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In an attempt to cut down on the whipsaws, I investigated only doing a switch if the difference in returns was greater than 1 BP (0.01% absolute difference).

If you're using market at close orders, the trading costs are limited to your commissions only, so it should be very small as a percentage of the trade.
In that case, trades are to be avoided primarily for the reason of hassle, and that it might actually make the thing work better.

For trading costs under (say) 0.15% of trade value, as they should be, a quick test of my three-way system seems to show it works a bit *better* by reducing trades.
e.g., compare the returns on what you've been holding this past month to the best performing of the three;
switch only if the best performing outperformed you by at least 35bp (0.35%) in the last month.
Even with no trading friction this backtests with slightly higher returns than switching willy-nilly to the recent best.
The advantage might or might not hold, but it certainly seems to show that there is no obvious penalty being a bit hesitant to switch.
The three-way strategy has more trades per year than the two-way strategy, but this reduces it from 7.7/year to 5.7/year.

This was a kind of "quickie" test so don't take that result as gospel, try it yourself.

Jim
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Thanks! Ugh!
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No. of Recommendations: 5
Due almost entirely to the performance difference in the last 2-3 years. IOW, to AAPL and AMZN.

The 10 years 1998-2018, $10,000 grows:
SPY: $37,642
BRK: $66,355

https://www.portfoliovisualizer.com/backtest-portfolio?s=y&a...

By every risk & performance metric, BRK was better than S&P 500.


I should have kept the AAPL I bought in 1998 and not sold it when it dropped 90% in 2001-2002. That $10K would be almost $7 MILLION now, instead of BRK's $71K. https://www.portfoliovisualizer.com/backtest-portfolio?s=y&a...
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No. of Recommendations: 28
Depressing.

But, looked at one way, I suppose one could interpret that as a buy signal for Berkshire.

There is no doubt that the actual value of Berkshire has risen at least as fast as the value of the S&P 500, so this dismal result can only be the result of changing valuation multiples.
It's also a good bet that changes in valuation levels are transient things.

Maybe the S&P 500 was unduly cheap many years ago and has been going through a period of catch up to Berkshire's still lofty valuation levels.
Maybe Berkshire was really overvalued 1, 3, 5, and 10 years ago.
But it seems more plausible that it's some mix of Berkshire now being transiently cheap-ish and/or the S&P 500 now being transiently expensive-ish.


As an aside---
The typical S&P 500 firm looks pricey to me, though that's not the same as a forecast that the prices will go down any time soon.

One basic yardstick for a broad set of firms is median sales: it's hard to fake, not very cyclical, and using the median avoids the distraction of outliers.
The median price to sales ratio among non-financial S&P 500 firms has averaged 1.56 since 1997.
On the peak day for that figure during the tech bubble it reached 1.639
On the peak day for that figure during the credit bubble it reached 1.844
It cracked 2 for the first time in US history (using a very generous definition of the S&P) in October 2013.
It cracked 2.5 for the first time in April 2017.
Today's figure is 3.206

So, is each dollar of sales for a middle-of-the-pack large firm really worth twice its average since the 1990s?
Not a superstar Google or Apple with outstanding economics, but an auto parts retailer. (the median P/S right now is O'Reilly Automotive)

It's hard to have ongoing progress in value without progress in sales.
The median real sales among non-financial S&P 500 companies has actually been falling by -0.60%/year since January 2007, and not just in 2020.
Meanwhile the median market cap in that group has risen 3.1%/year.

Jim
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Maybe the S&P 500 was unduly cheap many years ago and has been going through a period of catch up to Berkshire's still lofty valuation levels.
Maybe Berkshire was really overvalued 1, 3, 5, and 10 years ago.


Haven't we read repeatedly how S&P was overvalued every year for last decade.
So starting from a higher base, S&P out performed BRK which was super cheap "by every metric" at the beginning.

Meanwhile, Trillions of dollars of wealth has been generated with Gates on the board.
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No. of Recommendations: 17
Haven't we read repeatedly how S&P was overvalued every year for last decade.

Oddly enough, perhaps that's the key observation for investment strategy.
Berkshire's returns are surprisingly predictable, and those from the broad index aren't at all.
The *value* of the broad index is pretty predictable, but the pricing isn't anywhere close.

