data.
Shiller's data contains:
a. CPI-U by month - so one can calculate inflation over any period of time
b. Earnings (E) by month - so one can calculate earnings growth over any period of time
c. S&P price (P) by month - so one can calculate P/E by month and thus multiple expansion over any period of time
d. Dividends (D) by month, so one can calculate D/P (dividend rate) over any period of time.
(JR adds another source of discrepancy; for earnings growth he cites a source for the entire economy, not for the S&P 500.)
2. The order of magnitude of these discrepancies is roughly the same as that of percentage differences when comparing multiplicative and additive results.
That is, if one factor adds 3%/year and another factor adds 2%/year, we can combine them by adding and get a 5%/year gain, or we can multiple them to get (1+3%) x (1 + 2%) - 1 = 5.06%. It's just a small difference and comparable to differences introduced by using multiple data sources. Granted.
3. The percentages (which may be off slightly due to #2) are unchanged over time. For example, if one factor accounts for 2% of the gain in a year and another factor accounts for 3% of the gain in a year, the same will be true over 45 years. That is, compounding the returns doesn't change the factor impacts (here 40%:60%).
This is wrong, and this is the main point I've been driving at.
Consider inflation and multiplier expansion. For simplicity, we'll assume that no divs are paid and earnings don't grow.
Annualized rates are: Inflation 3.51% and multiple expansion 2.19% (from original column)
To allocate weights, we just take each value's percentage of the sum total.
Inflation accounts for 3.51/5.70 = 62% of the total, and
multiple expansion accounts for 2.19/5.70 = 38% of the total.
After 45 years, inflation has increased the price by (1.0351)^45 - 1 = 372%, and
multiple expansion has increase the price by (1.0219)^45 - 1 = 165%
Over 45 years, inflation accounts for 372/537 = 69% of the total, and
multiple expansion accounts for 165/537 = 31% of the total.
One cannot allocate percentage impacts by using annualized figures. Compounded over time, the larger factors loom ever larger while the smaller factors play less and less of a role. The reason for this is compounding, i.e. multiplying, rather than adding returns.
Worth a mention: None of these items obscure the general pattern. Tinker with them all, and inflation still comes out as the largest factor, followed by profits, then dividends, then multiple expansion
He looked at a 45 year period. But when we take the longer view, more than double that time, i.e. a century, the general pattern shifts. Dividends are more important than inflation.
Over 45+ years, annualized inflation is 3.51% and average dividend rate is 2.75% (I get 2.77%).
Over a century, annualized inflation is 2.77% and average dividend rate is 3.83%.
I won't bore you with the formulas, but I will make it easy for you to reproduce and check. Using Shiller's spreadsheet, here are the four expressions needed:
Jan 1976 - March 2021:
inflation =POWER(E1811 / E1268,1/45.25)-1
av div rate =SUMPRODUCT(C1269:C1811,1/B1269:B1811)/(45.25 * 12)
July 1921 - June 2021:
inflation =POWER(E1814/E614,12/1200)
av div rate =SUMPRODUCT(C615:C1814,1/B615:B1814)/(100 * 12)

I loathe dealing with Vanguard.
The last time I tried to make an XFER in, the rep kept directing me to open an online account. When I explained that I do not want to do an online account due to some recent experiences with identity theft, she proceeded to try to open an online account for me -- without really telling me what she was doing. When I figured out what she was doing, I kept asking: "please just send me a PDF form via email or regular mail". She kept saying in response "I can't do that ... and, we're trying to save you money by doing it all online"; to which I replied "I've spent over 45 minutes dealing with Vanguard today, which is taking away from my other work and thereby costing me money".
She kept refusing to help me in the way I was asking, so I finally put it her "...do you understand that I'm trying to transfer money into Vanguard -- I'M TRYING TO GIVE YOU MONEY -- and you are making it hard for me to do business with you....your way of performing this transaction is a disincentive for me doing future business with you".
She finally, finally, finally emailed me a partially filled-out PDF (something that at first she said she couldn't actually do). I never completed the transaction, and have not since transferred any more money over to Vanguard.
I really really loathe working with Vanguard. I have repeatedly directed family members away from investing with them.

But FIDO hopes you've at least thought about an exit strategy. I consider this thoughtful of them.
One may imagine the message you would have received from a RobinHood account.
"Don't you want to buy some more?" "You call yourself an investor?" "Looks like a pretty chicken s#*@ trade to our system."

Robinhood: "buy more! Don't you want to earn some confetti animations and more badges!"
[producer, to the director's earpiece]: "Because RH needs the order flow since 80% of quarterly revenue came from it."

WTF are badges? I've been using RH for more than 5 years and never heard of them.
I really don't get the hate on RH. People using the platform do benefit from PFOF in aggregate; I've also used Fidelity for 10+ years and have cumulatively saved less than $1 for "price improvements" because of their "better" execution.

