concept of cycle theory

1. Cycle Analysis

2. Cycle Analysis
Section I – 39%
 Cycle basics
 Temporal patterns & cycles
 Period longer than 4 years
 Period of 4 years or less
 January signal
Events
 Uncovering the cycle
 Maximum entropy
Cycle channel index
 Short cycle indicator
Phasing

3. Basic Cyclical Concept
Cycles bottoms are known as Troughs & tops referred as Crests.
•Cycle or wave. A recurring process that returns to its original
state.
•Amplitude (a). The height of the wave from its horizontal
midpoint (the x-axis).
•Period (T). The number of time units necessary to complete one
wavelength (cycle).
•Frequency (ω). The number of wavelengths that repeat every
360°, calculated as ω = 1/T.
•Phase. A measurement of the starting point or offset of the cycle
relative to a benchmark wave.
•Phase angle. Locates the position within the cycle measured as
the minute hand of a clock moving clockwise, where 0 ° is three
o'clock.
•Left and right translation. The tendency for a cycle peak to fall to
the left or right of the center of the cycle.

4. Basic Cyclical Concept

5. Basic Principle of Cycles
Summation Harmonicity
Synchronicity Proportionality

6. Basic Principle of Cycles
 Principle of summation holds that all price movement is the simple addition of all active
cycles. For Example 5 wave in Elliot is combination of 3&4 wave.
 Principle of Harmonicity simply means that neighbouring waves usually related by small,
whole number ,that number is usually 2.
 Principle of synchronicity refer to the strong tendency for waves of different lengths to
bottom at about same time,
 Principle of Proportionality describe the relationship between cycle period and amplitude .
The amplitude , or height , of a 40 days cycle for example should be double of 20 days cycle

7. Principle of Variation & Nominality
 Principle of Variation ,as the name implies ,
is a recognition of the fact that all of the
other cyclic principles are just strong
tendencies and not hard and fast rules.
 Principle of Nominality is based on the
premise that, despite the differences that
exist in the various markets and allowing for
some variations .

8. Principle of Variation & Nominality

9. Seasonal Pattern & Cycle
K - Wave
34 Year Cycle
Pattern
DECENNIAL
PATTERN
Seasonal
Patterns
Four-Year or
Presidential
Cycle
JANUARY
SIGNALS

10. Kondratieff Waves, or K-Waves
• Nicolas D. Kondratieff, an economist who lived in Communist Russia, studied
historical commodity prices in the 1920s.
• The long 50-60 year cycle that he measured, known as the Kondratieff wave
(or "K-wave"), is an economic phenomenon
• Waves are attributes of the world economy led by a major national economy
• Waves concern output rather than prices—sector output surges rather than
general macroeconomic performance
• Each K-wave affects the structure of the world economy into the future.

11. Kondratieff Waves, or K-Waves

12. 34-YEAR HISTORICAL CYCLES
• 34-year cycles, composed of a 17-year period of dormancy followed by a 17-
year period of intensity
• Warren Buffett, one of the wealthiest men in the world, is not widely known
to use technical methods; however, it is interesting to note that he has long
used the 17-year cycle in his investment planning.
• Buffet does not attribute the cycle to growth in the GNP, noting that in the
dormant cycle from 1966 to 1982, the GNP grew at twice the rate as during
the intensive 1982 to 2000 period.

13. 34-YEAR HISTORICAL CYCLES

14. DECENNIAL PATTERN
• Decennial pattern theory states that years ending in 3,7, and 10 (and
sometimes 6) are often down years. Years ending in 5, 8, and most of 9 are
advancing years
• Combining these two periods. Smith theorized that there must be a ten-year,
or 120-month, cycle. This would result from ten 12-month, annual cycles and
three 40-month cycles coinciding every 10 years.
• When Smith investigated prices more closely, he found that indeed there
appeared to be a price pattern in the stock market that had similar
characteristics every ten years. This pattern has since been called the
"decennial pattern."

