Some statistics about the S&P 100's 2018 return

The following figure shows the 2018 returns for stocks in the S&P 100:

Some comments:

• The mean (average) return is 5.5 percent.
• The median return is 6.6 percent. So half the stocks in the index returned less than this and half returned more (roughly).
• Skewness is 0.18, meaning the returns are skewed to the right.
• Kurtosis is -0.02, meaning the graph is flattish, not peaked (relative to a certain standard distribution).
• 35 percent of the stocks in the index earned a positive return.
• The 10th percentile return is -31 percent -- for these stocks, 2018 was a very bad year.
• The 90th percentile return is +18 percent -- in other words, despite a pretty bad year for the market, a reasonable number of stocks did quite well.

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The following figure takes the above returns and converts them to their continuously compounded equivalents:

The continuously compounded return is related to the annual return by the following relation:

\[
CtsCompReturn=ln(1 + AnnualReturn)
\]

It is interesting to compare this graph with the first. The mean return here is lower than that obtained by applying the above formula to the mean return of the first graph. On the other hand, and as expected, the percentiles here are just direct translations using the above formula. Unlike the first graph, which is positively skewed, this graph is negatively skewed. This graph is also much more peaked.

Top and Bottom 10 performers in the S&P 100 for 2018

Top 10 performers in the S&P 100 for 2018:

Stock	Return
FOX	41.3%
LLY	40.5%
MRK	39.9%
NFLX	39.4%
ABT	29.1%
AMZN	28.4%
MA	25.3%
PFE	24.8%
MSFT	20.8%
NKE	19.9%

Bottom 10 performers:

Stock

Return

AIG	-32.1%
PM	-33.3%
GS	-33.5%
FDX	-34.7%
F	-35.1%
CELG	-38.6%
KHC	-42.3%
HAL	-44.3%
SLB	-44.7%
GE	-55.4%

The median return for a stock in the S&P 100 in 2018 was -6.60 percent.

Odds of beating the market over many years -- continued

An earlier post shows just how difficult it is to beat the market over many years.

For instance, with a 45 percent chance of beating the market over one year, the probability of beating the market 9 or more years out of 12 is small -- just 36 times out of 1,000, or 3.6 percent (add the probabilities for 9, 10, 11, and 12 years in the figure below). And beating the market 11 or more years out of 12 is truly comically tiny -- just 11 times out of 10,000, or 0.11 percent.

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You may object to my 45 percent assumption, but this is roughly the (optimistic) probability of a mutual fund beating the market in a given year. Here's some proof.

In the 1996 edition of Burton Malkiel's exceptional book, "A Random Walk Down Wall Street," he states:

"Over the whole 22-year period since the first edition of this book, about two-thirds of the funds proved inferior to the market as a whole. [Thus the probability of beating the market (or equaling it) is about 33 percent. To be fair, I am not entirely sure whether this is per year. Nor am I sure of the type of return calculation.]"

However a nearby graph in his book gives plenty of detail. In the graph, Malkiel shows the probabilities of the broad market beating the typical general equity fund for each of the last 22 years. Averaging the values over the 22 years, 1973 through 1994, I get a 56.6 percent probability of the market beating the funds each year or a 43.4 percent of the typical general equity fund beating (or equaling) the market each year.

Thus, the 45 percent assumption is not silly.

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In fact, as the markets have become more efficient, I suspect this 45 percent assumption gives fund managers ample benefit of the doubt. For instance, you will often read that only 25 percent, or so, funds beat the market in the current year.

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I do not know the statistics for the individual investor but I suspect 45 percent is being quite generous. In fact, typical investor performances in mutual funds have badly trailed the already shoddy performance of the funds. In other words, the typical investor underperforms the typical mutual fund -- most likely because of the usual culprits, namely, greed and panic asserting themselves at precisely the wrong times.

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Finally, one last point. Some may argue it is the total compound return that matters over many years not how many times someone beats the market. That is certainly true but just remember generating 40 percent one year, far above the market (say), usually implies weak returns the next few years. And because of how investors behave, jumping in at the tail end of the 40 percent, then holding the fund for the next few years, net, they get killed.

Ideally, what you want is consistent returns just above market with moderate risk. Do that and you make a killing.

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So the next time someone tells you they beat the market, ask them how many times they have beaten the market over a long period. Only then will you get the honest truth -- in my opinion, 70 or 75 percent of the time over a long period is evidence of an extremely strong strategy and performance.

This isn't easy.