The S&P could be materially higher in five years, or a quarter of today's level. Both outcomes are entirely plausible.
(if the valuation multiples were the same as August 1982, adjusted for inflation the S&P would be at 619 today, down 81%)

FWIW,
Smoothed real earnings for the S&P 500 last ten years: up 3.62%/year
Average dividend yield: 2.05%
So, real total return if there had been no valuation multiple change: 5.67%/year
Unsurprisingly that's very close to the historical average, aka Siegel's constant.

Berkshire's "peak to date" book per share is up 9.21%/year in ten years.
Again, that's the likely real return if there hadn't been any change in valuation multiples.
(that multiple has fallen -10.6% or -1.1%/year)

Both of those have a quibble factor in the valuation method of maybe +/- 1% per year, conceivably 2%.
Mainly due to the TCJA in both cases.

Jim
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Haven't we read repeatedly how S&P was overvalued every year for last decade.
So starting from a higher base, S&P out performed BRK which was super cheap "by every metric" at the beginning.

If I could recommend this 100 times I would!

-BD
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No. of Recommendations: 7
Div30, I just wanted to challenge you to a bet about whose return will have been higher 10 years from now, Berkshire's or that of the S&P500.

Looking around how to publicly make such a bet I found longbets.org and also that I am a bit late to the game as our very own John C Leven already had this idea one year ago:

https://longbets.org/788/

Now here is the interesting part for you: His prediction is still UNCHALLENGED!

So you have the opportunity to put your money where your mouth is and publicly challenge his prediction!


P.S.: Should you prefer to rather bet for 10 years from now on, with today's prices of BRK and S&P, I am available for you, we can bet there (but unfair towards John who had this idea first).
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Div30, maybe also interesting for you: As contrary to you I am sceptical about Tesla's current price we could try to agree about the terms of a bet predicting Tesla's price 2 years from now on (2 years is the minimum period on longbets.org)?
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“I don't think people understand there's 100% correlation with what happens to a company's earnings over several years and what happens to the stock.”
Peter Lynch

My wager is on BRK and it’s predictable earnings but I do not dislike SPY.
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https://longbets.org/788/
Now here is the interesting part for you: His prediction is still UNCHALLENGED!


It should in theory be easier to find a challenger now than it was then...
S&P total return since then 13.31%, Berkshire 4.92%.

Of course, anybody can take either side of this bet by going long one and short the other.

Jim
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No. of Recommendations: 4
Div30, maybe also interesting for you: As contrary to you I am sceptical about Tesla's current price we could try to agree about the terms of a bet predicting Tesla's price 2 years from now on (2 years is the minimum period on longbets.org)?

Should we now ignore who said what about Amazon and Tesla over the last several years ?
The evidence is in front of us. Why wait 2 more years ?

My prediction for Tesla by 2030 is $2T+ market cap, Web will be no more and BRK will be split.
Most of us reading this are hopefully in good health and enjoying life with their loved ones.

All boards are irrational.
They think their stock will overperform and will upvote anything that enforces that view.
No one wants to listen to the other side.
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As an aside---
The typical S&P 500 firm looks pricey to me, though that's not the same as a forecast that the prices will go down any time soon.

One basic yardstick for a broad set of firms is median sales: it's hard to fake, not very cyclical, and using the median avoids the distraction of outliers.


I always struggle a bit with the use of Median for the S&P500. Probably good for an equal weight index valuation (e.g. RSP) but since the S&P500 is cap weighted shouldn't you compare aggregate sales with total market cap? Maybe of the non-financials.

StevnFool
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I always struggle a bit with the use of Median for the S&P500. Probably good for an equal weight index valuation (e.g. RSP) but since the S&P500 is cap weighted shouldn't you compare aggregate sales with total market cap? Maybe of the non-financials.

Exactly! Compare with what a Boglehead invests in. Vanguard has argued strongly that cap-weighted index is the simplest and the best way to invest. RSP behaves like VO (their midcap blend ETF). Not ideal for the brave new world we live in, where the dominant player gets 80+% market share. It was true for Intel vs AMD, Microsoft vs Apple (PCs) in the 90s, and now that tech trend is spreading to other industries.
Yes I read the SSRN paper and yet haven't seen a real world ETF/mutual fund doung it.
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No. of Recommendations: 11
I always struggle a bit with the use of Median for the S&P500. Probably good for an equal weight index valuation (e.g. RSP)
but since the S&P500 is cap weighted shouldn't you compare aggregate sales with total market cap?


It depends on what you're interested in.
I'm no more likely to buy a large S&P 500 company than a small one, so what I find most interesting is what's happening with the typical (though reasonably large) firm.