@BenWP - You are mostly correct. (But it has to do with moderating potential losses on the long end.) The rationale was explained somewhat better in my comment in @davfor’s recent thread.

A short South China Morning Post article with a few examples of how these terms are being put to work by Chinese regulators. The depth, breadth, and expected duration of the crackdown somewhat surprise me. But, suspect most Chinese businesses will adapt and continue to thrive. Still have the shares of MEGMX (30% China/Hong Kong per latest report) purchased when it opened for trading in mid spring 2020. Nothing so far is making me think about selling.
Xi Jinping says Big Tech crackdown is making progress, calls for Communist Party to ‘guide’ companies

Yesterday I opened a very small short inverse position on the Dow using DOG. I fully understand the dangers inherent in such an approach. Today I get this email …
“Now that you’ve placed a trade, don’t forget about the next important step – your exit strategy.
Having a plan from the start can help you: Take potential profits if you’ve reached your target gains.
Help manage potential losses by predetermining when to sell. Setting an exit plan for your latest trade doesn’t have to be complicated and Fidelity can help. Define and set one today.”
For my inspiration …

RCTIX seems to be TF at all 5 brokerages I checked, for brevity sake: F V S TDA and E-Trade. TDA wins the Awful Award for combining a tf with a $100,000 minimum !

Meanwhile, Fidelity’s on hiring binge.
Re TRP …
- One might attribute the poor customer support to Covid restrictions. I accepted that for nearly a year before recognizing their problems were deeper seated. I’ve tried unsuccessfully to uncover if in recent years perhaps they’ve out-sourced their phone support? I ask because 10-15 years back it was fairly easy to get kicked up to a manager. And usually that resulted in substantive results - be it a direct from the top answer about operations or resolution of some personal beef. But in recent years there seemed no continuity to the phone support operations. As others may have noted, sometimes different reps appear to be working at cross-purpose.
- The “nasties” in customer support seem apart from their outstanding investing capabilities. And their stock price has soared - up about 35% YTD by one report . If you can save $$ on the customer support, that’s extra cash in the pockets of investors in the company.

You're welcome MikeW!
Just posted description of this month's updates here.
It includes Brad's latest addition to Ferguson Metrics. It's called Mega Ratio, which he describes as a consistency, risk and expense outperformance measure, similar to other adjusted return measures, like Sharpe.
He's kind enough to discuss his methodology at our next webinar, 15 September, at 10:30 am Pacific.

Vanguard got new app past 5 days
Can't do sh@t with that new apps
Probably need restore old apps until they have the kinks worked out

https://www.marketwatch.com/story/the-s-p-500-is-headed-for-5-000-says-ubs-heres-the-when-and-how-11630407516?siteid=yhoof2
The S&P 500 is headed for 5,000, says UBS. Here’s the when and how.
On the last trading day of August, stock futures are pointing higher as markets look past downbeat economic news from China and continued COVID-19 contagion worries. It’s all part of a relentless march higher for stocks that barely paused this summer.
Unless we have Gama shutting us down like Australians for few months

The FT article (OP) is dated August 25. Here’s what it states:
“But Giroux has cut the fund’s equity exposure down from about 70 per cent at the market low of 2020 to the mid-50s per cent level now …”
Lipper, which is usually pretty accurate, still has it at 70%.

Here's a thought...you might want to access the TRP site (What? There is one? Who knew?) to get the latest published stock allocations as of 07/31/21 which was (if my addition is correct) 70.4%.
https://www.troweprice.com/personal-investing/tools/fund-research/PRWCX?src=USIFundRedirect&adobe_mc_sdid=SDID=7593B66782D33635-0C1AF59A7D98C5A2|MCORGID=D15D15F354F647770A4C98A4@AdobeOrg|TS=1630353056&adobe_mc_ref=https://www.google.com/#content-portfolio
And if you are a poster/investor questioning Giroux's allocation decisions, you might want to go play a round of golf and think that through a bit.

Yes @msf, I wasn't suggesting anything nefarious or against regulations. I just think that certain fund managers might get a 5-10 minute chat or a meet up that lesser known or renowned fund managers might not AND as you noted "where the way the response is phrased conveys information that goes beyond the disclosure itself" can speak volumes. Good point and thank you.

Today the Fed (and other central banks across the globe) is part of the market.

This is a conclusion I adopted in February 2019 ( Powell Put ). It became clear to me at that point the Fed had given up on reviving traditional interest rates. The Fed and the stock market are for now co-dependent and planning to live in a somewhat lower interest rate world. The pandemic and the Fed's more inclusive employment mandate have further solidified this change. My portfolio allocation to bonds was 37% on 1/4/19. It is 25% today. That 12% difference has been allocated to higher yield stocks (3%+ YOC). (Time will report to me on the ongoing benefit of that change.)

