How to tell when a blowoff move is over?  One sign is a doubling of price following a mature rally.  This phenomenon, named “period doubling” by chaos theorists, shows up repeatedly in a wide sample of commodity and equity markets.  The recent period doubling of internet stocks is no different.  And as the high beta segment of the technology group, any cracks in the internet group may spell big problems for the Nasdaq, other stock market indices, and the dollar.  Last fall, when the stock market and the US dollar fell in tandem, a gold rally provided the backbone to an explosive rally in gold shares.  With gold now priced at the lower end of its trading range, such a scenario can easily repeat itself during 1999-Q1.  The following report is divided into three parts:
1) chaos theory and financial market applications,
2) historical survey of financial market blowoff tops, and
3) implications for current investment strategy.

I. Chaos Theory and Financial Market Applications
Chaos theory can be thought of as a mathematical overlay on phenomena that appear to be random, but on closer observation operate according to a patchwork of mathematical properties.  While chaos theory may not help us predict the actual outcome of an event, it can help us to understand certain pieces of a process, such as when things might go ballistic and finally burst.  Such is the concept of period doubling: the tendency for chaotic systems to exhibit doubling in mathematical properties.  One example from wildlife biology has identified period doubling of  species populations under certain conditions.  Other examples have been identified in chemistry, physics, and mathematics.  Chaos theory uses the terminology “bifurcation point” for the point in time, or event, which triggers period doubling.  I will make use of both “period doubling” and “bifurcation point” in this report.

In the financial markets, the period doubling concept can be applied to prices of financial instruments which often double at terminations of large price moves (e.g., blowoff tops).  The swing low prior to the blowoff price high is named the “bifurcation point” and the price high is often very close to the period doubling target predicted by chaos theory. The market geometry school of technical analysis teaches this same concept as a 200% price expansion target, without the fancy chaos lingo.  Martin Armstrong of Princeton Economics has also used the period doubling concept when describing the 1997/98 rallies in European stock markets, the 1993/94 emerging market equity rallies, and other historical episodes.

At present, the CBOE Internet Index (CINX Index) and many individual internet stocks such as Amazon.com (AMZN) have reached period doubling targets.  What’s most interesting about this particular episode is the concentrated time period during which period doubling has occurred – in some cases as short as 7 trading days.  When reviewing the past history of blowoff tops, this time compression is unprecedented and warrants extreme caution.

II. Historical Survey of Financial Market Blowoff Tops
First a word on the choice of the bifurcation date.  Often the point of acceleration is not an actual low but a higher low which may mark the end of a consolidation period.  The point is to try to identify where the real acceleration occurs.  As this is not an exact science, other analysts may select different points but they will not change the overall conclusions of the study.  In the case of the Brazilian Bovespa Index, the market had been rising for some time but on January 6, 1997 it appears that “gasoline was poured on the fire.” One could have used an earlier point but this date is where the acceleration occurs.  Unless otherwise noted, the “days of the blowoff rally” listed are calendar days (CD) and the “days spent above period doubling target” are trading days (TD).  Finally, the survey is not meant to be comprehensive, but instead a sample of memorable blowoff tops in recent years that will be familiar to many of today’s investment professionals.

1. Gold (1979-80).  Gold’s blowoff top is a classic, with gold trading only 6 days above its period doubling target, mostly in sessions marked by limit moves and unsettled trading.  It retraced 50% of the blowoff move within 5 trading days of the actual high.

2. Silver (1979-80).  Silver is notable because it is the only example in this survey which substantially exceeded its blowoff top.  Significantly, most of the 44 days silver spent above its period doubling target were volatile limit moves.  On March 10, 1980, silver gapped below its period doubling target and completely retraced the blowoff rally in 7 trading days.

3. Platinum (1979-80).  Platinum is included in the survey because it is often overlooked.  Its behavior is similar to the other precious metals, with platinum trading only 10 days above its period doubling target and completely retracing its blowoff rally in less than one month.

4. XAU Gold & Silver Index (1986-1987).  Because of the high leverage gold companies’ earnings to the gold price, often large gold share moves occur in earlier phases of a rally when the earnings leverage is greater.  Such was the case during the 1986/87 rally when the XAU experienced its period doubling during the middle phase of its rally.  Even though its’ period doubling target was exceeded later in 1987, the XAU soon crashed during October 1987 and has not exceeded its September 18, 1987 high to this day.

5. COMEX Copper (1993-95).  Copper’s rally exhibited a near perfect period doubling, just 1.1 cents shy of a 144 cent period doubling target.  Copper marginally exceeded its period doubling target in mid-1995 but crashed shortly thereafter from increased mine supply and liquidation of Sumitomo’s vast copper hoard.

6. OSX Oil Services Index (1997).  The oil services group was one of the best hard asset stories in the 1995-1997 commodity equity boom.  The attraction of a large wave of momentum-based investors created a surging 1997 rally which fell only 1% shy of reaching its period doubling target.  Subsequent equity market volatility, an oil price decline, and cuts in capital spending by integrated oil companies caused the index to collapse in late 1997 and again during 1998.

7. Indonesia, Singapore, and Thailand (1993-94).  The 1993/94 emerging market boom created period doublings in most Asian markets including the Jakarta, Straits Times, and SET indices.  Because many of these period doublings occurred from a low base, often equity indexes were able to recover much of their losses and make new or retest highs within several years of the period doubling top.

8. Taiwan, Brazil, and Hong Kong equity indexes (1996-97).  The most recent phase of the emerging market boom created another set of period doubling examples.  The Hang Seng example is similar to the XAU Index which experienced its period doubling during the middle phase of its rally.  New highs beyond the period doubling target were unsustainable, as was the case in the XAU.  Of all examples, the Brazilian Bovespa Index takes the cake by exceeding its period doubling target by only 12 points for a few hours on a single trading day.  The Bovespa’s rally occurred following lengthy rally and its subsequent decline has been especially severe.

9. Italian and Spanish equity indexes (1997-98). European share markets surged in 1997 and 1998 on the potential good news of a common currency.  Peripheral markets, such as Italy and Spain, did better relative to core country share markets in Germany and France which fell 10-20% short of period doubling targets.  What’s notable is that the Spanish and Italian stock markets in the last week still reversed to the downside, after failing for a third time just inside of their period doubling targets (e.g., triple top).

10. Internet Stocks (1998-99). What is truly extraordinary is the limited amount of days internet stocks spent in their final blowoff moves, by far the shortest time period for any example in this study.  Amazon’s phenomenal doubling in 7 trading days is surely close to breaking any record for this behavior, while the entire group’s double as measured by the CBOE Internet Index moved in 42 trading days.

There are three conclusions of the historical survey.
First, period doublings are unsustainable and are usually indicative of long term trend changes.  In many cases, after reaching a period doubling target, the market in question was unable to recover for many years.
Second, period doublings which occur on the heels of long-lived rallies are more devastating. Gold’s blowoff rally was the culmination of a 4 year bull market and gold’s high price has not been exceeded to this day.  On the other hand, markets with period doublings from low bases may test or exceed period doubling targets within a few years or less (e.g., Jakarta, Singapore, Italy, Spain).  Third, some markets may not experience period doubling on the final move.  Both the XAU and Hang Seng exhibited period doubling on the middle leg of their rallies.  Still the final rally which exceeded the period doubling target by a substantial margin was followed by a crash in both cases.

III. Implications for Current Investment Strategy
The ramifications of period doubling in internet stocks are not only significant to the internet group but to the overall US share market, the dollar, and commodities such as gold.

1. All long positions in internet stocks should be exited. Option strategies, with limited downside risk, may also be appropriate from a risk management perspective for some investors, although high volatilities make this an expensive choice.  It must be emphasized that the period doubling of internet stocks on the heels of a prolonged rally is not a good omen for the long term outlook of this sector.  While certain historical examples of period doubling prove that markets can rally back to period doubling highs (e.g., European share markets retesting 1998 highs in 1999), the weight of the evidence suggests that blowoff tops in Internet stocks will mark long term highs which may not be exceeded for many years.

2. As the high beta sector of the technology group, a crack in the internet stocks poses a significant challenge for larger well-established technology companies which dominate the Nasdaq.  A lack of lengthy historical data prevents an extensive correlation between internet stocks and the Nasdaq over both bull and bear periods.  However, the fact that the Nasdaq itself is within 15% of a period doubling target measured from the October 1997 low is cause for great concern.  Whether or not the Nasdaq shakes off internet weakness and reaches its own period doubling target before crashing is uncertain.  Clearly however, the Nasdaq is on the brink of a serious selloff which should make the 1997 correction pale in comparison.

3. For gold investors, a bear market in US equities may bode well for gold investment demand.  While an old theme, it remains true that gold’s primary hurdle has always been higher returns from competing asset classes.  Cutting stock market returns will help.  And as the last half of 1997 proved, both a declining stock market accompanied by a falling dollar may be necessary for gold to compete not only as a store of value but as a currency alternative.  As long as gold holds the lower end of its trading range (e.g., $270-$275) in late January, my proprietary timing models suggest an intermediate term gold low in January will provide fuel for a substantial rally in gold shares lasting for one to three months.  We await upcoming events with special interest – especially if anyone trading internet stocks trades their Yahoo! for gold mining shares.
Sam Hewitt
Tuesday, January 12, 1999

SUMMARY TABLE OF PERIOD DOUBLING EXAMPLES
 

Security Bifurcation
Date Bifurcation
Price High
Date High
Price Period
Doubling
Target Blowoff
Rally in
Days (CD) Days Spent Above Period Doubling Target (TD)
COMEX Gold 11/1/79 365.0 1/21/80 873.00 730.00 81 6
COMEX Silver 11/23/79 15.90 1/21/80 41.50 31.80 59 44
NYMEX Platinum 11/1/79 465.00 3/9/80 1045.00 930.00 129 10
Philly XAU Index 12/30/86 72.03 4/14/87 145.36 144.06 105 1
COMEX Copper 10/29/93 72.00 1/20/95 142.90 142.90 448 0
Philly OSX Index 5/2/97 71.27 11/5/97 141.25 142.54 187 0
Jakarta Composite 12/25/92 270.45 1/7/94 612.89 540.91 378 47
Singapore Straits Times 8/21/92 1028.85 1/7/94 2180.67 2057.70 504 11
Thailand: SET Index 6/4/93 818.84 1/7/94 1789.16 1637.68 217 7
Taiwan TWSE Index 3/16/96 4690.49 8/30/97 10256.10 9380.98 532 50
Brazil Bovespa Index 1/6/97 6993.64 7/11/97 13999.20 13987.28 186 1
Hang Seng Index 1/23/95 6890.00 1/16/97 14005.00 13780.00 492 5
Italy: Milan MIB30 Idx 10/28/97 20127 4/7/98 38596 40254 161 0
Spain: Ibex 35 Index 10/31/97 5403.45 4/7/98 10949.82 10806.90 158 0
CBOE Internet Index 12/1/98 294.68 1/12/98 590.53 589.36 42 1
Amazon.com 12/30/98 101.30 1/8/99 199.13 202.59 9 0