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Notes:

The portfolio in "Investing in Dividend Growth Stocks" has beaten the market 11 times out of the last 12, and really 12 times out of the last 13 years, or 92 percent, a record that is matched by no more than a few, if any, (general purpose) mutual funds over this period. Available on Amazon, https://www.amazon.com/Investing-Dividend-Growth-Stocks-Realistic-ebook/dp/B01N30M6DR/ref=sr_1_4?ie=UTF8&qid=1548278535&sr=8-4&keywords=dividend+growth+stocks and https://www.amazon.com/Investing-Dividend-Growth-Stocks-Realistic/dp/0982287003/ref=sr_1_7?ie=UTF8&qid=1548278535&sr=8-7&keywords=dividend+growth+stocks

The portfolio in "Dividend Growth Whisperer," published in October, 2018, handily hammered the market in the fourth quarter of 2018. The portfolio in this book is an update to the portfolio in "Investing in Dividend Growth Stocks." It also presents a novel (and simpler) variation of the crucial concept of valuation. Available on Amazon, https://www.amazon.com/Dividend-Growth-Whisperer-Understanding-Investment-ebook/dp/B07JMMTM4R/ref=tmm_kin_swatch_0?_encoding=UTF8&qid=1548278590&sr=8-1

The latest edition of "A Random Walk Down Wall Street," https://www.amazon.com/Random-Walk-Down-Wall-Street/dp/1324002182/ref=sr_1_1?ie=UTF8&qid=1548277918&sr=8-1&keywords=a+random+walk+down+wall+street

How to lie with data, edition 1,000,007 -- corporate debt to gdp

In yesterday's NBR show, the host showed the following graph of corporate debt to GDP:

He pointed out (1) peaks in the graph coincided with recessions and (2) "now we seem to be at a peak again," in both cases, implying that these debt levels suggest a recession is surely on its way.

Putting aside other causes of recessions, and not making a call on the possibility of a recession, both these points are mistakes, mistakes common to the interpretation of many data series. There also is another issue with the graph.

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On the first point, one should never confuse cause and effect. What most likely is happening is investors' appetite for debt falls during, and in the immediate aftermath of, recessions. Thus, companies cannot issue new debt and corporate debt levels naturally fall. In other words, it is far more likely that it is not the debt causing recessions, but the recessions causing debt levels to fall.

On the second point, there is simply no way to determine in a time series, with no intrinsic a priori natural maximal level, when you are at a peak, until well after the peak. That small declining squiggle could be important or completely irrelevant. Note there was a similar squiggle a bit earlier.

Finally, note the range on the y-axis. The range is too small. By using a small range, the graph looks much more dramatic, though misleading.

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What is most likely happening is with interest rates so low and starting to rise, companies are taking on debt, very likely, long-duration debt. Many companies, in particular large and stable businesses, can and should do this.

Debt has two general concerns -- one is the interest paid and the other is the principal. As interest rates are so low, companies likely have enough cash flow to pay the interest. Even when cash flow levels fall during a recession, with interest rates so low, interest payments are manageable, and companies likely have an ample buffer. Principal is a more serious concern and can put companies out of business in a hurry. Here, intelligent debt management matters. Debt maturities must be spread out, for instance.

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The irony in all this is this variable is very likely not the right statistic, at all. After all, cash may be thought of as negative debt. Thus, net debt, equal to debt minus cash, is far more interesting and relevant. Companies likely have staggeringly large cash balances these days.

Odds of beating the market over many years, a (very) naive model

Suppose you knew, or estimated, the probability of beating the market over a year. What then is the probability of beating the market over many years?

Enter the parameters below, then click "Calculate!" to calculate the probability of a portfolio beating the market the stated number of years (or, for bonus points -- the stated number of years, or more).

Assumptions:

Probability that the portfolio beats the market in a given year (0 to 100, as a percentage, so enter 20 for 20 percent):

Number of years to consider in total (1 to 50, as a number):

Number of years when the portfolio beats the market (0 to the number of years to consider in total, as a number):

 

Notes:

• This calculation is based on a fairly simple model, the binomial model.
• Answers and bonus answers are rounded. Keep this in mind.
• KEYBOARD INTERFACE SHORTCUTS (WINDOWS): Use the TAB, SHIFT+TAB, and ENTER keys to navigate the interface. TAB moves you forward from the first box to the second box and so on. SHIFT+TAB (that is, pressing the SHIFT key and TAB key simultaneously) moves you backward. Pressing the ENTER key while the focus is on the Calculate! button calculates the estimated return.
• A bit technical: JavaScript must be enabled for the above calculation to work.

The figure below shows the probability of beating the market from 0 to 12 years, when the probability of beating it each year is 20 percent. As you can see, the odds of beating the market 7, 8, 9, ... years out of the 12 approach amoeba-like small.

Let's add some sugar to this cup of tea. Let's increase the probability of success. The figure below shows the probability of beating the market from 0 to 12 years, when the probability of beating it each year is now 45 percent. The odds of beating the market now improve dramatically, but are still just 1 out of 1000 to beat the market 11 years out of 12, for instance.

In case you are wondering (and who isn't?), the maximum in these graphs is given by (roughly) the product of 12 times the probability. So, the maximum in the first graph is 2.4 (12 * 0.2, 2.4, rounded to 2) and the maximum in the second graph is 5.4 (12 * 0.45, 5.4, rounded to 5). You will see that the graphs nod approvingly.

