Saturday, February 2, 2019

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.

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.

Friday, January 25, 2019

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.

Wednesday, January 23, 2019

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.


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.


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.


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.


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.


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.



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, and

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,

The latest edition of "A Random Walk Down Wall Street,"

Friday, January 18, 2019

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.


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.


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.


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.

Wednesday, January 16, 2019

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).


  • 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.

Monday, January 14, 2019

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.")


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.


Game on.



Wednesday, January 9, 2019

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..."


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.


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.


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?



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.

Performance page for VIG, the Vanguard Dividend Appreciation ETF,

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,

A 2008 article on Bill Miller's subsequent troubles, also highlighting the riskiness of his strategy,

Monday, January 7, 2019

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."


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?


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.


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.



Who's on First? (video: