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

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 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:

2016's week 1 return among the 50 worst since 1950

The following plot shows the 50 worst weekly returns of the S&P 500 since 1950 (data from Yahoo! Finance):

The first week of 2016, highlighted in the upper right, is bad -- but not the worst. The worst is the 18.2 percent loss for the week ending October 10. If you recall that amusing period, within a week, Warren Buffett wrote "Buy American, I Am," http://www.nytimes.com/2008/10/17/opinion/17buffett.html, where he advocated being greedy during periods when others are fearful:

"Be fearful when others are greedy, and be greedy when others are fearful. And most certainly, fear is now widespread, gripping even seasoned investors."

Fear is not quite as widespread now as it was then but this thumping has likely taken quite a few investors back to the days of Fall 2008's halcyon panic. Undoubtedly, the market looks awful now -- and the carnage has started to become indiscriminate. A number of decent stocks have been hit, based entirely (most likely) on margin calls, stocks that will nevertheless report excellent numbers in the quarters ahead.

This table shows that the first week of 2016 -- with a weekly return of -5.96% -- is 32nd on the list of worst weekly returns since 1950:

Based on the full set of data, the chance of getting such a bad week (a weekly return of roughly -5% or worse) is roughly 15 out of 1,000 or roughly 1 out of 70 or roughly one week every 16 months. The market did not encounter any such weeks during 2012, 2013, and 2014. In 2015, it encountered one - the week ending 08/21/2015. That week, which saw a loss of -5.77%, is 36th on the list.

Perhaps we are due. Buckle up? Typically, these things do tend to occur in clusters:

This pattern shows clustering -- a tendency for movements to occur close to each other. Certainly, the movements are not random, in the sense that they occur somewhat regularly but without any discerning pattern. This is very different from movements about the mean or 0 -- which do show randomness. For instance, in an earlier post, we saw that randomness is characteristic of monthly returns about 0. Sharp falls have a separate nature unto themselves. They occur relatively rarely and they tend to cluster. Of course, predicting the first is next to impossible. Once you have the first, however, you can be reasonably sure of one or two others upcoming. Maybe.

In my book, Investing in Dividend Growth Stocks, I emphasize stability of returns for long-term investors precisely because I am not a fan of extreme movements for the typical long-term holder of any stock (you have no choice if you hold the market, which I am also not a huge fan of, but that story is for another day). Moreover, it is not difficult to show that if you have stability in your returns you tend to have a higher compounded return (read: wealth), all else equal. When you invest in unstable stocks and many markets you have to be certain not to get continually hammered as your long-term returns will invariably suffer. With generally stable markets such as the U.S. market, this "suffering" is not nearly as great as it is with many other markets. Essentially, this has to do with excess volatility acting like a leech, bleeding off your compounded return, hence wealth. From my book:

"If you had to choose between (a) two years of returns at 10 percent a year and (b) a first-year return of 0 percent a year followed by a second-year return of 20 percent a year, which would you choose? Although the average of both choices is 10 percent a year (the average of two tens is 10 and the average of 0 and 20 is 10), the stable growth of the first choice results in more wealth. With the first choice, for every $100 that you invest, you end up with $121; with the second choice, for every $100 that you invest, you end up with $120. Yes, all of $1 less; but what counts is the general principle: For a given average return, where the average is computed simply as the sum of the annual returns divided by the number of years, stable growth is always more valuable than fluctuating growth."

For more, see pages 76-81 of my book. If you do not have the book, you may be able to view the pages on Amazon if you use Amazon's look-inside feature for the book, here.

What is the probability that the stock market closes higher on any given day?

The punch line: The probability that the stock market closes higher on any given day is (only) 53.7%. That's it. Better than flipping a coin, but not by much. The rest of the time it finishes lower (45.2% of the time) or unchanged (1.1%). Yet, because of compounding, this is all that it takes to produce a trend -- and a strong uptrend -- over time.*

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On any given day will the stock market rise or fall? I used daily adjusted closing price data from Yahoo! Finance for SPY, the S&P 500 ETF to find out. The data span 01/29/1993 to 12/11/2014. Here is a bar chart with results grouped by year:

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The bar chart is not zeroed on the y-axis and is scaled to make the differences apparent. The probability of up days spans a range of 47.4% (in 2002) to 59.2% (in 2014). On any given day, the stock market will rise 53.7% of the time (and fall or remain even 46.3% of the time). Your odds of making money are roughly 27:23, or even more roughly, 6:5. That's it. Don't bet the farm. For such a short period as a day, you're essentially tossing a coin.

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*  I'm almost certain that this phenomenon is similar to why a tiny preference by people for some attribute leads to a clustering of those attributes around a geographic area over time. In other words, what we expect to be a random distribution of attributes over geographic area instead exhibits a clustering effect. Likewise, for us, what we expect to be a random distribution of stock prices over time, instead behaves -- when there's a slight increase in chance -- as a strong trend of gradually rising prices.

How have the biggest losing stocks of 2013 fared so far

The punch line: The accepted wisdom, really theory, is that big losers of one year become big winners the next year. Buy the losers in December. This theory is invalid -- or at least should be modified as far as it pertains to all stocks. The theory may have validity for the huge companies of the Dow, where companies do tend to come back and companies rarely fail. With most other stocks, however, total failure is a genuine possibility. Big losers of one year can become even bigger losers the next year because they have systemic troubles. In general, stay away from companies with systemic troubles. They can dissolve into nothingness. If a preliminary pass to avoid such stocks is made, returns improve.

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Method: I took a random list of big stocks that were losers in 2013, "Fortune 500: Worst-performing stocks of 2013," http://money.cnn.com/gallery/investing/2013/12/19/fortune-500-worst-stocks/, and calculated how they have performed YTD in 2014. I just read off the returns from Yahoo! Finance. Thus things like bad data, dividends (potentially), and reorganizations are not considered.

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Results: A portfolio of the fifteen worst stocks of 2013 has returned -10% so far this year, underperforming the +10% return of the index. However, it gets more interesting when the group is broken down into two constituents: (a) companies with long-term troubles; and (b) the rest. The stocks in group (a), indicated by a comment in the last column below, have returned -37%. When you have that many coal stocks and one bankruptcy (or close to it, NIHD lost 97% and now trades on the pink sheets as NIHDQ -- I've used -100% in the table) that is bound to happen. The gold miner may not be in long-term trouble but gold has done poorly over the long term. The stocks in group (b) have returned a more respectable +13%, ahead of the market by 3 percentage points. Here is the breakdown:

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Conclusion: You have to be careful buying losers, as far as it pertains to most stocks. The best bet is to avoid those with systemic troubles. You need to do a preliminary pass and weed out such stocks. If this is done, buying the remaining losers (as a group) can work though you have to be careful and pretty patient.