It also tells you a lot about where the general valuation "mood" is.
When a refrigerator firm is selling at 20 times boring earnings, that's something to take note of.
It's a sign that exuberant and likely transient valuation levels are probably very widespread.
When multiples on the boring are high, multiples on the "story" stocks are usually too high as well, not justified by their economic futures.

Plus, the median embodies a lot more information than the average in some obscure ways.
The average is so skewed by a few giant firms that you're mostly just looking at them.
That's fine, but any small collection has a huge amount of randomness to it.
You're looking at figures that are heavily dependent on the fortunes of a few outliers, which may or may not continue.
The average wealth of the people sitting in a diner is strongly dependent on whether you check before or after Bill Gates arrives.
The median tells you more about how the town is doing.

And most prosaically, to get a meaningful figure from a price to sales ratio you need to use the median, because it's numerically pretty stable.
M&A and those big outliers can cause averages to swing all over the place.
P/S is a meaningless valuation metric for comparing two firms, but the median is quite meaningful for a very broad set of firms.

Trend earnings figures, on the other hand, work just fine with averages, since they correlate
very well with GDP and a couple of other factors like the labour share of national income.

Jim
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Exactly! Compare with what a Boglehead invests in. Vanguard has argued strongly that cap-weighted index is the simplest and the best way to invest.

It's true, they do say that.
Though it's very much against a century of hard evidence to the contrary : )

Of course, that is what they're in the business of selling. Never ask the barber if you need a haircut.

Almost any other plausible portfolio weighting will work better, even after trading costs. Equal weight gives higher and safer returns in most stretches, and on average through time.
Without a doubt the last four years haven't represented one of those normal stretches, and the supergigacaps have been the big winners.
That might last, or it might be another blue moon. We'll see.

Jim
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It depends on what you're interested in.
I'm no more likely to buy a large S&P 500 company than a small one, so what I find most interesting is what's happening with the typical (though reasonably large) firm.

It also tells you a lot about where the general valuation "mood" is.


Fair enough, however (maybe I misunderstood but) I thought you were using median sales to judge the value of the S&P500 index which is not quite the same as you mention in the quoted text above.

StevnFool
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Jim,
you elided over the other two points, which support Vanguard's view.

one - VO and RSP have similar returns though VO is cap-weighted. So why buy the weed-watering-flower-starving RSP?

two - the SSRN paper you and I have used to bash cap weight is not a real world SPY-beating strategy followed by any broad-market ETF or mutual fund, most of which, if not cap-weighted, have gotten their posterior handed to them by S&P 500.

The one escape clause of course, is that the S&P is overpriced and this too shall pass. And if I keep hitting my head on this brick wall, one day it is bound to crumble.
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...and the article I just posted may be relevant to what happens when, particularly with Berkshire vs. S and P.
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knightof3,

VO and RSP have similar returns though VO is cap-weighted. So why buy the weed-watering-flower-starving RSP?

VO is a cap-weighted ETF of mid-cap stocks, so doesn't include the biggies in the S&P 500. RSP is equal weight the S&P 500. They are not just weighted differently, they are composed differently.

If you want to compare apple weeds to apple flowers, try RSP vs. SPY. It looks like RSP has outperformed SPY over 15 years, but not over 5, which matches the observation that the biggest cap stocks have dominated performance lately. This begs the question: will the next 5 years will look more like the last 5 or the last 15?

Rob
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No. of Recommendations: 5
It looks like RSP has outperformed SPY over 15 years, but not over 5, which matches the observation that the biggest cap stocks have dominated performance lately.
This begs the question: will the next 5 years will look more like the last 5 or the last 15?


I suppose it depends mostly on the business economics and fashionability of a few gigantic firms.
Hard to call, though there does seem to be room for some exuberance to fade.

But if the "old normal" returns, RSP is the smarter bet.
It has beat the cap weight S&P and predecessors 70.2% of rolling five year periods since 1930, by a median of 1.70%/year.
And of course RSP is much lower risk. The largest position is 0.2% of the holding instead of 6.0%.

Unwilling to take a stance?
There's always my old suggestion: Each calendar month, own the one that did best the prior calendar month.
(month ends being important)
The advantage of one versus the other is sometimes persistent, so each time it is, you win.
This probably makes sense only in a tax sheltered account with very low trading costs.

Jim
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(month ends being important)

As in, make the switch on the last trading day of the month, or the first? In many sheltered accounts in the US, the trade would be based on closing price of the day the trade is made, I believe.