15. Four-Year or Presidential Cycle
• The four-year cycle, from price bottom to price bottom, is the most
widely accepted and most easily recognized cycle in the stock market.
• The U.S. presidential elections are also four years apart, the cycle is due
to the election cycle (see the next section, "Election Year Pattern"). It is
thus often called the "presidential cycle.“
• Typically, the year preceding the election (year 3 in the president's term)
posts the strongest gains for the market, followed by a reasonably strong
election year
• The two years after the election show returns below average as the reality
of politics reasserts itself and the new administration tries to implement
campaign promises that turn out to be unpopular.
• Eight-year period should be most informative if it represented only those
years in which the same president was in office.

16. Four-Year or Presidential Cycle

17. Cycle Advance
Analysis
(Cycle Identification Methodology)
Section I – 39%

18. Basic Cycle Identification
• A simple way to begin the
search for major cycles is to
look at a long-term chart,
displayed as weekly rather
than daily prices.
• The dominant half-cycle can
be found by locating the
obvious price peaks and
valleys, then averaging the
distance between them.
• A convenient tool for
estimating the cycle length is
the Ehrlich Cycle Finder.

19. Method of Identification of Cycles
Removing The
Trend
Triangular
Weighting
Hilbert
Transform
The Fisher
Transform &
Inverse
PHASING
CYCLE
CHANNEL
INDEX
SHORT CYCLE
INDICATOR

20. Removing The Trend
• The cycle can become more obvious by removing the price trend.
• While we traditionally only use one trend line to do this, the use of two trend lines
seems to work very well in most cases.
• First smooth the data using two exponential moving averages, where the longer
average is half the period of the dominant cycle (using your best guess), and the
shorter one is half the period of the longer one.
• Then create an MACD indicator by subtracting the value of one exponential trend
from the other;
• The resulting synthetic series reduces the lag inherent in most methods while
removing the trend.

21. Triangular Weighting
• One method for enhancing the cycle is the use of triangular weighting instead of exponential
smoothing.
• The weighting is triangular because it creates a set of weighting factors that are smallest at the ends
and largest in the middle, and typically symmetric.
• The weighting factors begin with the value 2.0/(P/2), and increase by the same value.
• If the calculation period P = 10, the weighting begins at t − P + 2, or t − 8, eliminating the oldest
value in order to have an odd number of prices. The weighting factors, wi, are then 0.4, 0.8, 1.2, 1.6,
2.0, 1.6, 1.2, 0.8, and 0.4. The triangular average is
• While this method creates a smooth representation of cyclic movement, it has the characteristics of
a momentum indicator because the peaks and valleys are not quite evenly spaced and the
amplitude of the cycles varies considerably. However, the smoothness of the indicator allows you to
anticipate the major changes in the direction of prices

22. Triangular Weighting
•

23. The Hilbert Transform
• Ehlers is able to recognize the cyclic component of price movement using very little data as
contrasted with the traditional regression methods.
• The Hilbert Transform is based on the separation of the cycle phase, represented by a
phasor, into two components, the Quadrature and In Phase.

24. The Hilbert Transform
• Continuous data is preferable in this
case to avoid any odd jumps in prices
when one contract is rolled to
another at expiration.
• The Hilbert Transform indicator does
a very good job of locating relative
peaks and the highest and lowest
values of the indicator could be used
for sell and buy signals.
• larger peaks in the indicator follow
periods of low volatility in prices
because the subsequent peaks will be
seen as relative highs.
• While the peak to valley might be an
ideal trade, the net returns will vary
due to individual market volatility.

25. The Fisher Transform
• Trend-following performance, or the increase in volatility
with price. The distribution of prices is called a probability
density function (PDF), and the normal, bell-shaped curve is
a Gaussian PDF.
• The way in which prices move between two bands is very
similar to the probability density function of a sine wave,20
which spends more time in the vicinity of the peaks and
valleys (where it changes direction) than in the middle
(where it moves the fastest).
• Figure 11.21a shows two cycles of a sine wave with the PDF
to the right (Figure 11.21b). Although the PDF is normally
shown with the phasor angle along the bottom, as in (Figure
11.21c), this chart is drawn to represent a typical frequency
distribution.
• The peaks of the sine wave occur when the phasor angle is
270° and the lowest points when the angle is 90°. The
frequency of the peaks (the top of the chart) and valleys
(the bottom of the chart) are much greater than the
frequency of the other angles, especially 0° and 180°.