Starting off on a high. Dividend growth stocks from "Dividend Growth Whisperer" trounce the market in Q4, 2018.

In my new book, Dividend Growth Whisperer, published October 2018, I list 17 dividend growth stocks. While 3 months is a silly period to consider the performance of an (investment) portfolio, just to amuse myself today, I looked at how the portfolio performed during the fourth quarter of 2018.

The portfolio in the book outperformed.

While the market lost 13.55 percent during the fourth quarter -- as measured by Vanguard's S&P 500 mutual fund, VFINX -- the portfolio in my new book lost - "only" - 8.48 percent, a performance 507 basis points ahead of the market. While this degree of loss is a Pyrrhic victory, it is a decent start, considering the blind panic that infected the market at times during the fourth quarter of 2018 -- when far too many people seemed to run out of their Oreo's.

Quite interestingly, and encouragingly, 14 of the 17 stocks profiled in my new book beat the market over this period, a testament to the high quality of the stocks and the portfolio in general.

And while beating the market is not that big a deal for stodgy stocks (many utilities, for instance), these stocks are not stodgy stocks. They share characteristics that should allow them to perform better than the market over the long term -- at least, that's the theory, and that's why I picked them!

If they do what the stocks in my first book, Investing in Dividend Growth Stocks, have done they should outperform the market in bad times (falling less) and good times (rising more) -- a favorable market trait of extreme rarity. Net, over a long period, 5 to 10 years, they should handily outperform the market. At least, that's the theory....

(Even if all this does not come to pass, I believe they should do quite all right. I believe that my dividend growth stocks -- the portfolios in both books -- should beat 90 percent of all funds over a long period, except in very rare instances: rabid markets or long-term performance off a starting atrocious bear period. The portfolio in Investing in Dividend Growth Stocks has done very well, for instance. Quoting from the Amazon page:

"In 2017, the average stock in the book's portfolio returned 23.2 percent, yet again outperforming the market, which returned 21.7 percent, making it ten years out of the last eleven that the portfolio has beaten the market. [It beat the market again in 2018, so that's eleven of the last twelve years that the portfolio has beaten the market.] The portfolio very likely remains the best general purpose diversified portfolio in the market, besting the vast majority of diversified mutual funds, with the best, or among the best, 10-year records to 2017. Over the last eleven years, $1.0 million invested in the portfolio, dividends reinvested, has vaulted to $4.4 million at the end of 2017, ahead of the market by a not too insignificant $2 million -- and with much less risk, meaning as well, for instance, that you are much more likely to hold onto these stocks and actually realize these returns. Such is the benefit to long-term investors of picking these wonderful companies correctly, that is, intelligently.")

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Many investors fail to appreciate the damage severely bad returns do to a portfolio. For instance, while the book portfolio did beat the market by 507 basis points, it actually is 641 basis points ahead of the market in terms of the returns needed to get back to par -- the book portfolio needs a return of 9.26 percent to get back to par while the market needs a return of 15.67 percent to do the same. That's a considerable victory for the good guys.

Another way to look at all this is to consider the amount of time needed to get these returns. At a market average of 9.5 percent a year, the book portfolio needs a little less than a year. The market however would need 1.60 years. So, in a sense, we are 7+ months ahead of the market -- and really considerably more, perhaps 9+ months to a year, since typically dividend growth portfolios outperform the market. Not a bad start.

You only have a finite time horizon in which to invest so time is indeed money.

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Game on.

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Notes:

Dividend Growth Whisperer, on Amazon, https://www.amazon.com/Dividend-Growth-Whisperer-Understanding-Investment-ebook/dp/B07JMMTM4R/ref=tmm_kin_swatch_0?_encoding=UTF8&qid=1547491648&sr=8-1

VFINX, https://investor.vanguard.com/mutual-funds/profile/performance/vfinx

We win again. Dividend Growth Stocks from "Investing in Dividend Growth Stocks" beat the market again in 2018.

2018 was a bad year for most U.S. stocks. The stock market, as measured by the S&P 500, returned -4.38 percent for the year. The typical fund did much worse. According to the January 7, 2019 edition of the Wall Street Journal, "the average manager overseeing a diversified U.S.-stock fund saw a total return of minus 7.73% in 2018..."

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As they are wont to do, dividend growth stocks fared better. VIG, Vanguard's Dividend Appreciation ETF, returned -2.1 percent in 2018.

The portfolio of dividend growth stocks from my book, Investing in Dividend Growth Stocks, typically beats both the Dividend Growth Index and the market. 2018 was no different. In 2018, the portfolio from the print edition of the book returned -1.39 percent, again besting both the market and VIG. The figure below shows that it has beaten the market for each of the last three years.

The longer-term pattern is just as dominant. As the figure below shows, the portfolio from the print edition of the book has beaten the Dividend Growth Index every (full) year since the index's inception in April, 2006. Likewise, the book's portfolio has beaten the market every year over this period except for slightly underperforming in 2014.

So the book portfolio has beaten the Dividend Growth Index for 12 straight years and has beaten the market 11 of the last 12 years, marginally trailing in the one year that it did not (2014). I would venture to guess no more than a handful -- literally -- of professional funds can stake such a claim -- the odds are very low. I remember, years ago, what a big deal magazines and websites were making of a fund manager that had beaten the market 10 then 15 years in a row. This kind of thing is not common, at all.

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The reason for our long-term consistent outperformance is quite simple: These are good companies that typically do not get outrageously valued. There are ample subtleties in this simple statement, of course, and that is the rub.

The trick is to have a sound dividend growth strategy, a sound dividend growth model! For instance, many investors in the naughts thought banking stocks were all the rage because they kept consistently raising their dividends -- they completely ignored the high and rising leverage inherent in these companies, as one self-evident and obvious mistake. As one of many examples, Lehman was raising its dividend at a 25 percent a year clip for several years. Meanwhile, and comically ignored by many, its leverage kept rising as well. We all know what happened to Lehman and many other banking stocks -- Lehman went kaput and many banking stocks are still in the doghouse -- with no real dividends to speak of. Likewise, many investors choose utilities as dividend growth stocks. That too is incorrect. You need growth. These fellows don't have it. Dividend and dividend growth investors ignore share buybacks. You simply cannot do that as well. And on and on it goes. These are logical mistakes that damage your returns.

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Any old dividend growth "strategy" will not work. Most of what you read, even in published and putatively well-regarded books, is incorrect. The underlying theory must be logically sound. At the very least, it must be consistent and complete. Where's the Beef?

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Notes:

The S&P 500 returned -4.38 percent in 2018. Many websites and publications quote a different value, very often, -6.2 percent. That value is incorrect. http://www.neocadence.com/2019/01/land-of-confusion-what-did-market.html

Performance page for VIG, the Vanguard Dividend Appreciation ETF, https://investor.vanguard.com/etf/profile/performance/vig

Bill Miller was the mutual fund manager who beat the market for 15 years in a row. He was a star for many years -- though he took big risks to generate these returns, risks that were unappreciated by many writers -- and he did struggle for a while later on. An old book about him, The Man Who Beats the S&P, https://www.amazon.com/Man-Who-Beats-Investing-Miller/dp/0471054909

A 2008 article on Bill Miller's subsequent troubles, also highlighting the riskiness of his strategy, https://www.wsj.com/articles/SB122886123425292617

Investing in Dividend Growth Stocks, print edition, on Amazon, https://www.amazon.com/Investing-Dividend-Growth-Stocks-Realistic/dp/0982287003/ref=sr_1_4?ie=UTF8&qid=1547051337&sr=8-4&keywords=investing+in+dividend+growth+stocks

Investing in Dividend Growth Stocks, kindle edition, (naturally!) on Amazon, https://www.amazon.com/Investing-Dividend-Growth-Stocks-Realistic-ebook/dp/B01N30M6DR/ref=sr_1_3?ie=UTF8&qid=1547051337&sr=8-3&keywords=investing+in+dividend+growth+stocks

Land of Confusion: What did the market return in 2018? Really, now.

In today's Wall Street Journal (the Monday, January 7, 2019 edition), Suzanne McGee, in the "Best Stock-Fund Managers of 2018" writes that the S&P 500 returned "a 6.2% loss for the full year."

Okay.

In the article immediately below this one, that is, on the same page, Mark Hulbert, in "The Skeptic's Guide to Yearly Performance Rankings," writes that the S&P 500 realized "a 4.4% loss [for the year]."

All right, then.

Who's on First?

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Meanwhile, VFINX, Vanguard's S&P 500 index fund, reports a loss of 4.52% for 2018.

This includes annual expenses of 0.14%. Thus, roughly, deducting this expense ratio from 4.52% gets you -4.38%, or to within one decimal, Mark Hulbert's 4.4%.

I would thus consider this -- a loss of 4.4% -- to be the "right" return for the S&P 500 for 2018. If anyone else says 6.2% or something like this you can bet they have not included dividends, let alone reinvested dividends -- a bad, bad mistake. Yet, you will see this loss of 6+% in many places. Not good.

One more point and perhaps an occasional cause of error as well: An annual return must start counting from the ending price on the last day of the prior year to the ending price on the last day of the current year. Anything else gets you a mess.

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If you'd like to calculate the return yourself, use Yahoo! Finance's S&P 500 total return index, counting from the adjusted close on the last trading day of 2017 to the adjusted close on the last trading day of 2018. If you do this, you will see the S&P500 returned a loss of 4.38% for the year:

(4984.22 - 5212.76)/ 5212.76 gives you -4.38%

This is the return for 2018. Just say no to anything else. Price indexes should never be used as the basis of your calculated returns. This is what the first author of the Wall Street Journal did. Not good.

