Author Topic: Buffett's 10K -> 51M S&P calculation seems wrong  (Read 1898 times)

Graham Osborn

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Buffett's 10K -> 51M S&P calculation seems wrong
« on: May 07, 2018, 07:24:48 AM »
Does anyone get Buffett's math at the annual meeting about the S&P return vs gold since 1942? He says that 10K invested in the S&P500 in 1942 would be worth 51M today. That would work out to about 12% compounded annually, which is definitely wrong. I don't have detailed data going back to 1942 for the S&P, but for the Dow that 10K would have turned into 2.6M (7-8% compounded annually). That sounds about right for all 3 of the major indices, although the IXIC has outperformed somewhat.

Buffett's gold calculation (10K -> 400K) works out to a rate of 5% compounded annually for gold, which looks about right.


globalfinancepartners

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Re: Buffett's 10K -> 51M S&P calculation seems wrong
« Reply #1 on: May 07, 2018, 07:31:06 AM »
Its the difference between dividends reinvested and compounded, vs not.  Annualized S&P return is something like 8% since 1942, but with dividends reinvested, compounding, it comes a lot closer to 12%

https://dqydj.com/sp-500-return-calculator/

Graham Osborn

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Re: Buffett's 10K -> 51M S&P calculation seems wrong
« Reply #2 on: May 07, 2018, 08:07:48 AM »
Its the difference between dividends reinvested and compounded, vs not.  Annualized S&P return is something like 8% since 1942, but with dividends reinvested, compounding, it comes a lot closer to 12%

https://dqydj.com/sp-500-return-calculator/

Thanks, I missed dividends.  Now, the SPXTR has returned about 10% annually since 1988 vs 8% for the SPX.  One will note that the S&P dividend yield was much higher in earlier times:
http://www.multpl.com/s-p-500-dividend-yield/

However, there are some major problems with the assumptions in this calculator:
1. the dividends are not taxed before reinvestment
2. transaction costs for buying a couple shares of an S&P500 ETF each month (or each year) would be a high % of the total
3. it's a bit hard to see how the dividend yield is being applied in this calculator, since the dividends received by the investor on his existing shares would be determined by his purchase price and not by the dividend yield for new purchasers in a given year - only the newly purchased shares would have that yield

I have to admit I am highly skeptical that dividends alone can increase the annualized return from 8% to 12% (a 50% increase).  Something doesn't smell right here.
« Last Edit: May 07, 2018, 08:19:01 AM by Graham Osborn »

Cigarbutt

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Re: Buffett's 10K -> 51M S&P calculation seems wrong
« Reply #3 on: May 07, 2018, 08:23:52 AM »
The 10k to 51M example implies a +/- 11,9% return.
A recent video of Mr. Buffett with a more specific example (see below) with 114,75$ invested in Q1 1942 with an expected value of 440K would imply a +/- 11,3% return.
https://www.youtube.com/watch?v=dphm5WzJRTU
From another site (see below), one gets 11,7% CAGR total return.
http://www.moneychimp.com/features/market_cagr.htm

To paraphrase Sir John Templeton, if you're pessimistic, don't be too often or for too long. :)


The limitations about taxes, transaction costs are valid but, like you mention, less so now since dividend yields are lower (or are prices too high?).
Still you can see the effect of dividends on the margin as an extra % of return (even if you have to adjust down for limitations).
Just remember the tables that show what happens if you change your CAGR by only 1 or 2% over long periods. The final value numbers get to be very different.

Interesting piece on the contribution of dividends (not dealing with limitations described though).
https://www.gafunds.com/wp-content/uploads/2012/11/imdf_WhyDividendsMatter.pdf
« Last Edit: May 07, 2018, 08:30:42 AM by Cigarbutt »

abyli

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Re: Buffett's 10K -> 51M S&P calculation seems wrong
« Reply #4 on: May 07, 2018, 08:38:06 AM »
Does anyone get Buffett's math at the annual meeting about the S&P return vs gold since 1942? He says that 10K invested in the S&P500 in 1942 would be worth 51M today. That would work out to about 12% compounded annually, which is definitely wrong. I don't have detailed data going back to 1942 for the S&P, but for the Dow that 10K would have turned into 2.6M (7-8% compounded annually). That sounds about right for all 3 of the major indices, although the IXIC has outperformed somewhat.

Buffett's gold calculation (10K -> 400K) works out to a rate of 5% compounded annually for gold, which looks about right.

He said from 1776...

Graham Osborn

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Re: Buffett's 10K -> 51M S&P calculation seems wrong
« Reply #5 on: May 07, 2018, 10:35:45 AM »
He said from 1776...

The first stock exchange wasn't founded in the US until 1790.  And the S&P wasn't created until 1923.
« Last Edit: May 07, 2018, 10:37:43 AM by Graham Osborn »

KCLarkin

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Re: Buffett's 10K -> 51M S&P calculation seems wrong
« Reply #6 on: May 07, 2018, 10:51:27 AM »
Does anyone get Buffett's math at the annual meeting about the S&P return vs gold since 1942? He says that 10K invested in the S&P500 in 1942 would be worth 51M today. That would work out to about 12% compounded annually, which is definitely wrong. I don't have detailed data going back to 1942 for the S&P, but for the Dow that 10K would have turned into 2.6M (7-8% compounded annually). That sounds about right for all 3 of the major indices, although the IXIC has outperformed somewhat.

Buffett's gold calculation (10K -> 400K) works out to a rate of 5% compounded annually for gold, which looks about right.

Somehow, WEB never gets these things wrong.

- He chose May 11, 1942 as the start date. This was a significant bear market low (due to WW2). The dow was at the same level first seen in 1905. If you use calendar years, you will get lower result.
- Dividend yields were extremely high during these years. ~8.5% in May 1942 (http://www.multpl.com/s-p-500-dividend-yield/table?f=m)


KinAlberta

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Re: Buffett's 10K -> 51M S&P calculation seems wrong
« Reply #7 on: May 07, 2018, 01:07:04 PM »
Paying taxes owing out of my salary for those reinvested dividends would be a struggle.  ;-)

Itís always easy to get very rich reinvesting everything in the stock market - when you do it on paper for propaganda purposes.  Itís a bit tougher in the real world.


KinAlberta

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Re: Buffett's 10K -> 51M S&P calculation seems wrong
« Reply #8 on: May 07, 2018, 01:08:11 PM »
$52 million! Paying taxes owing out of my salary or pension for those reinvested dividends would be a struggle.  ;-)

Itís always easy to get very rich reinvesting everything in the stock market - when you do it on paper for propaganda purposes.  Itís a bit tougher in the real world.

Dynamic

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Re: Buffett's 10K -> 51M S&P calculation seems wrong
« Reply #9 on: May 15, 2018, 01:32:31 AM »
I have to admit I am highly skeptical that dividends alone can increase the annualized return from 8% to 12% (a 50% increase).  Something doesn't smell right here.

Skepticism is to be applauded, as unlike cynics, true skeptics are willing to follow wherever the evidence leads (adjusted for prior plausibility).

In this case, the boost from dividend reinvestment matches a lot of similar studies.

One that is regularly repeated and updated and believed to have sound methodology is the UK Equity Gilt Study (currently sponsored by Barclays and published since 1956) which evaluates Equities versus UK Government Bonds (known as Gilts) in inflation-adjusted terms since 1899 and US data since 1925.

The 2016 version shows UK real returns since 1899 on page 58 and US real returns since 1925 on page 63, along with inflation, which you can add back to get nominal returns.

p61 talks about the importance of reinvestment of dividends or coupons/interest received. Figures 10 and 11 are quite astounding, showing the effect since 1899 of reinvesting dividends.

p66 does the same for US returns.

The general gist is that typically in the UK, the capital-only real return is a little under 4% and the real return with dividends reinvested is about 8% in the very long term, so reinvesting dividends over the whole period has led, on average to approximately doubling the annual real rate of return, and compounded over so many decades results in something like 1000x more capital being accumulated.

Lately, both US and UK markets have seen somewhat higher prices and reduced dividend rates, especially the US with a shift to increasing buybacks in the last decade or two, which ought to lower the dividend reinvestment effect and increase the capital-only return.

I track the S&P500 and its Total Return version SP500TR since around 1999, and I also track the FTSE100/FTSE100TRI, plus the FT All Share and its Total Return Index (which I can usually find only every 6 months, but which I estimate live using an assumed dividend effect).

1999-12-31 S&P500=1469.25, SP500TR=2021.40
2017-12-31 S&P500=2673.61, SP500TR=5212.76

18-year CAGR S&P500=3.38% (capital only), SP500TR=5.40% (reinvested without tax), therefore dividend effect = 2.02% (geometric), arithmetic average div eff = 2.07%
18-year overall return of SP500 = +132.88%, SP500TR = +221.98%, Dividend Reinvestment Effect = +89.10%

I have similar numbers for FTSE100 (approximated due to missing Total Return data from first 4 years):
18-yr CAGR FTSE100=0.58% (capital only), FTSE100TRI=4.51%, dividend effect = 3.93% (both geometric and arithmetic average)
18-yr overall return of FTSE100 = +10.93%, FTSE100TRI = +121.12%, Div Reinv Effect = +110.19%

18-yr CAGR of FT-All Share = 1.48%, FTAS-TRI = 4.94%, Div eff = 3.46% (geom), 3.49% (arith)
18-yr overall return FTAS = +30.22%, FTAS-TRI = +138.10%, Div Reinv Effect = +107.88%

(Much UK data sourced from http://siblisresearch.com/data/ftse-all-total-return-dividend/)

I have held some stocks bought at reasonable yields with growing dividends, e.g. HLMA (Halma plc) bought at 136p (an 8.5% FCF yield) in Oct 2001 returned me about 80%+ of my purchase price in dividends before I sold at about 838p in Feb 2016. That's substantial dividend contribution, much of it I wasted on bad investments where the moat had eroded.

Berkshire on the other hand has not paid a dividend since I bought in July 2003, but has reinvested profits satisfactorily internally and compounded at 9.81% (measured in USD) versus 9.22% for the SP500TR, giving $4.01 for every $1.00 invested 15 years ago versus $3.70 from the S&P500 Total Return Index.
 
In GBP the same return was £4.71 for every pound invested (11.02%), versus £4.35 for the S&P500TR converted to GBP (10.43%), again a 0.59% advantage to BRK.B.
My actual XIRR (in GBP) from my various purchases and sales of BRK.B has been 11.97%. Were it not for a temporary sale that cost me only 3.65% over about 8 months before I repurchased, my counterfactual XIRR would have been 11.75%, and had I held all my BRK.B instead of selling 27.7% of it to help buy a 25% position in AAPL at $95 in May 2016, it would have been 12.49% (or 12.19% without either sale).

XIRR is a bit weird like that. I lost 3.65% but because it was over 8 months this was less than the average compound growth rate so my XIRR increased! I lowered my XIRR on my BRK.B position by selling about 30% of it to by AAPL, but more than made up for it by earning 47.88% XIRR on the AAPL position (to date, after 30% withholding tax on dividends and currency effects). I've reinvested all of the AAPL dividend stream and more added cash besides into BRK.B.

Anyway, the gist is that dividend reinvestment does make a huge difference on average, though certain companies reinvesting internally without paying a dividend can still beat the market, so invest for Total Return, regardless of how it is returned to you and insist on a Margin of Safety and you should compound well for decades.