The advantage of one versus the other is sometimes persistent, so each time it is, you win.

Just eyeballing it, that strategy looks like it would have worked really well... it would have had you in RSP during most of the time period it was superior, and in SPY (or equivalent) most of the time it was leading. Do you have a ballpark idea of how much outperformance that would have yielded over holding RSP alone? Just wondering if it's worth the extra effort. (Though I suppose at some portfolio value every few basis points is worth something!)

Thanks,
Rob
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No. of Recommendations: 15
As in, make the switch on the last trading day of the month, or the first? In many sheltered accounts in the US, the trade would be based on closing price of the day the trade is made, I believe.

The best would be a "market at close" order on the last trading day of the month, which is what I tested.
You generally know long before market close whether you'd be switching or not, so you could put in both the buy an sell orders early and forget about it.
The advantage is that there is no bid/ask gap to pay with "market at close" orders: all buyers and sellers pay the same price.
And besides, if there is a change in leadership in the last few minutes it was probably so close that it's a toss up anyway.

I really should test a strategy that stays pat if it's very close to a tie, but that's a lot more typing and I'm lazy.
I have estimated the trading costs though, and they are definitely frequent enough to make the strategy a loser if you're not keeping them down.
No old school full service brokerages.

I have tested the switch. All it takes is a rather tedious Excel sheet and monthly returns for each from Yahoo.

And, just because "why not", I also looked at long the best an a pinch short the worst, e.g. 1.5 long best and 0.5 short worst, so still 100% net long.
Or, if you're feeling lucky, 2x long the best and 1x short the worst.
The risk isn't as large as it sounds: the choices are the same set of firms, just slightly different weights, so the long and short cancels out to a very high degree.
I also checked out a more conservative one, only 70% net long: 1.7x the best, 1.0 short the worst.

A third alternative is PRF, which is a nice large-cap-heavy alternative with a faint tilt towards
trivial "value" criteria by weighting based on the "size" of the firm rather than market value.
Quite some time ago I proposed the strategy of being long the best performing of the three choices the prior month.
So, one can looks at just 2 choices, or all 3 of the choices.

I proposed the 2 way switch publicly in July 2005, so we have a nice out-of-sample test of the idea.
Since then
SPY: 8.67%
RSP: 8.05%
Average of those, which you'd expect if the switches were random: 8.36%
Result of the switching strategy: 9.23%, so an out-of-sample improvement of 0.87%/year.
1.5x long the best last month, 0.5x short the worse: 11.66%, or improvement of 3.30%/year vs average
2.0x long the best last month, 1.0x short the worse: 12.84%, or improvement of 4.47%/year vs average
So, though any given year might be a toss up, I'd say the strategy has proven itself to work.

I proposed the 3-way switch in November 2006.
Since then
SPY: 8.37%
RSP: 7.63%
PRF: 6.94%
Average of those, which you'd expect if the switches were random: 7.65%
Simple three way switch, long the best last month: 8.27%, improvement of 0.62% vs average.
1.5x long the best, 0.5x short the worst: 10.87% or improvement of 3.22%
2.0x long the best, 1.0x short the worst: 13.45% or improvement of 5.80% (my personal fave)
Conservative version, net 70% long:
1.7x long the best, 1.0x short the worst: 11.06%/year, or improvement of 3.41%.
Despite being only partly long, that one is up a remarkable 21% year to date.

Note, the figures including leverage have not had the cost of borrowing, nor the interest you'd earn on the cash raised by the short.
The sum of those would be a slight net drag.

These figures look particularly good right now, as SPY has been the winner 15 of the last 20 months.
Long stretches of one winner is what this strategy likes best.


SPY only RSP only PRF only 1.5x long, 2.0x long, 1.7x long,
0.5x short 1.0x short 1.0x short
2004 10.7% 16.5% 14.8% 15.8% 16.2% 11.5%
2005 4.8% 7.3% 6.1% 5.4% 5.1% 3.4%
2006 15.8% 15.4% 18.6% 17.6% 18.2% 12.8%
2007 5.2% 0.8% 1.3% 7.3% 10.0% 8.6%
2008 -37.0% -40.1% -40.2% -35.0% -30.5% -19.1%
2009 26.7% 44.9% 42.5% 48.8% 56.5% 42.9%
2010 15.1% 21.4% 19.5% 22.0% 25.5% 19.8%
2011 1.8% -0.8% -0.5% 3.9% 6.8% 6.7%
2012 15.9% 17.0% 16.7% 19.1% 20.4% 14.7%
2013 32.5% 35.8% 35.5% 36.0% 37.3% 25.8%
2014 13.5% 14.0% 12.1% 10.4% 9.4% 6.1%
2015 1.2% -2.7% -3.2% -0.6% 0.4% 1.2%
2016 12.0% 14.8% 17.2% 11.5% 10.4% 6.7%
2017 21.8% 18.2% 16.4% 21.5% 22.8% 16.3%
2018 -4.6% -8.0% -8.8% -9.2% -8.9% -6.0%
2019 31.3% 29.2% 27.5% 31.0% 32.7% 23.1%
YTD 1.8% -7.8% -10.9% 11.2% 21.1% 20.8%