26. The Fisher Transform
• Values for the Fisher Transform range from +1.0 to −1.0. The peaks of the Fisher
Transformation are remarkably in line with the price peaks, and show very little lag
compared to the Hilbert Transformation although they occasionally peak out early and hold
that level until prices reverse.
• The bottoms are also good, although there is an occasional lag. The Fisher Transform
produces clearer, sharper turning points than a typical momentum-class indicator. A trigger
is also included that corresponds to the MACD signal line.
• A sell signal occurs when the Fisher Transform value crosses the trigger moving lower.
Experience shows that the best signals are those occurring just after an extreme high or low
value and not after a turning point where the value is near zero, similar to MACD rules.
Programs for creating the Hilbert, Fisher, and Inverse Fisher transforms are TSM Hilbert
Transform, TSM Fisher Transform, and TSM Fisher Inverse, which can be found on the
Companion Website

27. The Fisher Transform

28. The Inverse Fisher Transform
• One more variation produces a very credible momentum indicator, the Inverse Fisher
Transform.
• While the Fisher Transform uses the price to solve for the distribution, the Inverse Fisher
Transform does the opposite, However, implementation of this is wrapped around the
RSI indicator .
• RSI and I WAVERAGE are the functions for the RSI and the linearly weighted average.
• This process gives a bipolar distribution, where results are most likely to cluster near the
extremes, +1 and –1.

29. The Cycle Channel Index
• A trend-following system that operates in a market with a well-defined cyclic pattern
should have specific qualities that do not exist in a basic smoothing model.
• In order to confirm the cyclic turning points, which do not often occur precisely where they
are expected, a simple moving average should be used, rather than an exponentially
smoothed one.
• Exponential smoothing always includes some residual effect of older data, while the moving
average uses a fixed period that accommodates the characteristics of a cycle.
• The cyclic turning point will use part of the data that represents about ¼ of the period,
combined with a measure of the relative noise in the series which may obscure the
• CCI calculations, the use of 0.015 × MD as a divisor scales the result so that 70% to 80% of
the values fall within a +100 to −100 channel. The rules for using the CCI state that a value
greater than +100 indicates a cyclic turn upward; a value lower than −100 defines a turn
downward.
• The CCI concept of identifying cyclic turns is good because it accounts for the substantial
latitude in the variance of peaks and valleys, even with regular cycles

30. Commodity Channel Index
• Developed by Donald Lambert and featured in Commodities magazine in 1980, the
Commodity Channel Index (CCI) is a versatile indicator that can be used to identify a new
trend or warn of extreme conditions.
• Lambert originally developed CCI to identify cyclical turns in commodities, but the indicator
can be successfully applied to indices, ETFs, stocks, and other securities
• CCI measures the current price level relative to an average price level over a given period of
time.
• CCI is relatively high when prices are far above their average. CCI is relatively low when
prices are far below their average. In this manner, CCI can be used to identify overbought
and oversold levels.
• For understanding Calculation please refer notes link.

31. Commodity Channel Index
• CCI measures the difference between a security's price change and its average price
change.
• High positive readings indicate that prices are well above their average, which is a show of
strength.
• Low negative readings indicate that prices are well below their average, which is a show of
weakness.
• The Commodity Channel Index (CCI) can be used as either a coincident or leading indicator.
• As a coincident indicator, surges above +100 reflect strong price action that can signal the
start of an uptrend.
• Plunges below -100 reflect weak price action that can signal the start of a downtrend.
• chartists can look for overbought or oversold conditions that may foreshadow a mean
reversion.
• Similarly, bullish and bearish divergences can be used to detect early momentum shifts and
anticipate trend reversals.

32. Commodity Channel Index
Overbought/Oversold
• First, CCI is an unbound oscillator.
Theoretically, there are no upside or
downside limits. This makes an
overbought or oversold assessment
subjective.
• Second, securities can continue moving
higher after an indicator becomes
overbought. Likewise, securities can
continue moving lower after an
indicator becomes oversold.
• ±100 may work in a trading range, but
more extreme levels are needed for
other situations. ±200 is a much harder
level to reach and more representative
of a true extreme.