You're welcome to attempt to calculate your own version of what the four factors contributed, over that same time period. What you will find is -
1) Once you have determined each of the four factors, and you attempt to multiply them, they will not equal the S&P 500's total return. Inconsistencies among your data sources do not permit such accuracy.
2) Thus, if you wish to complete the effort, you will be forced to make alter your results into order to make the numbers fit. These assumptions will introduce variances that will likely be as large as the difference betweent the multiplicative and additive approaches.
3) Shifting the time period that is studied by a year or two will have the same effect of changing the underlying factor results.
None of these items obscure the general pattern. Tinker with them all, and inflation still comes out as the largest factor, followed by profits, then dividends, then multiple expansion. But depending upon your choices, the individual numbers will vary.
It's an exercise with a margin of error, but that margin is not larger than the differences among the findings, assuming that the time period studied doesn't greatly change. (Except perhaps the role of profits vs. dividends.)

Does anyone suppose that manager longevity not only relates to their performance success but also to their access to businesses and company managers they've built up over the years? I tend to think that the likes of Danoff, Tillinghast, Miller, etc., etc. might have quicker or easier access to their time and insight.
I forgot to add that I had owned Fidelitys Contrafund FCNTX since roughly 1982. I was generally always pleased with its performance and saw little reason to change until it became quite massive in AUM and returns seemed to track that of the S&P500 +/- a percent or two here and there. Two years ago I sold a good chunk and invested the proceeds into BIAWX. Since then BIAWX has returned 83.82% to 47.61% for FCNTX. It has been a reasonable exchange so far.

Today the Fed (and other central banks across the globe) is part of the market. To support the stock market, quantitive easing, QE was introduced back in 2008. During the COVID-19 pandemic and the country is being locked down. The broader market fell over 30% within 2 weeks. As part of the rescue plan, the Fed cut the interest rate to near zero. In addition, they bought $80B treasury and $40B mortgage backed bonds on a monthly basis. The market responded quickly and marching upward toward recovery. By fall 2020, the recession is over.
Below is a short piece from Brookings Institute on tapering of Fed's bond buying.
https://brookings.edu/blog/up-front/2021/07/15/what-does-the-federal-reserve-mean-when-it-talks-about-tapering/

I don't know how one chooses.
Isn't that really the point? That one doesn't know, except in hindsight, whether one's manager will be there tomorrow, whether a fund's method is "solid" or will change, or even if it doesn't change whether it will continue to be successful over time or in the next bear market or whatever.
Sticking with an investment should involve continual evaluation. Is this a fund I would buy today? If not, then why am I holding it?
Out of curiosity, I ran a screen for funds that currently have a manager who has been there for at least two decades. Aside from five oddball funds without star ratings, the remaining 144 distinct funds break down as:
5 star: 10 funds, 7%
4 star: 30 funds, 21%
3 star: 50 funds, 35%
2 star: 34 funds, 24%
1 star: 20 funds, 14%
The M* "neutral" distribution is 10%/22.5%/35%/22.5%/10%. This is about as close to that as one would expect to get when pulling 144 funds out of a hat. Longevity would appear to count for nothing. Perhaps even less than nothing, given survival bias (funds that stay around for decades tend to be better performing ones, so these should have skewed toward more stars).
There are several funds in the list that I recognize. A couple are:
LLPFX, "One of the best mutual funds in history" - Jaffe, 2/6/2000. This fund, along with its sibling LLSCX have had the same managers for over three decades. Both are currently rated 1 star.
TEFQX (Firsthand e-Commerce Fund until May 2010): "[M*'s] top rated 5 star funds were all technology and telecom funds that met investors fancy 2 1/2 years ago [mid 1997]. This led to their subscribers pouring money into the Janus and Firsthand Funds". TEFQX not only survived, but is currently rated 4*.
However, Kevin Landis' Firsthand funds generally imploded. His flagship Technology Value Fund (TVFQX) was converted into a business development company, technically not even a registered investment company. That happened not as a result of the dot com bust, but as a result of the GFC years later.
This is all a long winded way of saying that I agree, one can't know how to choose. As a corollary, one can't know whether to stay the course.
Regarding Fidelity's management turnover (i.e. expectation that a new fund manager would still at the fund a few years later), late 80s/early 90s:

This is typical: A look through Fidelity's long list of equity funds finds only about six managers who have been managing the same fund for five years or more. A tenure of one to three years for one fund is much more common, though most managers have been with Fidelity longer than that, graduating from one fund to another.

June 15, 1992
https://www.sun-sentinel.com/news/fl-xpm-1992-06-15-9202140732-story.html