Possible vs. Probable: "So you're telling me there's a chance!"
By Chris Puplava, April 8, 2009
In last week’s article, “Fixed on the VIX,” I highlighted how important the VIX is as a valuable technical as well as fundamental indicator as it shows a strong correlation to many other indicators (ISM reports, employment, S&P 500, bond spreads, etc…). For this reason the resolution of the VIX to break either its declining trend line or lower trend line would be sending investors a strong signal. Currently the VIX is testing support at its lower trend line and we should have resolution of a breakdown or breakout soon as the two trend lines are converging.
Another indicator that I have my eyes fixed on and have shown in my past two Wednesday articles is the cross rate between the Euro and Yen, which I use to gauge risk appetites in the currency market, the largest financial market. The breakdown in the cross rate in August of 2008 was sending a warning sign that the unwinding of leverage in the currency markets (yen-carry trade) was beginning, which turned into a waterfall crash in September through October of last year. Since then the currency pair stabilized and the stock market began to show some internal strength as several sectors began to dance to their own tune, with the technology (green below) and consumer discretionary (blue below) sectors as prime examples, outperforming the S&P 500 by roughly 11% since late November. The Euro/Yen currency pair broke out of its trading range in March which was bullish, and a breakout above the 200d moving average (yellow below) would add even more support for the bullish case for the markets, while a breakdown back down into the trading range would be bearish, though support at the 50d MA (green) is moving up quickly and should act as support for any decline.
S&P 500 Sector Performance Relative to the S&P 500 (11.18.08 to 04.07.09)
After viewing the various relationships with the VIX as well as some other risk measures I look at, I made the following comment in last week’s article, “Looking at these relationships appears to be sending a collective message that the worst may indeed be over, with a complex bottoming process likely to ensue in the months ahead.”
For turning even moderately bullish on the intermediate term picture I was taken to task by a reader for my stance given the overall economic climate. To further explain why I am bullish in the intermediate picture I’d like to use a little statistical support to make a distinction between possible outcomes (all outcomes being possible) and probable outcomes (what is likely or reasonable to expect). (The following information may be a little technical for some but I will try to explain it as simply as I can with associated figures to illustrate the concepts).
To make a clear distinction between possible and probable events we can turn to statistics, which helps place a quantitative number (probability) for a particular outcome. To do this we can use the normal distribution which “can be used to describe, at least approximately, any variable that tends to cluster around the mean” (Wikipedia). The area under the curve is used to give the associated probability for the data to fall within particular values.
For example, 95% of observations should lie within 1.98 standard deviations (a measure of dispersion about the mean), and 99% of observations should lie within 2.58 standard deviations from the mean. People will often use descriptions such as a “100-year storm” or statistics to show how rare a particular event is. An event that is more than or less than three standard deviations should occur only 1/10 of 1% of the time (0.001), while an event more than or less than four standard deviations from the mean (average) should occur only 0.0032% (0.000032) of the time. A normal distribution is shown below along with the standard deviations (z-scores) and associated probabilities.
One variable that I have shown over the last several months to illustrate how oversold the market has been is using the deviation of the S&P 500 from its 200d moving average. Oversold markets are seen when the S&P 500 is well below its 200d MA and overbought markets are characterized by the S&P 500 being well above its 200d MA. As normal distributions are mean reverting (observations far from the mean (average) typically gravitate back to the mean, much like gravity pulls objects back to the earth), we see that when the S&P 500 is far from its 200d MA it tends to be pulled back towards it.
The deviation (variability) of the S&P 500 around its 200d MA follows a normal distribution which can be seen below, with the large deviations below its 200d MA in 1929 and 2008 shown in the “left tail” of the normal distribution. The S&P 500’s average deviation from its 200d MA is 2.2%, which supports the claim that the markets are bullishly leaning and tend to move up in the long run, with the standard deviation (variability) around the mean at 10.0%.
We can see the tendency of the market to move back to its 200d MA as the S&P 500 made several moves back towards its 200d MA during the Great Depression, with the deviation from its 200d MA often reverting back to 0% (second image below). We can see the same concept currently with the wide gap seen in the S&P 500 in October/November of 2008 when it was more than 35% below its 200d MA, which was used to show how oversold the market was and why a rally was likely.
The low seen in November of 1929 witnessed the S&P 500 34.6% below its 200d MA and marked a 3.67 standard deviation event. To give you an idea of how oversold the market was, a reading of -3.67 standard deviations or more negative should be seen only 0.0121% of the time (0.000121), while readings above -3.67 standard deviations should be seen 99.9879% of the time.
To state differently, 99.9879% of the time the S&P 500 should be higher than 34.6% below its 200d MA. Or to state differently once more, observations that are 3.67 standard deviations below the mean should be seen once every 8,264 days (33 years using 252 day trading year). Because it was so rare (0.0121%) for the S&P 500 to be that far below its 200d MA, it was not surprising to see the markets rally nearly 50% over the next several months as the S&P 500 moved back up to its 200d MA in 1930.
Looking at the current bear market, the S&P 500 was 39.6% below its 200d MA on November 20th of last year, which was a -4.17 standard deviation event, even more unlikely than the November 1929 low. A -4.17 standard deviation event should be seen only 0.0015% (0.000015) of the time, or to put it differently, observations above -4.17 standard deviations should be seen 99.9985% of the time. This means there was a 99.9985% probability of the next observation being above that number while only a 0.0015% probability of the next event being below -4.17 standard deviations. To put the number in the context of time, a -4.17 standard deviation event should be seen once only 66,666 days (once ever 265 years). The November lows that we just witnessed was more than a “100-year storm,” it was a “265 year storm!”
Putting it All Together
What I hope readers grasp from the above statistical analysis is that moves in the S&P 500 significantly below its 200d MA, such as more than three standard deviations below the mean, are far more likely to be followed by a move/rally back towards the mean (~ 200d MA) as opposed to a further move away from it. What I also hope readers grasp is that even during the Great Depression stocks staged a very impressive rally that saw the S&P 500 advance nearly 50% in several months, meaning it is possible and even probable to expect a rally from such severely depressed levels.
Interestingly enough, comparing the current market’s action to that seen after the 1929-1930 market crash shows some uncanny resemblances. For example, the S&P 500 began to correct in September of 1929 only to experience a crash in October, with a further plunge in November. Sound familiar?
S&P 500 (1929-1930)
As seen above, the S&P 500 then began an advance off the November lows with a rally up to roughly 26.00 and just slightly above its 200d MA (not shown). We can see the similarities between the two bear markets using the percent deviation (and standard deviation, z-score) of the S&P 500 from its 200d MA. As seen below, not only do the magnitudes show similarity in the sell offs but so too the seasonal pattern, though the 1929-1930 experience showed a sharper rally than the current experience. As Mark Twain said, “History does not repeat itself, but it does rhyme.”
(Note that the time scale used is for the current period, meaning that 1929 corresponds to 2008 and 1930 corresponds with 2009 to overlay the two series. Only the years were shifted, not the actual month or day).
I was going to show some fundamental support for why I believe the rally has further to run, but this article is long enough. I will say that we are by no means out of the woods in terms of this bear market as my U.S. Financial Stress Index (FSI) is still well below zero, with bull markets associated with the FSI north of zero. What is encouraging though is that the FSI broke out of a two month trading range and is heading higher.
Because of several positive developments I am seeing within the markets and on the economic front I am more inclined to give the current rally the bullish benefit of the doubt. I would start to become concerned if the S&P 500 breaks support at ~ 777, which would be the late March low, the 38.2% Fibonacci retracement level, as well as the 200 hour moving average (green line) which is fast approaching 777. A move below that key level would imply further weakness toward the 50% and 61.8% Fibonacci retracement levels of 756.20 and 735.10 respectively.
Another reason why I believe the markets can continue heading higher is that the S&P 500 was roughly 18% below its 200d MA as of yesterday’s close, or 2.04 standard deviations below its mean. This level of oversold condition should be seen only 2.1% of the time, meaning there is a 97.8% probability the market is moving higher, or in the words of Jim Carrey in the movie Dumb and Dumber, “So you’re telling me there’s chance…” that the market can head higher.
© 2009 Chris Puplava