33. Commodity Channel Index
Bearish & Bullish Divergences
• Divergences signal a potential reversal
point because directional momentum
does not confirm price. A bullish
divergence occurs when the underlying
security makes a lower low and CCI
forms a higher low, which shows less
downside momentum.
• Before getting too excited about
divergences as great reversal indicators,
note that divergences can be
misleading in a strong trend. A strong
uptrend can show numerous bearish
divergences before a top actually
materializes. Conversely, bullish
divergences often appear in extended
downtrends.

34. Short Cycle Indicator
• Francisco Lorca-Susino presents the Short Cycle Indicator. It is applied to intraday bars and
is best interpreted over multiple time frames.
• The formula is based on the squared difference of two exponential moving averages, and
the relationship of those trend lines with the highest low and lowest high of the slower
period, a form of stochastic indicator.
• The indicator tends to stay above or below the trigger line but reacts to changing volatility,
recognized as divergence of the trend lines and the price extremes. These usually occur
before prices change direction. It is interesting to note the multiple divergence signals that
occur as prices rally on the first part of the chart, and that the indicator posts its lows in
advance of the lows

35. Short Cycle Indicator

36. Phasing
• J. M. Hurst in The Profit Magic of Stock Transaction Timing. He uses phasing, the
synchronization of a moving average, to represent cycles.
• Hurst treats the cyclic component as the dominant component of price movement and
uses a moving average to identify the combined trend-cycle.
• The system can be visualized as measuring the oscillation about a straight-line
approximation of the trend (a best-fi t centered line), anticipating equal moves above and
below. Prices have many long- and short-term trends, depending on the interval of analysis.
• The full-span moving average period may be selected by averaging the distance between
the tops on a price chart (a rough measure of the cycle). The half-span moving average is
then equal to half the days used in the full-span average.

37. Phasing
• A 40-day moving average is considered to
be 20 days behind the price movement.
• The current average is normally plotted
under the most recent price, although it
actually represents the average of the
calculation period and could be lagged by
one-half the period.
• Hurst’s method applies a process called
phasing, which aligns the tops and
bottoms of the moving average with the
corresponding tops and bottoms of the
price movement.
• To phase the full- and half-span moving
averages, lag each plot by half the days in
the average; this causes the curve to
overlay the prices

38. Phasing
• With the trend identified and projected, the next step is to reflect the cycle about the trend.
• When the phased half-span average turns down at point A (Figure 11.25), measure the greatest
distance D of the actual prices above the projected trend line.
• The system then anticipates that prices will cross the trend line at point X and decline an equal
distance D below the projected centered trend line. Once the projected crossing becomes an
actual crossing, the distance D can be measured and the exact price objective specified.

39. Seasonality
and Calendar
Patterns
Section I – 39%
 Seasonality and Calendar Patterns
A Consistent Factor
The Seasonal Pattern
Popular Methods for Calculating
Seasonality
Seasonal Filters
Seasonality and the Stock Market
Common Sense and Seasonality

40. SEASONALITY AND THE STOCK MARKET
Holiday effect
Month end
effect
The Hirsch
Strategy
The January
Effect
McGinley’s
January
Indicator
Risks of
September
and October

41. Holiday Effect
• Arthur Merrill In his studies of price
movement before and after major holidays,
Merrill demonstrates a strong bullish
tendency in advance of a holiday with a weak
day immediately following.
• Kaeppel is more specific, recommending
buying on the close of the third day before an
exchange holiday and selling on the close two
days later (one day before the holiday).
• Norman Fosback’s confirmed Merrill’s results
by studying the returns based on a strategy
that bought two days prior to a major holiday
and exited on the day prior to the holiday,
rather than waiting until the day following
the holiday. Fosback’s strategy yielded returns
of 880% from 1928 through 1975 with 70% of
the trades profitable, while holding long
positions during the remaining days of the
year would have lost 41%.

42. Month End Effect
• Perhaps some investors close out positions before the end of the month in
order to realize profits or losses; this is even more likely to happen at the end of
a quarter or the calendar year
• This effect could be helped by large funds that may exit positions to balance
redemptions
• Merrill, Fosback, Kaeppel, and Freeburg all confirm the success of a strategy
that buys on the last day of the month, or the second-to-the-last day, then exits
the trade on the fourth trading day of the new month. That takes advantage of
large-scale, month-end liquidation, followed by resetting positions.
• This pattern is effective after launch of monthly futures.