CAGR 8.7% 8.6% 8.0% 11.3% 13.5% 10.9%
Annl Stdev 16.2% 19.6% 19.4% 18.6% 19.2% 13.7%


Jim
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Awesome. Thanks Jim!

The long/short idea is a great twist... the extra performance would go a long way to offset the tax implications.

Rob
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Each calendar month, own the one that did best the prior calendar month. (month ends being important)
...
"market at close" order on the last trading day of the month,


Which month is "prior" , this one or the last one? IOW, on Sept 30 you go with the one that had the best return in Sept? or the best in August?

And total return (incl dividends) or price-only return?


=========
I swear, Jim, you are suggesting so many good sounding schemes that I would quickly run out of money to invest. ;-)
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Which month is "prior" , this one or the last one? IOW, on Sept 30 you go with the one that had the best return in Sept? or the best in August?

The first.
At market close on Sept 30, and for the whole month of October, you would go long whatever did best in September (close end Aug to close end Sept).
That sounds like fast work determining your signal, but as mentioned, the winner is usually clear quite a while before month end.

And total return (incl dividends) or price-only return?

They all include reinvested dividends.

Alas, that's with the usual not-quite-realistic rules people always use.
No tax on dividends, you use the dividends at close on ex-date to buy more, even though you won't
actually have the cash for many days, no transaction cost for the effective DRIP, and you can buy fractional shares.

Jim
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I proposed the 2 way switch publicly in July 2005, so we have a nice out-of-sample test of the idea.
Since then
SPY: 8.67%
RSP: 8.05%
Average of those, which you'd expect if the switches were random: 8.36%
Result of the switching strategy: 9.23%, so an out-of-sample improvement of 0.87%/year.


I get, for Jul'2005 to (excluding) Sept'2020:
SPY 9.47%, stdev 14.95%
RSP 8.91%, stdev 17.44%
switch 10.21%, stdev 15.95%

SPY held 98 months.
RSP held 85 months.
88 switches. There are several strings where you switch every month for 5-7 months in a row.


For Jun'2003 (earliest possible date) to Sept-2020:
SPY 9.87%
RSP 9.97%
switch 10.80%

SPY held 106 months.
RSP held 101 months.
99 switches.

So, reasonable expectation is about 1% improvement.

Growth of $10,000 from 6/1/2003 to 9/1/2020:
SPY: $50,727
RSP: $51,497
Switch: $58,685


-------------
In an attempt to cut down on the whipsaws, I investigated only doing a switch if the difference in returns was greater than 1 BP (0.01% absolute difference). Reduced the switch count from 99 to 29. SPY held 83 months, RSP held 124 months. CAGR: 10.65%.
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In an attempt to cut down on the whipsaws, I investigated only doing a switch if the difference in returns was greater than 1 BP (0.01% absolute difference).

If you're using market at close orders, the trading costs are limited to your commissions only, so it should be very small as a percentage of the trade.
In that case, trades are to be avoided primarily for the reason of hassle, and that it might actually make the thing work better.

For trading costs under (say) 0.15% of trade value, as they should be, a quick test of my three-way system seems to show it works a bit *better* by reducing trades.
e.g., compare the returns on what you've been holding this past month to the best performing of the three;
switch only if the best performing outperformed you by at least 35bp (0.35%) in the last month.
Even with no trading friction this backtests with slightly higher returns than switching willy-nilly to the recent best.
The advantage might or might not hold, but it certainly seems to show that there is no obvious penalty being a bit hesitant to switch.
The three-way strategy has more trades per year than the two-way strategy, but this reduces it from 7.7/year to 5.7/year.

This was a kind of "quickie" test so don't take that result as gospel, try it yourself.

Jim
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