Yearly Archives: 2017

Fifteen or so years ago, my wife asked me to frame our series of family Christmas photos, as a gift to her.  We started taking these photos after our son was born, to include in our Christmas cards.  We stopped sending cards and taking annual photos after our daughter left for college and our son moved to another state.

Anyway, after fifteen years, I finally got around to finishing this project, and we hung the frames yesterday.  I was not always the most careful photographer, so I had to do some heavy-duty photoshop work to turn the scans (remember film?) into something printable.  While I was at it, I also replaced a couple of unsmiling faces in the original prints with better versions from our outtakes.  Photo editing software was not available back then (and there was no way to view images on the spot), so we would have to take ten or twenty shots and hope that one of them was good enough.  Our kids somehow put up with this routine — I don’t remember us bribing them.  Maybe we did.

As a photographic record, this might not be as captivating as what Diego Goldberg and his family publish in his Arrow of Time series, but it’s ours.  So here is a Happy Hanukkah and/or Merry Christmas and/or Happy Kwanzaa to our observant friends.*


* And Donald Trump, may you receive a holiday visit from the jolly old souls at The FBI.
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The Trend, Again

I have written two posts about long-term trends in the U.S. stock market, as represented by the S&P 500 price index.  My first post, The Trend, showed how the index swings above and below its long-term trend but eventually returns to the trendline.  My second post, The Trend Revisited, introduced the sidebar widget I created for the blog which compares the current index to the value predicted by The Trend.

My third post on this subject tries to address a point that always bothered me: why offer information about stock market trends (or any topic for that matter) unless it allows one to act on it?  I hope the following analysis makes a contribution toward that end.

My goal is to show whether the amount that the current price is above-or-bel0w-trend says something useful about the return one may expect over the next twelve months and the chance that this return is positive.  This is the type of information one might act on.

To get started, I downloaded a list of the monthly closing prices of the S&P 500 index from January 1950 to November 2017.  Next, I calculated the amount that each price was above or below the trend and used that to sort the prices into buckets: 50% to 30% below trend, 30% to 10% below trend, 10% below to 10% above, and so on.  Finally, for each of the month-end prices, I wrote down how much the price had increased (or decreased) twelve months later.

I present this data in the chart below.  Each horizontal bar represents the one-year return for a specific month in the timeframe, using blue bars for positive returns and red bars for negative returns.  For example, the lowest red bar at bottom right represents the change (-28.8%) in the S&P 500 index from September 30, 2000 (when the monthly closing price was 99.4% above trend) to September, 30, 2001.

You will notice a weak (but noisy) correlation between the amount that the current price is above or below trend and the one-year-later price change.  Roughly speaking, the expected one-year-later return decreases by 1% for every 7.25% that the current price is above trend.

Because there were relatively few data points in the uppermost trend buckets, I combined the four highest buckets for this analysis.  Here are the results of interest, in tabular form:

Above/Below Trend Range n Average One-Year Return (%) Std Dev One-Year Return (%) Chance of Positive Return
-50% to -30% 106 15.0 15.0 84%
-30% to -10% 164 13.8 14.1 84%
-10% to +10% 227  7.9 14.8 70%
+10% to +30% 167  7.5 16.1 68%
+30% and up 139  1.0 15.2 53%

First take note of the one-year returns.  The average one-year-later return is pretty decent, as long as the current price is less than 30% above trend.  If the current price is more than 30% above trend, one’s expected one-year return is close to zero.

But also take note of the standard deviation (uncertainty) of the one-year-later returns.  The uncertainty in the return, in every trend range, is about 15 percent.  This means that, about two-thirds of the time, the actual return will be somewhere from 15 percent less to 15 percent more than the average return.  This is a large uncertainty for a one-year return: 15 percent represents about two years’ worth of typical returns.