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References:

Who's on First? (video: https://www.youtube.com/watch?v=kTcRRaXV-fg)

VFINX, https://investor.vanguard.com/mutual-funds/profile/performance/vfinx

Yahoo! Finance's S&P 500 total return index, https://finance.yahoo.com/quote/%5ESP500TR/history?period1=1512104400&period2=1546837200&interval=1d&filter=history&frequency=1d

Valuing a Dividend Growth Stock with the Magic Formula (Dividend Growth Whisperer)

Enter the parameters below, then click "Calculate!" to calculate the estimated return for a dividend growth stock with those parameters.

Assumptions:

Payout Ratio (50 to 90, as a percent):

Earnings Growth Rate (3 to 14, as a percent):

Current P/E Ratio (10 to 30):

 

Notes:

• This calculation is based on the magic formula detailed in my recently published book, Dividend Growth Whisperer. The magic formula, with a couple of heuristics, provides a complete, reasonable valuation methodology to value dividend growth stocks (and really all stable stocks, as well).
• KEYBOARD INTERFACE SHORTCUTS (WINDOWS): Use the TAB, SHIFT+TAB, and ENTER keys to navigate the interface. TAB moves you forward from the first box to the second box and so on. SHIFT+TAB (that is, pressing the SHIFT key and TAB key simultaneously) moves you backward. Pressing the ENTER key while the focus is on the Calculate! button calculates the estimated return.
• Payout ratio is not the dividend payout ratio. Instead, it includes dividends, (net) share buybacks (that is, cash spent on share buybacks minus cash collected from shares issued), and any cash that the company can return to shareholders but for whatever reason does not, allowing for the company to retain some for adverse times. Obviously, this is estimated and requires a good understanding of the company's business.
• (Average) earnings growth rate is the average earnings growth rate (not the average earnings per share growth rate!) over the next 30 years, the earnings pattern similar to the pattern of earnings stipulated in the model in my book, Investing in Dividend Growth Stocks. Per the book, implicitly, therefore, I assume any stated average earnings growth rate incorporates earnings growth rates of R percent a year for 10 years, S percent a year for the next 10 years, and T percent a year for the last 10 years (of the 30), where R >= S >= T. Earnings growth after 30 years is assumed to be 3 percent a year, continuing for 170 years (!), essentially, then, until the present value of the values at those later years hits, effectively, zero.
• Earnings growth rate is roughly earnings per share growth rate minus the net share buyback rate. So if a company has an earnings per share growth rate of 8 percent a year and buys back its shares, net, at 2 percent a year, its earnings growth rate is 6 percent a year.
• Moderate growth here signifies the moderate earnings per share growth typical of dividend growth stocks as defined in my books, so 8-12 percent a year for large-caps and 8-16 percent a year for midcaps. Here, somewhat arbitrarily, the valid ranges are set from 3 percent to 16 percent.
• Current P/E ratio, ideally, reflects average earnings 6 months in the past and 6 months in the future. Roughly, it is the current price divided by the sum of eps for the last 2 quarters and the next 2 quarters.

Valuing Chipotle

Ticker: CMG

Sector: Consumer Discretionary

Size: Large-cap

Website: http://www.chipotle.com


A "messy" recent history: In the last few months, Chipotle has had a bad case of burrito indigestion (chipotle.com). Five incidents of outbreaks have been reported (WSJ):

"Since July, there have been a total of five outbreaks linked to Chipotle, including a little-reported case of E. coli that sickened five people in Seattle and which was a different strain unrelated to the larger outbreak that began in October, as well as a norovirus case in Southern California, a salmonella outbreak in Minnesota and the Boston [norovirus] outbreak."

From a close of $720 in September 2015, the stock closed at $448 yesterday, a fall of 38 percent. Its stock chart is a mess -- though the downward momentum of the fourth quarter of 2015 seems to have abated:

Not surprisingly, analysts have ratcheted down their earnings per share estimates sharply. For the fourth quarter of 2015, estimates have fallen 57 percent from $4.37, ninety days ago, to $1.86 today. For 2016, estimates have fallen 37 percent from $20.46, ninety days ago, to $12.86 today (Yahoo! Finance).

In terms of earnings per share, roughly, 2016 represents a setback of 2.5 years.

General Analysis: Chipotle is a high-growth stock, a class of stocks notoriously difficult to value because high growth tends to be unstable. With Chipotle, however, growth is stable, making it easy to value. In this post, I follow the guidelines and format in Twenty dividend growth stocks to consider in Investing in Dividend Growth Stocks (pages 219 - 272) (Amazon). Chipotle is not a dividend growth stock -- it does not pay a dividend -- but its underlying business stability makes it, with one tweak for two scenarios, similar to value. I use Chipotle's results from 2010 through 2014 to unearth the underlying characteristics of the business. Incorporating a messy 2015 would distort the analysis.


The Business: Chipotle sells burritos, tacos, burrito bowls, and salads -- "a few things, thousands of ways" -- at its more than 1,900 fast casual restaurants, primarily in the U.S. The company also operates a much smaller chain of 11 Southeast Asian Kitchen restaurants and invests in an entity that operates 3 Pizzeria Locale restaurants. The company's by-line is "food with integrity." Its grander aim is to change "the way people think about and eat fast food."


Risks: After the outbreaks, will consumers return? According to the company, same restaurant sales fell about 15 percent in the fourth quarter of 2015 (Bloomberg). Nevertheless, I believe consumers will eventually return. With good, honest companies, the underlying business eventually recovers. In the 1980s, Johnson & Johnson had the Tylenol scare. They fixed it. Consumers returned. A few years ago, Johnson & Johnson had problems with manufacturing. They fixed it. Consumers returned. Where there is value -- and integrity -- in the brand, as with Johnson & Johnson and Chipotle; and problems are addressed, as Johnson & Johnson did and Chipotle is doing (chipotle.com), consumers do eventually return.

Of the other risks, commodity costs are one. Consumers do visit restaurants less often during recessions -- though Chipotle's relatively inexpensive food may mean it may not see the dramatic declines symptomatic of higher-priced restaurants.

Few other risks, longer term, meaning, in the next 10 or so years.


The Numbers: Profit margins have averaged ten percent the last five years. Asset turnover is 1.6. Chipotle does not have long-term debt -- in the traditional sense. It does, however, disclose deferred rent obligations. Financial leverage is low, 1.3. Return on equity is 22 percent. Likewise, return on equity has averaged 22 percent the last five years. Moreover, because the company has excess cash and investments on its balance sheet, its "true" return on equity is higher.


Dividends and Share Buybacks: The company does not pay a dividend. The company does buy back shares, mostly, it seems, to offset dilution. Over the last five years, the company has retired its shares at a modest 0.4 percent per year clip. (Comparatively, dividend growth stocks typically retire their shares at a much higher rate, but Chipotle is a high-growth stock. In fact, that it even retires its shares is somewhat of a bonus.)


Spreadsheet Parameters: (I use the spreadsheet described in Investing in Dividend Growth Stocks (Amazon) -- with a slight tweak to adjust for the possibility of a robust recovery in earnings per share -- to value the stock. See pages 158 - 176.) Actual dividend payout ratio of 0 percent; assumed payout ratio of 35 percent. Return on beginning equity: 30 percent. It is currently 29 percent. It has averaged 27 percent the last five years. In fact, because the company has excess cash and investments on its balance sheet, its "true" return on beginning equity is higher -- I am likely conservative with my 30 percent. Earnings growth has averaged an impressive 29 percent the last five years. Few large companies can sustain such high growth rates over long periods and, in that sense, Chipotle is one of the rare ones. Dividend growth: n/a. Earnings per share growth roughly mirrors earnings growth because share buybacks are muted. Chipotle operates more than 1,900 restaurants. The company opens more than 200 net new restaurants a year. It is not unreasonable to assume they can maintain this pace for at least the next several years. I do not believe the market is near saturation. For instance, McDonald's is virtually everywhere in the U.S. -- and McDonald's has 14,300 U.S. restaurants (though they do intend to close a handful this year (New York Times)). Moreover, Chipotle will almost certainly expand outside the U.S. more aggressively at some point and the company is testing a few new restaurant ideas. Reasonable growth rates for our spreadsheet, if sales were to resume their historical growth rates: (Years 1-5: 26 percent) (Years 6-10: 22 percent) (Years 11-20: 16 percent) (Years 21-30: 10 percent) (Years 31+: 3 percent).


Sample Spreadsheet Results: Because earnings per share can vary dramatically the next several quarters, I use four potential scenarios to gauge the scope of variability:

• (1) Reset -- current depressed earnings per share.
• (2) Quick Reset -- higher current earnings per share.
• (3) Reset ++ -- current depressed earnings per share, then full recovery next year.
• (4) Quick Reset ++ -- higher current earnings per share, then full recovery next year.

Explicitly, I use the following values:

Scenario	Stock Price	EPS - current	P/E ratio - current	EPS - next
(1)	450	11	41	13.86
(2)	450	15	30	18.90
(3)	450	11	41	22.55
(4)	450	15	30	22.55

These earnings per share are for periods centered on January 1 -- thus the last 6 months of 2015 plus the first 6 months of 2016 for the current period, for example.

Of course, even within these patterns, we have many other possibilities -- but at least they help establish a range. Using a current stock price of $450, and the spreadsheet described in Investing in Dividend Growth Stocks (Amazon), I get the following results:

Scenario	Expected Return
(1)	12.33%
(2)	13.85%
(3)	14.80%
(4)	14.79%

Screenshots from the spreadsheet for scenario (3), also showing the slight tweak in red (also needed in scenario (4)) I made in the Projections section:

These are long-term returns. All are outstanding -- because growth remains deliciously high. If Chipotle produces these gains, investors will be well ahead of the market. That said, none of these results make any sense if growth permanently collapses (YouTube) but I do not believe this happens.

In addition, risk is not low under any of our scenarios -- as the relatively high P/E ratios attest.

