Six Sigma Buffett, Taxes, Fund Returns etc.

Whenever I read about Buffett and other great managers, what I tend to see all the time are things like, "xx has beaten the market y out of z years; the odds of that happening are 1 in 5,000!" or some such thing. Not too long ago, there was an article about managers with outstanding performance and the screen was based on who beat the market five years in a row, ten years in a row or something like that.

But for me, I tend not to care about that at all. In fact, I would rather invest with someone who only beat the market seven out of the last ten years but with a wider and more consistent margin than someone that beat the market ten years in a row, and only with a small margin.

So that got me thinking about what I should look at. Well, when I say that, I don't mean that I would use this stuff to choose investment managers since I don't really invest in funds at all. What I mean, I guess, is that if I don't like the above 'beat the market x out of y years', what is a better indicator?

Tax Digression
But before that, I just happened to be reading the 1986 Berkshire Hathaway letter to shareholders and came across this comment about taxes.  Trump is expected to do something about taxes and I heard Buffett or Dimon mention somewhere recently that any tax cut will be competed away by the market implying that it won't make a difference to investors.  Anyway, this is what he wrote about it back in 1986 after the last big tax change:

Taxation

     The Tax Reform Act of 1986 affects our various businesses in 
important and divergent ways.  Although we find much to praise in 
the Act, the net financial effect for Berkshire is negative: our 
rate of increase in business value is likely to be at least 
moderately slower under the new law than under the old.  The net 
effect for our shareholders is even more negative: every dollar 
of increase in per-share business value, assuming the increase is 
accompanied by an equivalent dollar gain in the market value of 
Berkshire stock, will produce 72 cents of after-tax gain for our 
shareholders rather than the 80 cents produced under the old law.  
This result, of course, reflects the rise in the maximum tax rate 
on personal capital gains from 20% to 28%.

     Here are the main tax changes that affect Berkshire:

   o The tax rate on corporate ordinary income is scheduled to 
decrease from 46% in 1986 to 34% in 1988.  This change obviously 
affects us positively - and it also has a significant positive 
effect on two of our three major investees, Capital Cities/ABC 
and The Washington Post Company.

     I say this knowing that over the years there has been a lot 
of fuzzy and often partisan commentary about who really pays 
corporate taxes - businesses or their customers.  The argument, 
of course, has usually turned around tax increases, not 
decreases.  Those people resisting increases in corporate rates 
frequently argue that corporations in reality pay none of the 
taxes levied on them but, instead, act as a sort of economic 
pipeline, passing all taxes through to consumers.  According to 
these advocates, any corporate-tax increase will simply lead to 
higher prices that, for the corporation, offset the increase.  
Having taken this position, proponents of the "pipeline" theory 
must also conclude that a tax decrease for corporations will not 
help profits but will instead flow through, leading to 
correspondingly lower prices for consumers.

     Conversely, others argue that corporations not only pay the 
taxes levied upon them, but absorb them also.  Consumers, this 
school says, will be unaffected by changes in corporate rates.

     What really happens?  When the corporate rate is cut, do 
Berkshire, The Washington Post, Cap Cities, etc., themselves soak 
up the benefits, or do these companies pass the benefits along to 
their customers in the form of lower prices?  This is an 
important question for investors and managers, as well as for 
policymakers.

     Our conclusion is that in some cases the benefits of lower 
corporate taxes fall exclusively, or almost exclusively, upon the 
corporation and its shareholders, and that in other cases the 
benefits are entirely, or almost entirely, passed through to the 
customer.  What determines the outcome is the strength of the 
corporation’s business franchise and whether the profitability of 
that franchise is regulated.

     For example, when the franchise is strong and after-tax 
profits are regulated in a relatively precise manner, as is the 
case with electric utilities, changes in corporate tax rates are 
largely reflected in prices, not in profits.  When taxes are cut, 
prices will usually be reduced in short order.  When taxes are 
increased, prices will rise, though often not as promptly.

     A similar result occurs in a second arena - in the price-
competitive industry, whose companies typically operate with very 
weak business franchises.  In such industries, the free market 
"regulates" after-tax profits in a delayed and irregular, but 
generally effective, manner.  The marketplace, in effect, 
performs much the same function in dealing with the price-
competitive industry as the Public Utilities Commission does in 
dealing with electric utilities.  In these industries, therefore, 
tax changes eventually affect prices more than profits.