43. The Hirsch Strategy
• He simply bought on the first day of November and sold on the last day of
April, holding the position for six months.
• The Hirsch strategy would have avoided the spectacular October losses as well
as the disaster of 9/11/2001 but benefited from the subsequent recovery.
• Hirsch had discovered that virtually all gains in the stock market took place
during those six months
• Hirsch’s original strategy reinvested dividend income during the six months
when you were not in the market.
• That advantage has diminished, but leveraged investing can replace that loss.
Using futures, exchange traded funds, or leveraged funds available through
Rydex and ProFunds can make up the difference.

44. The Hirsch Strategy
• He simply bought on the first day of November and sold on the last day of
April, holding the position for six months.
• The Hirsch strategy would have avoided the spectacular October losses as well
as the disaster of 9/11/2001 but benefited from the subsequent recovery.
• Hirsch had discovered that virtually all gains in the stock market took place
during those six months
• Hirsch’s original strategy reinvested dividend income during the six months
when you were not in the market.
• That advantage has diminished, but leveraged investing can replace that loss.
Using futures, exchange traded funds, or leveraged funds available through
Rydex and ProFunds can make up the difference.

45. JANUARY Effect
• It is perfectly sensible to look for a
pattern in the way many of the long-
term investors set positions at the
beginning of the year, the result of a
reallocation of their portfolios, or
resetting positions liquidated before
the end of the year for tax reasons.
• If January is a leading indicator of
stock market movement throughout
the rest of the year, a combination of
patterns should be considered based
on the few days immediately after the
year begins, and the net market
direction for the month of January

46. McGinley’s January Indicator
• John McGinley in his recent study,
if each of the first five trading days
of January are up, buy the S&P and
hold for the entire year.
• If the end of January is up, then buy
on February 1 and hold as well,
although the end of January trade is
not as good as the first five days.
• McGinley states that, if the first 5
days are up at least 4%, the year
has always been up.

47. Risks of September and October
• The tragedy of September 11, 2001;
Black Monday on October 28, 1929;
and the market crash of October 19,
1987. However, these months have
other negative attributes that are not
as noticeable.
• October may hold the record for the
most volatile price moves and the
most risk, it also has great opportunity
for timing an entry into a new
position.
• October, September seems to capture
consistency in underperformance in
both recent years and throughout the
past 100 years

48. Risks of September and October
• The tragedy of September 11, 2001;
Black Monday on October 28, 1929;
and the market crash of October 19,
1987. However, these months have
other negative attributes that are not
as noticeable.
• October may hold the record for the
most volatile price moves and the
most risk, it also has great opportunity
for timing an entry into a new
position.
• October, September seems to capture
consistency in underperformance in
both recent years and throughout the
past 100 years

49. EVENTS
• Short-term traders sometimes practice what is called "event trading." This
is when either a news announcement is due, a surprise news
announcement occurs, or a holiday is soon to occur. Holidays are seasonal
and thus included here
• Independence Day pattern.
• Stock market performance tends to be the strongest five days prior to
Independence Day. Diminishing average performance generally occurs the
five days following Independence Day. The sixth day after Independence Day
is associated with very strong stock market performance.
• "Buy stocks on Monday and sell stocks on Friday. "However, monthly,
weekly, and daily patterns have the same statistical problems as holidays.
Any patterns observed once adjusted for underlying trend and for
randomness show little in the way of consistent return.

50. Seasonal Patterns
• A seasonal pattern in agricultural prices has been known for centuries.
More recently, interest rates have followed a seasonal pattern as money was
borrowed for seed and returned when the crops were gathered
• "Sell in May and go away," usually until October 1, refers to the tendency for
the stock market to decline from May to September and rise from October
to April. In the past ten years, August and September have been the worst
months for performance, and October, November, and January have the best
gains, with another small rise in April. May, under this model, is the month
to sell, and August is the month to start looking for a bottom. This model has
been very consistent .

51. THANK YOU
Topics are covered under:
Seasonal Pattern - Perry Kauffman (Chapter – 10) Page no -475 to 484
Cycle Advance Analysis – CMT BOOK
Cycle Basic – Charles – Chapter 9 (Cycles)