This brings me to the last column, Chance of Positive Return.*  As these figures show, one has an 84% chance of making money a year later if the current price is 10% or more below the trend.  This offers the best opportunity.  If the current price is 10% below to 30% above the trend, one still has a 68% chance of making money a year later.  But if the current price is 30% or more above trend, the chance of coming out ahead one year later is only 50-50.

[This sentence exists for the sole purpose of allowing your mind to absorb these figures.]

As I said earlier, information is useless if one cannot take action by knowing it.  The action one might take based on the amount the S&P 500 index is above (or below) trend would be to sell (or buy) stocks.  Based on this analysis, I suggest that one consider selling stocks if the current price is 30% greater than that predicted by the trend, because one’s chance of coming out ahead a year later is no better than 50-50.

In all other cases, I would suggest holding onto your investments if you can weather the possibility of a negative return.  (If you cannot weather that possibility, you should not be investing in the stock market or mutual funds in the first place.)

One last item.  You may ask, why did I focus on one-year returns as opposed to some other time period, such as six months or three years?  It is because once-a-year is about the right frequency for most people to review their savings and investments and make adjustments.  The Trend is only one factor (and a minor one at that) to take into account when reviewing your investments.  As the table suggests, The Trend is mostly useful for detecting bubbles and avoiding their collapse.

Today, as I publish this article, the S&P 500 index is about 10% above trend.  My analysis suggests this is nothing to get excited about.  There is a roughly two-thirds chance that the price one year from now will be somewhere between 7.8% lower and 23.2% higher, with an expected increase of about 7.7% and a 69% chance of making money.

Here is hoping that you will now find The Trend useful, at last.


* To estimate the chance that the one-year return would be positive (for a given range), I first found the mean and the standard deviation of the return data for that range.  Then, using the assumption that the one-year return data would be normally distributed, I calculated the Z-score for the zero-return point and then the fraction of the normal distribution that falls above this Z-score.  That fraction of the distribution represents the chance that the one-year return is positive.


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•  If it walks like a duck and quacks like a duck but it isn’t a duck, then it is an impostor.  That is, a quack.

•  People in deep thought scratch their heads or stroke their chins as if doing so will help something intelligent to emerge.  How did such behavior evolve?  I would encourage some aspiring psychology major to conduct a study that answers the question, “Do people who touch their faces make better or faster decisions than those who refrain from doing so?”

•  Online product reviews often reveal more about the reviewer than they do the product.  For example, one reviewer rated a set of wood drill bits two stars (out of five) because they were “not good for drilling into cement.”  Was he trying them out on his skull?

•  Open letter to editorial columnist Maureen Dowd of The New York Times: why not just retire and spare yourself (and the rest of us) your unending misery from having to live in the same universe as Bill and Hillary Clinton?

•  You are sitting in a church pew during a religious service, but you do not observe that faith, and then a tray is passed to you, and you just smile and hand it to the next person in the row.  If only that tray had not been handed to you, everything would have been cool!  But now you’re getting looks.  That’s just one of the prices you pay for not believing.

•  Disillusionment wasn’t invented in 1964.  I doubt there was ever a generation that did not experience disillusionment — how the establishment thwarted us, how powerless and ineffective we are, what little hope remains.  Each generation (and person) defines itself by its response to disillusionment.

•  If I’ve said it once, I’ve said it a thousand times.

•  When Reince Priebus left, Donald Trump became the first president in over 100 years to not have a pet dog in the White House.

•  There are three kinds of books: the ones you’re glad you read, those that were a waste of time, and those you need to read.  Here is my three-column list of said books:

The Mind’s I
Slaughterhouse Five
The Last Temptation of Christ
Paris 1919
A Map of the World
Owl at Home
Consciousness Explained
Guns, Germs and Steel
Roger’s Version
The Ottoman Empire, 1700-1922
Journey to Ixtlan
The Brothers Karamazov
Works of Abraham Lincoln
Of Human Bondage
The Barbarians


I invite you to share yours in the comments.

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