     In the case of unregulated businesses blessed with strong 
franchises, however, it’s a different story:  the corporation 
and its shareholders are then the major beneficiaries of tax 
cuts.  These companies benefit from a tax cut much as the 
electric company would if it lacked a regulator to force down 
prices.

     Many of our businesses, both those we own in whole and in 
part, possess such franchises.  Consequently, reductions in their 
taxes largely end up in our pockets rather than the pockets of 
our customers.  While this may be impolitic to state, it is 
impossible to deny.  If you are tempted to believe otherwise, 
think for a moment of the most able brain surgeon or lawyer in 
your area.  Do you really expect the fees of this expert (the 
local "franchise-holder" in his or her specialty) to be reduced 
now that the top personal tax rate is being cut from 50% to 28%?

     Your joy at our conclusion that lower rates benefit a number 
of our operating businesses and investees should be severely 
tempered, however, by another of our convictions: scheduled 1988 
tax rates, both individual and corporate, seem totally 
unrealistic to us.  These rates will very likely bestow a fiscal 
problem on Washington that will prove incompatible with price 
stability.  We believe, therefore, that ultimately - within, say, 
five years - either higher tax rates or higher inflation rates 
are almost certain to materialize.  And it would not surprise us 
to see both.

OK, the last paragraph is kind of interesting too. Buffett said he bought $12 billion in stocks after the election so I guess he is not so worried about the fiscal position of the U.S.

Back to fund performance stuff...

Comparing Two Distributions
I said that I don't care for the 'beat the market x out of  y years' idea. So that got me thinking about the simple high school statistics problem of comparing two normal distributions. I am aware of the argument against using normal distributions in finance, but I don't really care about that here. I am just looking for some simple descriptive statistics. I'm not creating a derivatives pricing model to price an exotic option for a multi-billion dollar book where modeling errors can cause huge losses. So in that sense, who cares. Normal distribution is fine for this purpose.

Plus, I am not so interested in factor models that try to assess fund manager skill. Some people use factor models and whatever is left over is what they define as 'skill'.  Well, say the model cancels out 'quality' as a factor and doesn't give the manager credit for it; what if the manager intentionally focused on quality investments? Should he not get credit for it? Having said that, I don't know much about these models so whatever...  I don't get into that here. Whatever factor exposures these managers have, I assume the manager intentionally assumed those risk factors to gain those returns.

Basically I just want to compare two distributions and see how far apart they are. It's basically the question, is distribution A, with 99% confidence, the same as distribution B? In other words, are the two distributions different with any degree of statistical significance? Or are we just looking at a bunch of noise resulting from totally random chance?

The simple comparison of two distributions is:

standard deviation of the difference between two means (Std_spd) =

   Sqrt[(Vol_A^2/n) + (Vol_B^2/n)]

   where: Vol_A = standard deviation of distribution A and
               n = number of samples

So the z-score would be:
  (mean_A - mean_B) / Std_spd

And then you can just calculate or look up the probability from this z-score.

Looks good.  This would tell me how significantly different a manager's return is versus the market.

But the problem is that these two distributions are not independent. In your old high school statistics text book, the example is probably something like number of defective parts in factory A versus factory B.  Obviously, those distributions would be independent.

This is not so in the stock market. A fund manager's returns and the stock market's return are not independent. Hmm... Must account for that.

The answer to that goes back to my derivative days; calculating tracking error. Sometimes fund managers or futures traders wanted to use one index to hedge against another. An example might be (in the old days!) an S&P 100 index option trader wanting to hedge their delta using the S&P 500 index futures.  Does this make sense? What is the tracking error between the two indices? Does it matter? Is the tracking error too big for it to be an effective delta hedge? How about using the S&P 500 futures to hedge a Dow 30 total return swap? TOPIX index swap with the Nikkei 225 futures?

Anyway, the calculation for tracking error simply makes an adjustment by making a deduction for correlation (getting square root of the covariance).

