Stock-market

Mainly focusing on Elliott's Wave Theory to help determining the market trend and golden ratios to determine price.

• Stock-market
  • Introduction
  • Basic formation
  • Basic principle
  • Number the waves
  • Calculation of the waves
  • Speical cases for Corrective Wave Patterns
    • The Zig-Zag Formation
    • The Flat Formation
    • The Triangle Formation
  • Price determination using golden ratios

Introduction

Elliott Wave Theory is a technical analysis used to describe price movements in the financial market. The stock price movements and consumer behaviors can be identified as waves according to Elliot.

Basic formation

As shown in the above graph, a whole big wave consists of 8 small waves. There are two types of waves, one called Impulse (Motive) wave and the other called Corrective wave. In the above graph, wave 1,3 and 5 are Impulse waves, and wave 2 and 4 are Corrective waves. However we can see that the 5-wave trends are then corrected and reversed by 3-wave countertrends: A-B-C.

The Impulse wave is not always in the upward direction and the Corrective wave is not always in the downward direction. That's because the definition of Impulse wave is to make a net movement in the same direction as the trend of the next-largest degree while the definition of Corrective wave is to correct the direction of the movement. For example, in the bear market shown in the following graph,

wave 1,3, and 5 are still Impulse waves, but they are moving downwards.

Basic principle

• The movement of Wave 2 will not exceed the starting point of wave 1.
• Wave 3 is usually the longest wave, but cannot be the shortest (compared to Wave 1 and 5).
• Wave 4 will never enter the domain of Wave 1.

Number the waves

Sometimes a big wave can consist of a whole 5-3 wave. It will be shown as follows:

Here, Wave (1) consists of Wave (i), (ii), (iii), (iv), (v); Wave (2) consits of Wave (a), (b) and (c);... These will usually happen when you look at different time scales.

Calculation of the waves

The calculation of prices usually involves Fibonacci Sequence.

• %Wave 2 = (%Wave 1) $^{0.5}$ or (%Wave 1) $^{0.618}$. Here is the Python code below which helps you calculate:

# Bull market, po4 and po5 are the most common ones (as stated above)
def wave_positive(x,y):
    po1 = p1 * ((1-pe)**0.125)
    po2 = p1 * ((1-pe)**0.236)
    po3 = p1 * ((1-pe)**0.382)
    po4 = p1 * ((1-pe)**0.5)
    po5 = p1 * ((1-pe)**0.618)
    po6 = p1 * ((1-pe)**0.764)
    po7 = p1 * ((1-pe)**0.875)
    po8 = p1 * ((1-pe)**1)
    return po1, po2, po3, po4, po5, po6, po7, po8
# Enter the highest value in Wave 1
x = float(input("Enter the final value" + " "))
# Enter the lowest value in Wave 1
y = float(input("Enter the initial value" + " "))
# Calculate the increasing rate of prices
pe = (x-y)/y
# Enter the value to start calculating (In this case is the highest value of Wave 1)
p1 = float(input("Enter the value you want to start" + " "))
result4 = wave_positive(x,y)
# pe is indeed greater than 0 as it is in bull market and the final value is the highest value of Wave 1
if pe > 0 and x == p1:
    print(str(result4))

• %Wave 3 = (%Wave 1) $^{1.618}$ or (%Wave 1) $^{2}$ or (%Wave 1) $^{2.618}$. Here is the Python code below which helps you calculate:

# Bull market, poc11, poc12 and poc13 are the most common prices, while other prices are convenient for calculating prices compared Wavee 5 to Wave 1
def wave_poscor(x,y):
    poc1 = p1 * ((1+pe)**0.236)
    poc2 = p1 * ((1+pe)**0.382)
    poc3 = p1 * ((1+pe)**0.5)
    poc4 = p1 * ((1+pe)**0.618)
    poc5 = p1 * ((1+pe)**0.764)
    poc6 = p1 * ((1+pe)**0.875)
    poc7 = p1 * (1+pe)
    poc8 = p1 * ((1+pe)**1.236)
    poc9 = p1 * ((1+pe)**1.382)
    poc10 = p1 * ((1+pe)**1.5)
    poc11 = p1 * ((1+pe)**1.618)
    poc12 = p1 * ((1+pe)**2)
    poc13 = p1 * ((1+pe)**2.618)
    return  poc1, poc2, poc3, poc4, poc5, poc6, poc7, poc8, poc9, poc10, poc11, poc12, poc13
x = float(input("Enter the final value" + " "))
y = float(input("Enter the initial value" + " "))
# rate of change = (final value - initial value)/initial value 
pe = (x-y)/y
# Enter the value to start calculating (In this case should be the lowest value in Wave 2)
p1 = float(input("Enter the value you want to start" + " "))
result2 = wave_poscor(x, y)
# pe is indeed greater than 0 as it is in bull market and the final value is not the hightest value of Wave 1
if pe > 0 and x != p1:
    print(str(result2))

• %Wave 4 = (%Wave 3) $^{0.382}$. Here is the Python code below which helps you calculate:

# Bull market, po3 is the most common ones (as stated above)
def wave_positive(x,y):
    po1 = p1 * ((1-pe)**0.125)
    po2 = p1 * ((1-pe)**0.236)
    po3 = p1 * ((1-pe)**0.382)
    po4 = p1 * ((1-pe)**0.5)
    po5 = p1 * ((1-pe)**0.618)
    po6 = p1 * ((1-pe)**0.764)
    po7 = p1 * ((1-pe)**0.875)
    po8 = p1 * ((1-pe)**1)
    return po1, po2, po3, po4, po5, po6, po7, po8
# Enter the highest value in Wave 3
x = float(input("Enter the final value" + " "))
# Enter the lowest value in Wave 3
y = float(input("Enter the initial value" + " "))
# Calculate the increasing rate of prices
pe = (x-y)/y
# Enter the value to start calculating (In this case is the highest value of Wave 3)
p1 = float(input("Enter the value you want to start" + " "))
result4 = wave_positive(x,y)
# pe is indeed greater than 0 as it is in bull market and the final value is the highest value of Wave 3
if pe > 0 and x == p1:
    print(str(result4))

• %Wave 5 = %Wave 1 or (%Wave 1) $^{0.618}$ when %Wave 3 > %Wave 1 or (%Wave 3) $^{0.236}$, (%Wave 3) $^{0.382}$ when %Wave 3 < %Wave 1. Here is the Python code below which helps you calculate:

# Bull market, porc4, poc5 and poc7 are the most common prices.
def wave_poscor(x,y):
    poc1 = p1 * ((1+pe)**0.236)
    poc2 = p1 * ((1+pe)**0.382)
    poc3 = p1 * ((1+pe)**0.5)
    poc4 = p1 * ((1+pe)**0.618)
    poc5 = p1 * ((1+pe)**0.764)
    poc6 = p1 * ((1+pe)**0.875)
    poc7 = p1 * (1+pe)
    poc8 = p1 * ((1+pe)**1.236)
    poc9 = p1 * ((1+pe)**1.382)
    poc10 = p1 * ((1+pe)**1.5)
    poc11 = p1 * ((1+pe)**1.618)
    poc12 = p1 * ((1+pe)**2)
    poc13 = p1 * ((1+pe)**2.618)
    return  poc1, poc2, poc3, poc4, poc5, poc6, poc7, poc8, poc9, poc10, poc11, poc12, poc13
x = float(input("Enter the final value" + " "))
y = float(input("Enter the initial value" + " "))
# rate of change = (final value - initial value)/initial value 
pe = (x-y)/y
# Enter the value to start calculating (In this case should be the lowest value in Wave 4)
p1 = float(input("Enter the value you want to start" + " "))
result2 = wave_poscor(x, y)
# pe is indeed greater than 0 as it is in bull market and the final value is not the hightest value of Wave 1
if pe > 0 and x != p1:
    print(str(result2))

• %Wave A = (%Wave 5) $^{0.5}$ or (%Wave 5) $^{0.618}$. Here is the Python code below which helps you calculate:

# Bull market, po4 and po5 are the most common ones (as stated above)
def wave_positive(x,y):
    po1 = p1 * ((1-pe)**0.125)
    po2 = p1 * ((1-pe)**0.236)
    po3 = p1 * ((1-pe)**0.382)
    po4 = p1 * ((1-pe)**0.5)
    po5 = p1 * ((1-pe)**0.618)
    po6 = p1 * ((1-pe)**0.764)
    po7 = p1 * ((1-pe)**0.875)
    po8 = p1 * ((1-pe)**1)
    return po1, po2, po3, po4, po5, po6, po7, po8
# Enter the highest value in Wave 5
x = float(input("Enter the final value" + " "))
# Enter the lowest value in Wave 5
y = float(input("Enter the initial value" + " "))
# Calculate the increasing rate of prices
pe = (x-y)/y
# Enter the value to start calculating (In this case is the highest value of Wave 5)
p1 = float(input("Enter the value you want to start" + " "))
result4 = wave_positive(x,y)
# pe is indeed greater than 0 as it is in bull market and the final value is the highest value of Wave 5
if pe > 0 and x == p1:
    print(str(result4))

• %Wave B = (%Wave A) $^{0.382}$ or (%Wave A) $^{0.5}$ or (%Wave A) $^{0.618}$. Here is the Python code below which helps you calculate:

# Bull market, so Wave A is corrective, and ne3, ne4 and ne5 are the most common ones (as stated above)
def wave_negative(x,y):
    ne1 = p1 * ((1+abs(pe))**0.125)
    ne2 = p1 * ((1+abs(pe))**0.236)
    ne3 = p1 * ((1+abs(pe))**0.382)
    ne4 = p1 * ((1+abs(pe))**0.5)
    ne5 = p1 * ((1+abs(pe))**0.618)
    ne6 = p1 * ((1+abs(pe))**0.764)
    ne7 = p1 * ((1+abs(pe))**0.875)
    ne8 = p1 * ((1+abs(pe))**1)
    return ne1, ne2, ne3, ne4, ne5, ne6, ne7, ne8
# Enter the lowest value in Wave A
x = float(input("Enter the final value" + " "))
# Enter the highest value in Wave A
y = float(input("Enter the initial value" + " "))
# Calculate the increasing rate of prices
pe = (x-y)/y
# Enter the value to start calculating (In this case is the lowest value of Wave A)
p1 = float(input("Enter the value you want to start" + " "))
result3 = wave_negative(x,y)
# pe is less than 0 as it is in bull market and the final value is the lowest value of Wave A
if pe < 0 and x == p1:
    print(str(result3))

• %Wave C = %Wave A or (%Wave A) $^{0.618}$ or (%Wave A) $^{1.382}$ or (%Wave A) $^{1.618}$. Here is the Python code below which helps you calculate:

def wave_negcor(x,y):
    nec1 = p1 * ((1-abs(pe))**0.125)
    nec2 = p1 * ((1-abs(pe))**0.236)
    nec3 = p1 * ((1-abs(pe))**0.382)
    nec4 = p1 * ((1-abs(pe))**0.5)
    nec5 = p1 * ((1-abs(pe))**0.618)
    nec6 = p1 * ((1-abs(pe))**0.764)
    nec7 = p1 * ((1-abs(pe))**0.875)
    nec8 = p1 * (1-abs(pe))
    nec9 = p1 * ((1-abs(pe))**1.236)
    nec10 = p1 * ((1-abs(pe))**1.382)
    nec11 = p1 * ((1-abs(pe))**1.5)
    nec12 = p1 * ((1-abs(pe))**1.618)
    return nec1, nec2, nec3, nec4, nec5, nec6, nec7, nec8, nec9, nec10, nec11, nec12
# Enter the lowest price of Wave A
x = float(input("Enter the final value" + " "))
# Enter the highest price of Wave A
y = float(input("Enter the initial value" + " "))
# rate of change = (final value - initial value)/initial value 
pe = (x-y)/y
# Enter the highest value of Wave C
p1 = float(input("Enter the value you want to start" + " "))
result1 = wave_negcor(x, y)
# pe is less than 0 in bull market and the final value is the highest value of Wave B
if pe < 0 and x != p1:
    print(str(result1))

Note here all the code is provided in bull market, full code including bear market will be attached in the file.

Speical cases for Corrective Wave Patterns

The Zig-Zag Formation

• Zig-zag formations are very steep moves in price that go against the predominant trend.
• Wave $B$ is typically shortest in length compared to Waves $A$ and $C$.
• These zig-zag patterns can happen twice or even three times in a corection (2 to 3 zig-zag patterns linked together).
• Each of the waves in zig-zag patterns could be broken up into 5-wave patterns.

The Flat Formation

• Flat formations are simple sideways corrective waves.
• The lengths of the waves are Generally equal in length, with wave $B$ reversing wave $A$'s move and wave $C$ undoing wave $B$'s move.
• Generally in above means sometimes wave $B$ can go beyond the beginning of wave $A$.

The Triangle Formation

• Triangle formations are corrective patterns that are bound by either converging or diverging trend lines.
• Triangles are made up of 5-waves that move against the trend in a sideways fashion. These triangles can be symmetrical, descending, ascending or expanding.

Price determination using golden ratios

• When we look at price charts over a long period of time, or a chart where the stock price has moved in a wide vertical range, the common linear price chart is not as useful as the semi-log chart.
• The semi-log chart has a logarithmic scale for the vertical axis while the time axis is still linear - hence the chart is a semi-log chart (not a log chart).

How do we determine the price of correction or price of impulse?

• Consider the above graph, we would like to calculate the correction price in nearly 2009-05-24, which is a correction to the price from 2002-05-24 to 2007-05-24.
• We use golden ratio to calculate.
• Let the highest price be $p_{h}$, which is the price in approximately 2007-05-24, and the lowest price be $p_{l}$, which is the price in approximately 2002-07-24.
• Then the correction price $p_{c}$ usually can be $$p_{c} = p_{h}^{0.125}\times p_{l}^{0.875}\quad\text{or}\quad p_{c} = p_{h}^{0.236}\times p_{l}^{0.764}\quad\text{or}\quad p_{c} = p_{h}^{0.382}\times p_{l}^{0.618}\quad\text{or}\quad p_{c} = p_{h}^{0.5}\times p_{l}^{0.5}.$$
• Similar for impulse wave, but this time the lowest price should take the exponential of $0.125,0.236,0.382$ and $0.5$.
• Overall, the most important thing is to find the corresponding wave which the price is correcting or pushing.

I have also included my own python file named 'high_low' for calculation, which makes it easier to store and list all the possible values.

def high_low(x,y):
    p1 = x**(0.125)*y**(0.875)
    p2 = x**(0.236)*y**(0.764)
    p3 = x**(0.382)*y**(0.618)
    p4 = x**(0.5)*y**(0.5)
    p5 = x**(0.618)*y**(0.382)
    p6 = x**(0.764)*y**(0.236)
    p7 = x**(0.875)*y**(0.125)
    return p1,p2,p3,p4,p5,p6,p7
x = float(input("Enter the maxima" + " "))
y = float(input("Enter the minima" + " "))
result = high_low(x,y)
print(str(result))