As a comparison, if we were to live in a parallel universe (YouTube), with the recent company-specific indigestion nonexistent and Chipotle humming along, at a stock price of (say) $600 (to account for the recent market decline -- the market still declines in the parallel universe) and earnings per share of $19, all other assumptions the same as above, the expected return is 13.59 percent a year -- and, yes, with a P/E ratio of 32, the stock is still not low risk. Blame those high P/E ratios -- even in the parallel universe.

Disclosure: I own a tiny position in Chipotle, entirely for fun. I always order a carnitas burrito. It rocks. Do not interpret this post as a recommendation to buy or sell or trade or whatever, including buying a Chipotle burrito. Always do -- and depend -- on your due diligence.

Why weekly up-moves are likelier than daily up-moves

Historically, the probability of an up-day in the market is about 54 percent and the probability of an up-week is somewhat higher. In fact, as long as the probability of an up-day is over 50%, the probability of an up-week is also over 50% -- and the probability of an up-week exceeds the probability of the up-day, whatever it is.

To do so, I make one important simplification, for now: I assume the market closes up for the week if it closes higher on more days than it closes lower. (Regarding unchanged closes, just consider down to include these). In other words, I assume the market closes up for the week if it closes higher three or more of the five trading days in a week. Of course, this is not necessarily true as, for instance, one big up-day can make up for four down-days, but for now I will stick with this simplification -- I do not want to assume a particular distribution for the underlying distribution of returns. I leave the more complex stuff for later.

Thus, our problem reduces to the following: Out of the five trading days in a week what is the probability that the market closes higher three, four, or five days of the week. If p denotes the probability of the market finishing higher on a day, (1-p) is the probability that the market finishes lower. You can think of each day as the toss of a coin -- and all five days as a sequence of five coin tosses. The totality of probabilities is then given by the various terms in the expansion of the binomial formula when n is 5:

\[
\left(p+\left(1-p\right)\right)^{5}=\sum_{i=0}^{5}\binom{5}{i}p^{i}\left(1-p\right)^{5-i}
\]

Our answer is simply the sum of last three terms of this expression. Thus, in reverse order,

\[
p^{5}+5p^{4}(1-p)+10p^{3}(1-p)^{2}
\]


The trick now is to establish that this expression is greater than p. If so, we have shown what we had intended, that weekly market gains happen more often than daily market gains. In the following plot, the blue curve represents the function, the probability of an up-week, the green line, p, the probability of an up-day:

As you can see, the blue curve exceeds the green line -- it is above the green line -- when p is between 0.5 and 1.0.

The following graph makes this clearer. It is a straightforward modification of the above, simply taking the difference between the probability of an up-week and the probability of an up-day and plotting this against the probability of an up-day:

As before, when the daily up-probability is between 0.5 and 1.0, the difference between weekly and daily up-probabilities is positive, meaning the probability of an up-week exceeds the probability of an up-day. In the real world, p needs to typically average above 0.5, long term, or else the market is doing nothing or destroying wealth. (I guess theoretically this could happen, but it has not and generally should not happen in more established markets.) Thus, as p is typically more than 0.5, we have proved our assertion: weekly market gains happen more often than daily market gains. (As an aside, in the graph, when p is between 0.5 and 1.0, the maximum difference is achieved when p is 0.76.)

Let us see how our expression meshes with the historical data noted earlier. From an earlier post, we saw that the probability that the stock market closes higher on any given day is (only) 53.7%. Thus, p = 0.54 (rounded to 2 significant digits). Using this value of p in our expression, we get that the market finishing higher during the week is 0.57, or 57%, in agreement, essentially, with our result from a previous post that the S&P 500 encounters an up-week 56.5 percent of the time.*

Kind of spooky cool, though probably a fair bit lucky.

* [Updated:] I reran the calculations based on a set of daily returns that essentially matches the years (1950 through 2015, roughly) under consideration for the weekly returns. In this case, p is 0.53, and I get that the market finishing higher during the week is 0.56, or 56%, again close enough to the result from the previous post about weekly returns.

How dividend growth stocks outperform the market

The following graph plots the weekly returns of the market versus VIG (Yahoo! Finance), the dividend growth ETF from Vanguard, which I use as a proxy for dividend growth stocks:

The graph shows that dividend growth stocks have a higher peak than the market and the distribution of weekly returns "spreads" less, that is, the distribution has a lower standard deviation, and is therefore less risky (Wikipedia). With dividend growth stocks, probability is concentrated in the center -- with a much smaller left tail and a smaller right tail than the market. Thus, dividend growth stocks do not suffer from collapses and manias nearly as much as the market -- especially with regard to collapses -- and their outperformance during bear markets more than makes up for their somewhat muted performance during bull markets. Net, they march silently up and to the right.


