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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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The Trend, Revisited

Once again, the news media are reporting new highs in popular stock market indexes.  Does this mean it is a good time to invest?  Or is it a good time to sell and take profits?

I have absolutely no idea.  What I can do is tell you where we stand relative to The Trend.  (For details, please refer to my earlier post on this topic.)  After a little programming, I was able to add an information box to my sidebar that shows:

  • the current price of the S&P 500 index (updated every hour)
  • the predicted value of the S&P 500 index based on The Trend
  • the percentage difference between the index and its predicted value
  • the number of days that the index is ahead or behind its trend line

The S&P 500 index increases, on average, 7.1% every year — some years more, some less.  Since the index often goes up or down 1% or more in a single day, small departures from The Trend are meaningless.  As I write this, the S&P 500 index is almost right on trend — neither “on sale” nor historically overpriced.  It could stay this way for years, or the index could plunge or skyrocket overnight.  But it will inevitably return to the trend line.

For what it’s worth.

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The Trend

The news media has been giving a lot of play to the recent highs in the U.S. stock market.  With all due credit to Burton Malkiel and his book “A Random Walk Down Wall Street” (which I just finished), I would like to put some of the hype into perspective.

While I am not a financial expert, I am determined to manage our own retirement savings because I am unconvinced that the “experts” know much more than I do.  I have arrived at a pretty simple conclusion about investing — I call it “The Trend.”  It is hardly original.

The S&P 500 Index represents the total stock market value of the largest 500 companies in the U.S.  In the chart above, I show how the value of this index has risen over the years 1950 to 2012.  Note that the vertical scale is an “equal-percentage” scale — values double from one tick mark to the next.  Plotting the numbers this way lets me draw a straight line through the price data and calculate how much the index increases, on average, from one year to the next.  That number is 7.1% per year.  This is “The Trend.”

[Note: the average annual return on an investment in the S&P 500 index would be more than 7.1% per year, because many of those companies pay dividends.  On the other hand, inflation erodes the value of an investment by about the same amount.]

In a nutshell, The Trend reflects the long-term profit-making ability of U.S. corporations.  As a company’s profits rise, so does the price of a share of its stock — generally.  But there are long periods of time when stock prices are lower than usual and equally long periods when they are higher.  (In the chart, I shaded those areas in red and green, respectively.)  For example, the S&P 500 Index was higher than its long-term trend for 15 years, from 1955 to 1970.  The index followed the trend line for a few years, then it fell and remained below the trend for another 15 years.  Rinse and repeat for a decade or two.

The second chart shows the same data, except plotted in terms of the percentage that the index is above or below The Trend.  As you see, it is not unusual for stock prices to deviate 20% to 40% from than the long-term trend.  Sometimes 50%.  Even 100%.

Plotted this way, the dot-com bubble of the late 1990s clearly stands out — at its peak, stock prices were nearly double what one would expect based on The Trend.  Such levels were not sustainable, and the index returned to the trend line within a few years.

Where do we stand since the Great Recession and the recent recovery?  The current price of the S&P 500 Index is 1495.  If we were on The Trend, the index would be 1725, about 15% higher than where we are now.  Good time to buy stocks, yes?  Well, not so fast.

Let’s say you invested in an index mutual fund 40 years ago, at the end of January 1973.  The price of the S&P 500 index at that time was 118 — right on the long-term trend line.   The index would return to this price level many times, doing so for the final time in September 1982, over nine years later.  If you had been forced to sell your investment at that point, you would have made nothing on your money for nine years (other than the dividends minus inflation).  The Trend does not promise quick payoffs.

However, if you had held onto that 1973 investment for 40 years and sold it this month, you would have made about 6.6% per year, before dividends and inflation.

In August 2000, the S&P 500 Index closed at a price of 1485.  If you bought an index fund that month, when the price was 103% over The Trend, you would be just about even today, twelve years later.  Some people probably did just that.

One might conclude that a person should never invest in the stock market unless the price is below the trend line.  That too would be a mistake.  In the summer of 1956, the index was running 30-40% above The Trend.  If you had decided to wait for the stock market to fall below The Trend before investing, you would have waited until February 1970.  Stocks returned about 4.2% per year, on average, during that 14-year period.  While you might have made just as much money from treasury bonds in that timeframe, the point is that you would not have lost money either.

Here is the best way, in my opinion, to view The Trend.  Invest in the market with the idea that you are going to hold onto your shares as long as you can — 30, 40, 50 years or more.  (It is not just marketing when mutual fund companies tell you to invest for the long term.)  Remember that stock prices go up and go down but will eventually return to the trend line. If you buy shares when the price is below The Trend, you could think of it as a discount — but you will only get the discount if you sell the shares when the price is above The Trend.

The stock market is unpredictable.  No one can say when it will rise or fall or by how much or how long it will stay there.  If someone tells you otherwise, just pretend you didn’t hear.  But it is a characteristic of the market that the index is usually within 40% of The Trend (look again at the second chart).  If the index is more than 40% above The Trend, it may signal a bubble — probably a good time to sell (or at least not buy).  Similarly, if the index is more than 40% below The Trend, it may be a good time to buy (or at least not sell).

Summary: Invest in index funds, as much as your personal situation and comfort allows, then hold onto the shares the rest of your life.  Sell only when you must, preferably when the price is above The Trend.

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