So, the above formula becomes:

    Sqrt[(Vol_A^2/n) + (Vol_B^2/n) - ((2 * Vol_A * Vol_B * correlation(A,B)) / n)]

Using this formula, I calculated all this stuff for the superinvestors, just for fun.

I just wanted to know simple things like, is it harder to outperform an index by 10% per year over 10 years, or by 3% per year over 20?  Or something like that.  The Buffett partnership was only 13 years, and Greenblatt's Gotham returns in the Genius book is only 10 years. But the spread is so wide that it is yugely anomalous to achieve, or is it? This is sort of what I wanted to know. It normalizes the outperformance spread versus the length of time the outperformance lasted.

Few Standouts
A few of the standouts looking at it this way, not surprisingly:

• Buffett Partnership 1957-1969:  a 6.0 sigma event, 1 in 1 billion chance of occurring (yes, that b is not a typo!) 
• Walter J. Schloss 1956-1984:  5.2 std, 1 in 9.4 million 
• BRK 1965-2015:  4.8 std, 1 in 1.3 million
• Greenblatt (Gotham 1984-1994): 3.8 std, 1 in 14,000
• Tweedy Brown 1968-1983: 3.7 std, 1 in 9,300

For the Graham and Doddsville superinvestors, I looked first at the "beat the market x out of y years" to see the probability of that happening assuming a 50% chance of beating the market in any given year. And then I'll compare the two distributions as described above. At the end, I also added Lou Simpson's returns from the 2004 Berkshire letter.

Keep in mind that just because a manager is not in the 4-5 sigma range, that doesn't make them bad managers. Some of these numbers are just insanely off-the-charts and can't be expected to happen often.

Anyway, take a look!

Buffett Partnership (1957-1969)
Beat the market 13 out of 13 times: Chance of occuring: 0.012% or 1 in 8,192.

Given that Buffett partnership gained 29.5%/year with a 15.7% standard deviation while the DJIA returned 7.4%/year with a 16.7% standard deviation and the Partnership had a 0.67 correlation, the partnership returns is 6.0 standard deviations away from the DJIA.  6 standard deviations make the partnership returns a 1 in 1 billion event.

What's astounding is that the standard deviation of Buffett's returns is actually lower than the DJIA.


BRK 1965-2015
Beat market 40 out of 51 years:  0.003% chance or 1 in 35,000

                     BRK        S&P500
Return          19.3%        9.7%
std                14.3%      17.2%
correl             0.61

4.8 std, 1 in 1.3 million

This uses book value, which may not be fair as not everything in BPS is marked to market (over 51 years). Using BRK stock price, it would be a 3.2 std event, or 1 in 1,455. But this too may not be fair as the volatility of the price of BRK is more a function of Mr. Market than Mr. Buffett.  This may be true of all superinvestor portfolios, but in the case of BRK, there is a penalty in that we are looking at the volatility of a single stock (BRK), and not the underlying portfolio.  Single stock volatility is usually going to be much higher than that of a portfolio.

Munger 1962-1975
Beat the market 9 out of 14 years: 21% chance or 1 in 5

                    Munger     DJIA
return           19.8%       5.0%
std                33.0%      18.5%
correl:            0.73
#years: 14

2.4 std, 1 in 122.

Sequoia 1970-1983
Beat the market 8 out of 14 years: 40% chance or 1 in 2.5

                Sequoia        S&P 500
return       17.2%        10.0%
std            25.0%        18.1%
correl         0.65

1.4 std or 1 in 12.

This is the in-sample period; the period included in the Superinvestors essay.

Sequoia 1970-2016
Beat the market 26 out of 47 years, 28% chance or 1 in 3.6


                  Sequoia       S&P500
return        +13.7%        +10.9%
std               19.3%          17.1%
corr 0.67

1.3 std or 1 in 10

Sequoia 1984-2016
This is the out of sample period; the period after the essay.

Beat the market 18 out of 33 years, 36% chance or 1 in 3

                  Sequoia      S&P500
return          11.9%         10.9%
std               16.0%         16.6%
corr               0.73

0.5 std or 1 in 3

Sequoia 2000-2016
And just for fun, a recent through-cycle period starting in 2000. They have been underperforming the market since 2007, though.

Beat 9 out of 17 years, 50% chance or 1 in 2.

                   Sequoia     S&P500
return           7.3%          4.5%
std              13.7%        18.1%
correl           0.69

0.9 std or 1 in 5

Walter J. Schloss 1956-1983
Beat the market 22 out of 28 years, 0.2% chance, or 1 in 540

                   WJS      S&P500
return         21.3%     8.4%
std              19.6%   17.2%
corr:             0.75

5.2 std or 1 in 9.4 million


Tweedy, Browne Inc. 1968-1983
Beat the market 13 of 16, 1.1% chance or 1 in 94

                   Tweedy   S&P500
return           20.0%       7.0%
std                12.6%     19.8%
corr:               0.71

3.7 std or 1 in 9,300


Pacific Partners Ltd. 1965-1983
Beat the market 13 of 19 years, 8% chance or 1 in 12

              Pacific       S&P500
returns    32.9%         7.8%
std          60.2%       17.2%
corr:         0.37

1.9 std or 1 in 35


Gotham 1985-1994
Beat the market 9 out of 10 times: 1.1% or 1 in 93 chance

3.8 std, 1 in 14,000

Lou Simpson (GEICO: 1980-2004)
18 out of 25 years. 2.2% chance or 1 in 46.

               GEICO   S&P
return      20.3%    13.5%
std           18.2%   16.3%
corr:         0.74

2.7 std, 0.4%, 1 in 288


Conclusion
So that was kind of interesting. It just reaffirms how much of an outlier Buffett really is. There is a lot to nitpick here too, so don't take these numbers too seriously. I used standard deviation of annual returns, for example. I suspect some of these correlations may be higher if monthly or quarterly returns were used.

This sort of thing may be useful in picking/tracking fund managers. At least it can be one input.  For example, it gives you more information than the Sharpe ratio; whereas the Sharpe ratio doesn't care how long the fund has been performing, the above analysis takes into account how long someone has been performing as well as by how much. But yeah, Sharpe ratio is trying to measure something else (return per unit of risk taken).

Anyway, as meaningless as it may be, it's one way of seeing if it's harder to create a long term record like Buffett (1965-2015) or a shorter super-outperformance like Greenblatt (1984-1994). This analysis says that Buffett's 1965-2015 performance is a lot more unlikely to be repeated (well, at least on a BPS basis; using BRK stock price, Greenblatt's performance is more unlikely!).

I sliced up Sequoia Fund's return into various periods for fun as it is the only continuous data (other than BRK) out of the Graham and Doddsville Superinvestors. I was going to look into their performance since 1984 a little more deeply, but this took a little more time than planned (despite the automation of a lot of it; well, debugging and fixing takes time, lol...).

So maybe I will revisit the Sequoia Fund issue in a later post. My hunch is that the Superinvestor returns were achieved on a much lower capital base so the universe of potential investments were much larger than what Sequoia (and others) are looking at now despite their efforts to keep AUM manageable.

Also, you will notice that comparing the two distributions gives a more nuanced or accurate picture of the performance than just looking at how many years someone has outperformed; it incorporates the spread, correlation, volatility etc...

Anyway, I guess that's enough for now...

Bogle Book, Indexing etc.

I have watched and listened to John Bogle for years and always thought he was great, but I never read any of his books. I understand his message and agree with him for the most part. But the other day while I was browsing the library, I came across this book and just grabbed it and decided to read it even though I have a big stack of books that I started and have yet to finish.




There is nothing new in here in terms of message (active managers don't outperform, costs is primary determinant of performance over time; low cost beats high cost in every category, every time period etc...), but it is still amazing to read with all the tables and facts laid out.

Every time non-industry people ask me about stocks and how to learn about them, I go through the usual books that we've all read. I noticed, though, that if they are not in the industry, or not a true market fanatic, people don't ever read the books you recommend.

I understand telling someone to read all of the Berkshire Hathaway letter to shareholders going back to 1977 (available for free, I tell them, at the BRK website) seems like such a tedious thing that no normal, non-financial person would actually do it.

From now on, I think, I will just direct them to this book. It's that good, and it would answer most questions I typically get in the usual 'cocktail party' conversation about markets.

As for stock picking, from now on, I will tell them to just pick stocks based on what you like and believe to be truly good businesses at reasonable valuations.  Even overpriced is OK as long as it is kept small and it's not bubble-like; compensate for the assumption of price risk by keeping dollar exposure low. But keep most of the equity exposure indexed (OK, BRK is fine too, but most people won't know what to do when something happens to Buffett, and may not want to deal with the volatility/uncertainty related to the headlines).

Expensive Stocks
Every once in a while, you just come across businesses that you think are just really, really great, as a customer and as a business analyst. For me, that was Chipotle Mexican Grill (CMG). I bought some a while ago and did very well with it, even selling out at the top once and buying back in at a low and then selling out again (most recently in late 2014).  I know others who have owned Starbucks (SBUX) forever, and I kick myself for not owning that one too. I go there way more often than I'd like to admit, and when you travel, there is never a SBUX anywhere that doesn't have a long line in the morning. And often, it's the only place to get a bagel and coffee.

(By the way, this section has nothing to do with the Bogle book!)

So, on those occasions where you actually see and verify for yourself a great business in action, and the price is reasonable, or even a little on the high side, I say go for it. Own it and hold it for as long as it's good. We value investors are usually afraid of high P/E stocks because we remember 1999/2000 and many high P/E disasters.

Value investors who run value funds might get into trouble owning such growth stocks, but for individuals managing their own money, why not?

I know this goes against the idea of having discipline, but if most of someone's equity exposure is indexed and they 'play' with a small portion of their portfolio on their own picks, it's probably not a bad idea.  Plus, those opportunities don't come up all that often. That's all the more reason to go for it.

Worse is actually going out and trying to find stocks that will go up; buying stuff that you have no idea about etc.  At least with some businesses, you have a strong idea about their competitive position etc. What you absolutely don't want to do is to bend that rule and overpay for things just because everyone says it's the next Chipotle,  Starbucks, Facebook or whatever.  Forget about those "this is the next..." stocks.  Only go for the ones that you really understand.  The "this is the next..." argument is a shortcut; it allows people to pump stocks with minimal bandwidth.  Who's adrenaline doesn't start to flow when you hear about the next CMG, or next Buffett?  (Well, I do some of that here...).

Market Timing
Bogle is also anti-market timing, and that's been a constant theme on this blog too. Market timing is a waste of time unless you are a Druckenmiller-type active trader. But market timing when you are supposed to be allocating assets / investing doesn't make much sense.

I was thinking of this the other day, seeing a lot of market-timers doing horribly in recent years. A lot of people have horrible performance because they were short the market for the past few years.

Gambler's Fallacy
And I realized that this "the market is expensive so it must go down. Therefore, I am short"-type manager is falling for the gambler's fallacy.  OK, well, not exactly.  With the gambler's fallacy, for example, if a coin toss results in heads ten times in a row, people tend to believe the next one must be tails. But the fact that the coin landed on heads ten times in a row doesn't affect the probability of the next coin toss.  Each coin toss is independent. Regardless of how many times you had heads in a row, the odds on the next flip is still 50/50.

In the stock market, this is not true. The higher the market goes, the more expensive it gets, and the lower the prospective returns will be.  So the probability distribution of going forward returns actually shifts lower; the probability of a loss increases as the market gets more expensive.

So this is not an accurate analogy. But for me, it still is interesting because when the stock market is expensive, my temptation is to ask, when the market is this expensive, what tends to happen in the following year?  Greenblatt does this and mentions it just about every time he is interviewed. And even in the past few years, using 30 years of data, I think, his prospective returns one year out from the then current valuation has always been positive.

Even many of the bears have long term expected returns that are positive, but just low. Yet they are short. Even more recently with negative long term expected returns, it is usually low negative. So maybe -2%/year or some such.  In that case, it's still better to invest in corporate bonds or other fixed income at something higher than that to earn a positive return than shorting the market.  What if the market went into a bubble like in 1999/2000? The stock market valuation is nowhere near that silliness. If the market did rally like that, it would put a lot of those bearish funds out of business.

Now, what are the odds of some sort of blow-off like that? Versus what are the chances of an imminent collapse/bear market? These are things that you usually don't hear about, and to me, are the more relevant statistics to look at if you insist on timing the market.  And I suspect those are some things that the more successful quant funds are good at evaluating (and therefore don't lose money being net short for multiple consecutive years!).

Hasty Generalization?
The other related and more precise fallacy is the fallacy of hasty generalization or maybe faulty causality. Actually, I'm not sure this is the right one, but let's use it. Initially I was thinking it was fallacy of composition, but my understanding is a little bit different there. I'm referring to the fallacy of assuming that since all bank-robbers had guns, that all gun-owners must be bank robbers.

We all look at these long term valuation charts and go, hey look!,  the market P/E was over 20x before 1929, 1987 and 1999! So, the thinking goes, the market is now over 20x P/E so a crash must be imminent! But then we tend not to look at all the people who own guns that are not bank robbers.

Also, when someone says that the stock market is 90% percentile to the expensive side, there is a tendency to want to believe that there is a 90% chance that the market will go down in the future. Well, if the market is 90% percentile to the expensive side over the past 100 years, then it means that the market will be valued at a lower level 90% of the time in the next 100 years if the same conditions occur.

Anyway, since I was so curious about the year-forward returns and was worried about the declining interest rate bias of Greenblatt's sample (as he uses the past 30 years), I decided to look at this data for myself.

First let's look at Greenblatt's time span. That would be starting around 1985 or 1986.

Just so we can actually see the data, I will use annual figures.  I will look at the P/E ratio (as reported) of the stock market at the beginning of the year and compare it to how the market did during that year (actually, the P/E ratio of the end of the previous year is used).

Using Greenblatt's time period and looking at years when the stock market started with a P/E ratio of over 20x, here are the results:

P/E level of over: 20
Number of up years: 11
Total # years: 15
Percent up years: 73.33%
Average change: 5.5%

Date	P/E	return
1991.12	24.33	15.32%
1992.12	22.82	9.85%
1993.12	21.29	0.52%
1997.12	24.23	25.34%
1998.12	31.56	21.45%
1999.12	29.66	-5.70%
2000.12	26.62	-12.79%
2001.12	46.37	-20.06%
2002.12	32.59	22.11%
2003.12	22.17	12.77%
2004.12	20.48	7.09%
2007.12	22.35	-38.75%
2008.12	58.98	29.08%
2009.12	21.78	13.86%
2014.12	20.08	2.10%
2015.12	23.74

The data excludes total return for 2016, but we know it was more than 11%, so the results would be even stronger.  From the above, when the market started the year with a P/E ratio of over 20x, the market was still up more than 70% of the time, for an average gain of 5.5%.  Sure, 5.5% is lower than the 10% or so long term average.

But if you own a fund that is short and is losing money with the market going up, it makes no sense. Actuarially speaking, it makes no sense to short the market just because the P/E ratio is over 20x.  Any middle schooler would know this is a bad bet to make.

Oh, and this only looks at the period since 1985. Interest rates have been declining so there has been a huge tailwind.  So let's look at the same table over a longer time period.

Here is the analysis using data since 1871:

P/E level of over: 20
Number of up years: 14
Total # years: 20
Percent up years: 70.0%
Average change: 5.9%

Date	P/E	return
1894.12	26.88	4.88%
1896.12	20.10	16.82%
1921.12	25.21	27.09%
1933.12	22.66	-2.61%
1961.12	22.49	-9.72%
1991.12	24.33	15.32%
1992.12	22.82	9.85%
1993.12	21.29	0.52%
1997.12	24.23	25.34%
1998.12	31.56	21.45%
1999.12	29.66	-5.70%
2000.12	26.62	-12.79%
2001.12	46.37	-20.06%
2002.12	32.59	22.11%
2003.12	22.17	12.77%
2004.12	20.48	7.09%
2007.12	22.35	-38.75%
2008.12	58.98	29.08%
2009.12	21.78	13.86%
2014.12	20.08	2.10%
2015.12	23.74

And I was sort of surprised that using data that goes all the way back, the results aren't all that different. This includes periods of increasing and decreasing interest rates, so you can't say the data is biased due to a bond bull market tailwind. You can still argue that it is biased by a U.S. bull market tailwind, though.

So yes, my gambler's fallacy analogy is not accurate, but check it out. If someone says that the coin landed heads ten times in a row so the next flip must be tails, you'd think he is an idiot. But if you are short the market because the market is overvalued at 20+x P/E ratio, you are even more of an idiot because at least the coin flipper and real fallacious gambler has a 50% chance of being right whereas if you are short a 20x P/E market, you only have a 30% chance of being right!

That's kind of surprising.

What happens if we do the above with a 25x P/E threshold?

Since 1871:

P/E level of over: 25
Number of up years: 5
Total # years: 8
Percent up years: 62.5%
Average change: 8.3%

Since 1985:

P/E level of over: 25
Number of up years: 3
Total # years: 6
Percent up years: 50.0%
Average change: 5.7%

The average change is still up. Since 1985, the market was up only 50% of the time in years the market started at a 25x or higher P/E ratio. But these figures are questionable as there isn't enough data points to be significant.

Even the earlier figures are questionable with only 15 or 20 years in the sample size.

All Months, not just year-end
Just to be thorough, I reran all of the above using all months, not just year-end.  I looked at all months where the P/E ratio was over 20x or 25x and what the total return was 12 months later.

PE >= 20

Since 1871:
P/E level of over: 20
Number of up years: 139
Total # years: 223
Percent up years: 62.3%
Average change: 3.5%


Since 1985:
P/E level of over: 20
Number of up years: 111
Total # years: 162
Percent up years: 68.5%
Average change: 4.8%


PE >= 25

Since 1871:
P/E level of over: 25
Number of up years: 58
Total # years: 96
Percent up years: 60.4%
Average change: 5.1%

Since 1985:
P/E level of over: 25
Number of up years: 54
Total # years: 90
Percent up years: 60.0%
Average change: 5.2%

Using all months, you still get positive expected return with P/E's over 20x and 25x over the next 12 months, with the market rising 60%-70% of the time. I think markets are usually up 70% of the time, 12 months after any given month.

This sort of shows you why it doesn't make too much sense to point to an 'overvalued' stock market, go short and stay short. There are people who have been net short for years and it's amazing to think anyone would do so given the above statistics.

It also explains why Buffett and others can keep buying stocks even as many 'experts' claim the market is way overvalued and due for a correction. Buffett is a numbers and odds guy so I'm sure all of the above figures, at least intuitively, are in his head.

Anyway, the next time someone tells you that they are short because the market is expensive, run away! If they have your money, get it back.

But as usual, this is not to say that the market won't correct at some point. It will correct, as it always does.

Indexing
So, why am I advocating indexing here on a value investing, stock-pickers blog? I don't know. That's a good question. I do believe that most funds over time will not outperform the market so I do believe that indexing is probably right for most people. But do I believe that the market is totally efficient? Well, no. I am a big fan of Buffett, Greenblatt and many others who have outperformed over time.

The stats in Bogle's book are amazing. He shows how top performing funds almost always revert to the mean, even in the long term.

I was going to post more about this here, but this is already getting long and I would like to get this out, so my next post will be about funds, indexing and things like that. Just my random thoughts on the subject.

I was thinking about the above analysis and was playing around with Python and ended up writing a script to calculate all of that. I loved how Greenblatt always said the market is valued at so-and-so percentile and the going forward expected return from these levels is x%.  And he uses 30 years as his history and it always sort of nagged at me that the entire sample period was during a huge decline in interest rates. The above work sort of comforts me.

Trump
Oh yeah, and on Trump. Hmm.  What can I say. We live in interesting times. I binged House of Cards last year and loved it, but nowadays, it seems like truth is stranger than fiction (fiction has to make sense!).

Am I worried? Well, I am worried about all sorts of things, but although I may be wrong, I am not that worried about economic issues. I am not expecting some huge infrastructure binge or anything like that. All that was needed is just a leaning in the other direction from over-regulation. Just the lifting of some of that pressure, and not even a lot of deregulation, I think, is enough to lift business sentiment.

I am comforted by the fact that Trump is surrounding himself with people I respect (business world people, not the alt-right), and I hope they will be listened to.

As for the tweeting and big pronouncements, I do think a lot of that is posturing. He is a negotiator so it's to his advantage to start at the extreme and then work his way down.

At least that's my hope. That' what I hope he's doing. But we can't be sure.

We shall see.