The following statistics compare dividend growth and the market:

	Dividend Growth	Market	Difference
Mean	0.14	0.11	0.03
Standard Deviation	2.26	2.61	-0.34
Quantiles: 0%	-15.76	-18.20	2.44
25%	-0.95	-1.06	0.11
50%	0.29	0.22	0.07
75%	1.41	1.42	0.00
100%	10.42	12.03	-1.60

As unquestionable positives, dividend growth stocks have:

• a higher mean than the market,
• a lower standard deviation,
• a higher median, and
• a shorter left-tail.

In exchange, what dividend growth stocks give up is:

• a shorter right-tail.

The following plots show the spread of returns in another way. The line within the boxes is the median, the lower border the 25th percentile, the upper border the 75th percentile. The first plot compares the full pattern of returns (extreme returns show up as gray points though you have to look closely to spot the gray dots -- they also appear as duplicates, though this is not relevant here, and I ignore this):

The second plot zooms in on the left tail. Importantly, dividend growth stocks perform quite a bit better than the market in the left tail --  these are weekly returns so the 0.11 difference, as shown in the table above, is material. These stocks do not collapse nearly as much as the market when the nasty times arrive. In my opinion, this relative outperformance is one of the key reasons long-term investors should invest in dividend growth stocks.

The third plot zooms in on the right tail. Importantly, dividend growth stocks perform just slightly weaker than the market in the right tail --  the difference is just 0.01:

Thus, dividend growth stocks underperform during bull markets (but not by much, in general) and outperform during bear markets (by a lot). This combination helps ensure good risk-adjusted long-term returns and explains how dividend growth stocks outperform the market.


As far as the current (early 2016) market malaise goes, not surprisingly, dividend growth stocks are outperforming the market. Admittedly, they are getting hit but these are high-quality companies and they are not getting hit nearly as much as many other segments of the market, or the market itself:

An important tenet of Investing in Dividend Growth Stocks (Amazon) is that dividend growth stocks are core holdings because they generate good long-term risk-adjusted returns. They do so through a combination of moderate returns and relatively low volatility. Quoting from page 20:


"[A] portfolio [of dividend growth stocks] rises less than the market during bull markets and falls less than the market during bear markets. The latter more than makes up for the former. These stocks march to the beat of a different drummer -- but a very sensible one."



In my opinion, these stocks are excellent long-term investments (subject to not paying too much, as always, of course) for anyone who wants to preserve and build their wealth.


These are not gimmicky companies or slow-growth companies or risky companies. These are companies that last. They grow moderately over long periods, which when combined with relatively low return volatility results in strong gains in long-term wealth.

Probabilities for the S&P 500 weekly return

The previous post highlighted the relative rarity of 2016's week 1 return in the context of history. The following plot shows this in another way. It shows the probability density function (Wikipedia) for the S&P 500 weekly return based on history:

The green area highlights areas where the weekly return is positive; the red area highlights areas where the weekly return is less than -5 percent; and the blue area highlights the in-between areas.

With this probability density function, we deduce probabilities for the S&P 500 in any given week:

• Probability of S&P 500 returning less than -10 percent in a week is 0.1 percent.
• Probability of S&P 500 returning less than -5 percent in a week is 1.4 percent.
• Probability of S&P 500 returning less than -2 percent in a week is 12.5 percent.
• Probability of S&P 500 returning less than -1.5 percent in a week is 17.9 percent.
• Probability of S&P 500 returning less than -1 percent in a week is 25.3 percent.
• Probability of S&P 500 returning less than -0.5 percent in a week is 33.2 percent.
• Probability of S&P 500 returning less than 0 percent in a week is 43.5 percent.
• Probability of S&P 500 returning less than 0.5 percent in a week is 54.9 percent.
• Probability of S&P 500 returning less than 1 percent in a week is 66.5 percent.
• Probability of S&P 500 returning less than 1.5 percent in a week is 77.9 percent.
• Probability of S&P 500 returning less than 2 percent in a week is 85.1 percent.
• Probability of S&P 500 returning less than 5 percent in a week is 98.6 percent.
• Probability of S&P 500 returning less than 10 percent in a week is 99.9 percent.

The second bullet agrees with the observation of the previous post, that the S&P 500 losing more than 5 percent in a week is about 1 in 70, or about 1.4 percent.

According to the  seventh bullet, the S&P 500 suffers a down-week 43.5 percent of the time. Consequently, the S&P 500 encounters an up-week 56.5 percent of the time. This fits the conclusion of an earlier post about daily returns -- that the market closes up on any given day about 53.7 percent of the time (though that post was based on a different set of data). Weekly returns show positive closes with a slightly higher up-probability than daily returns because of compounding. In fact, this logic works sequentially for all types of returns -- thus monthly returns have higher up-probabilities than weekly returns, annual returns have higher up-probabilities than monthly returns, five-year returns have higher up-probabilities than annual returns, and so on.

I zoomed in on the red area, where life is unpleasant:

If you are unfamiliar with probability density functions, here is the same data shown as a histogram. A histogram sorts the data and organizes it into buckets with the height of each bucket, in this plot, a count:

And a zooming-in of the nasty left tail shows the location of the first week of 2016: