Opinions and observations expressed on this blog reflect the authors' individual experiences and should not be construed to be financial advice. None of the members of this blog are licensed financial advisors. Please consult your own licensed financial advisor if you wish to act on any recommendations here.

Wednesday, November 23, 2011

Is there such a thing as an "average" year?

Since we're coming up on the end of the year, we'll no doubt hear about how the next year will be an "average" year.  Very nearly every year I've followed the markets, just about every market commentator, or at least two-thirds of them, have called for a "typical" year of stock market performance.  If it was a bad year in the prior year, they'll say "Things were tough and we're still coming back so I think it will be a slow, average year of recovery."  If it was a good year, "We saw some good things last year, so we'll probably be coming off that somewhat and go back to a more typical rate of return." Even if it was an average year, they would use that as the basis for forecasting an average year.

The reason for this is all very simple, which is that people have an immutable faith in the central tendency of a long-running time series.  The problem is that stock market returns don't follow anything close to a normal distribution (CLICK ON PICTURE FOR LARGER IMAGE):

First of all, I would like to point out that there is a big difference between the compounded annual growth rate (CAGR) and the "average".  This is because averages almost completely ignore the effect of significant down years.  To explain it in a clear example, if you drop 50% in the first year and rise 50% in the next year, the two year average is 0%, but you're actually down 25%.  The CAGR captures this, but the average does not.  As such, the long term typical rate of return is about 140-150 basis points lower, depending on how you draw your time horizon.  The difference is notable, by the way.  At 7.9% per year over 40 years, $1,000 turns into $20,932.  At 6.5% per year over 40 years, it's $12,416.  In other words, please don't base any projections you are doing for your retirement on the average rate of return.

By my count, there is only one year that was +1% or -1% from the long-term CAGR, which was 1993.  Hell, make that a 3% band and you still only get about 7 or 8 years, depending on how you round off trailing digits.

As you can see, this is not a normal distribution by any stretch of the imagination.  

As such, when you see the annual forecasts come out toward the end of this year, feel free to snicker when you see people project that we will see the long-term average rate of return. 

Sunday, November 6, 2011

On Economic Troglodytes

One of the things I see on more "populist" forms of financial news commentary is a grave mistrusting of seasonally adjusted data.  For the uninitiated, a seasonal adjustment is a filtering process for volatile data series that have a clear seasonal pattern.  By correcting for the observed historical seasonal patterns, you can get a smoothed look at what the data are without the typical chop.  Good examples of data with significant seasonal oscillations are housing starts (with far more in the spring and summer than in the winter) and employment (with massive amounts of layoffs right after the holiday season and robust hiring in the summer).

However, there is a group of people who don't trust seasonally adjusted data, largely because I don't think that they understand it.  Take this post from Minyanville.  The author boldly dismisses seasonally adjusted jobless claims data as not being "real" and asks that readers look at the non-seasonally adjusted data.  Then, there is a choice quote later:
The actual weekly initial claims data exhibits week to week patterns each year that are consistent, as certain industries tend to add and subtract workers at the same time each year. Rather than smoothing the data to obscure what really happened last week, we can compare the numbers directly with prior years' performance during the same weeks to get an accurate reading of the current trend. Like an optometrist, we can look at small changes and ask whether they are better, worse, or about the same as last year. By carefully evaluating subtle changes, we gain clarity of vision.
As it so happens, that is precisely what the seasonally adjusted data does, however imperfectly.  The reason that, beyond a simply seasonal adjustment, economists like to look at a 4-week moving average for jobless claims is that, even after going through the rigors of a seasonal adjustment, large one-time events can occur like a major corporate bankruptcy, a strike, or a major weather event.  By taking a simple average, you can somewhat smooth this out.  Doing so is, by definition, somewhat backward looking, but it is a tool that you can use if you so choose.  One thing I've learned in my line of work is that there is no one right way to analyze data.  The circumstances may call for a few different ways of looking at it.

What some of the troglodytes like to do is use a 12-month moving average or something like that instead of a seasonally adjusted number, claiming that actually represents the real data.  A neat little trick here is that the 12-month moving averages of the non-seasonally adjusted data and the seasonally adjusted data come out almost exactly the same, which is what you would expect if the seasonal adjustment is worth its salt.  See this below with housing starts data:

However, 12-month moving averages don't capture "real time" changes in the data.  It's for much the same reason that year over year comparisons are useless.  If you had a huge run up in the early months of the 12 month period, the leveled off and are now starting on a downward trend, you won't catch it in the moving average or the year over year numbers for another few months.  Look at the three measures of potentially judging what housing starts were doing during the housing boom and bust of the last decade (CLICK ON PICTURE FOR LARGER IMAGE)

The seasonally adjusted data catches the inflection point earlier and more decisively than either of the other two measures.  In the other two, you can eventually see it, but the seasonally adjusted data provides the much clearer signal.  This is because, with the seasonal filter, you can look at a current month and judge what it means on a "real time" basis rather than being dependent on backward looking measures that take months to provide a signal.  Also, compared to non-seasonally adjusted numbers, which at best rely on a year on year comparison, you can much more easily detect the trend.

This is why, even though seasonally adjusted numbers are not "real" numbers, they do provide the best picture of what is going on of all the data that get presented.  Frankly, people who reject seasonal adjustments as being some statistical creation are nothing but troglodytes.