Tuesday, September 12, 2017

بورس: تحلیل تکنیکال یا بنیادی

در تحلیل تکنیکال از شکل روند دیاگرام قیمت سهام یا نرخ بازگشت سرمایه یک شرکت که در طول یک بازه زمانی چندین بارتکرار شده برای پیش بینی قیمت سهام استفاده میکنند. حتی با اینکه من به تکرار و دوره تناوب بازار سرمایه باور دارم اما در حال حاضر ریسک استفاده از این روش بدلیل افزایش خیلی سریع تغییرکه توسط تکنولوژی اتفاق افتاده, بسیار بالاست به دو دلیل مهم:
 1) شکل دوره تناوب همیشه دایره نیست گاهی اوقات شبیه یک حلزون هست و گاهی اوقات شبیه دوره های تناوبی هست که من در مقالات زیر به آن اشاره کرده ام:




2) طول یک بازه زمانی که همان دامنه و یا شعاع های دوایر یا حلزون متحدالمرکز است بعلت تغییرات شکل گرفته توسط تکنولوژی قابل پیش بینی نیست. این یعنی مبدا بازه زمانی شما برای یک دوره تناوب کجا بایدباشد؟

اساس تحلیل بنیادی بر اطلاعات مالی شرکت شامل حساب سود وزیان و ترازنامه مالی میباشد. در حقیقت وقتی شما سهام یک شرکت را خریداری میکنید درست شبیه به این است که یک کالای الکتریکی ومکانیکی را از یک شرکت میخرید که دارای مشخصات فنی منحصر بفرد است. اگر این کالا براساس مشخصات فنی کارنکند, شرکت  تولید کننده کالا در این خصوص مقصر میباشد. در مورد سهام هم همینطور است در حقیقت حساب سود وزیان و ترازنامه مالی هر شرکت مشخصات فنی سهام شماست. اگر شرکت در تنظیم این اطلاعات مالی قصور کند و یا شفاف عمل نکند, نهایتا با هر مدل بنیادی پیشرفته هم تحلیل کنید, شما ضرر خواهید کزد. بنابراین وقتی میخواهید از این روش برای تحلیل استفاده کنید قدم اول اطمینان از اعداد وارقام مندرج درحساب سود وزیان و ترازنامه مالی شرکت میباشد.

روشهای مختلفی برای کنترل ارقام وجود دارد بطور مثال مهمترین قسمت یک حساب سود و زیان, رقم فروش سالیانه است. همیشه اگر میخواهید از عدد فروش و با پیش بینی فروش اطمینان حاصل کنید به یک کسب و کار مثل آرایشگاه که تا شعاع 500 متری آن هیچ رقیبی (آرایشگاهی) نیست فکر کنید و ببینید شرکتی که میخواهید تحلیل بنیادی کنید شبیه این آرایشگاه هست. یعنی کالایی تولید کند که همه مردم درهر شرایطی نیاز دارند و این کالای تولیدی بدون رقیب است مثل کالاهایی با تکنولوژی بکاررفته بالا. قسمت مهم بعدی در حساب سود و زیان, قیمت تمام شده کالا باضافه هزینه های بالاسری میباشد. برای کنترل هزینه ها میتوانید از مشاوره یک کارشناس با سابقه زیاد در صنعت آن شرکت استفاده کنید.

اما به نظر من بهترین روش, ترکیب و استفاده ازهر دو روش تکنیکال و بنیادی است. در حقیقت از روش تکنیکال, شرکتی را که دارای شرایط تحلیل بنیادی است را میتوانید انتخاب کنید. سپس از مدل زیر برای تحلیل بنیادی استفاده کنید.
گام بعدی برای تحلیل بنیادی, پیش بینی یک دوره پنجساله برای پارامترهای اقتصادی مثل: سود بانکی ,تورم, رشد اقتصادی و غیره میباشد
بهترین مدل برای تحلیل بنیادی استفاده همزمان از روش DCF ((Discounted Cash Flow Analysis و روش مونت کارلو برای کاهش ریسک میباشد این همان روشی است که من برای پیش بینی قیمت سهام شرکت نایک (Nike Inc.) استفاده کردم. (لینک زیر)

در این مدل با بازی کردن با فرضیات مثل پیش بینی فروش و هزینه ها و پارامترهای اقتصادی میتوانید به کمترین و بیشترین پیش بینی قیمت سهام شرکت دست پیدا کنید.

Sunday, August 27, 2017

The Change Depends on the Direction of the Motion: The Gradient Vector and Symmetric Group Action (1)

Following to article of “The Change Depends on the Direction of the Motion: The Symmetric Group Action (2)” posted on link: http://www.emfps.org/2017/08/the-change-depends-on-direction-of_9.html?m=1, before I start new operators with four points, I would like to inform you that there are many other properties which can be derived from previous theorems. The purpose of this article is, to use the gradient as an operator accompanied by symmetric group action in which they work together. In this article as an example, I only examine the properties of an operator 3*3 which works with gradient vector of function:

f (x, y, z) = x^n + y^n + z^n  

Regarding to my previous articles, I introduced to you many symmetric groups actions and 11 theorems where all of them accompanied by the gradient vector of any function will generate many properties and theorems.

As you saw, we had matrix “M” as below operator 3*3:

M =

The property of function:  w = f (x, y, z) = x^2 + y^2 + z^2


The gradient vector of this function is:

Theorem 12: Maximum and minimum magnitude of the vector produced by operator M and the gradient vector of function f (x, y, z) = x^2 + y^2 + z^2 are obtained by below formulas:

Where:

r1 = radius in operator M

r2 = radius of each point on surface or space in accordance with its polar coordinates

Theorem 13: Maximum and minimum magnitude of the vector produced by operator M and the gradient vector of function f (x, y, z) = x^3 + y^3 + z^3 are obtained by below formulas:

Where:

r1 = radius in operator M

r2 = radius of each point on surface or space in accordance with its polar coordinates

Theorem 14: Maximum and minimum magnitude of the vector produced by operator M and the gradient vector of function f (x, y, z) = x^4 + y^4 + z^4 are obtained by below formulas:

Where:

r1 = radius in operator M

r2 = radius of each point on surface or space in accordance with its polar coordinates

Theorem 15: Maximum and minimum magnitude of the vector produced by operator M and the gradient vector of function f (x, y, z) = x^5 + y^5 + z^5 are obtained by below formulas:

Where:

r1 = radius in operator M

r2 = radius of each point on surface or space in accordance with its polar coordinates

The property of function:  w = f (x, y, z) = x^n + y^n + z^n

As we as well as know, “n” time partial differential of this function will be calculated by using below formula:

Theorem 16: For function w = f (x, y, z) = x^n + y^n + z^n and operator M, we have:

Example:

Suppose you have below function:

w = f (x, y, z) = x^5 + y^5 + z^5

And also you have below conditions for operator M:

r1 = 22.6

θ = 51 Degree

β = 13 degree

Then, operator M will be:

M = 


According to above formula, we have:

Therefore, we can see:

In the reference with theorem 16, we can find a very interesting theorem as follows:

When we say n! , it means that we can consider it as a constant value for any vector:

V = c (i + j + k)

Theorem 17: Each vector V = c (i + j + k) multiplied by operator M will be equal zero.


Wednesday, August 9, 2017

The Change Depends on the Direction of the Motion: The Symmetric Group Action (2)

Following to article of “The Change Depends on the Direction of the Motion: The Symmetric Group Action (1)” posted on link: https://emfps.blogspot.com/2017/08/the-change-depends-on-direction-of.html, the purpose of this article is to introduce some properties of operators and transformations which are formed by moving three points on circle and sphere.
 But, before starting of this article, let me tell you more explanations about theorems mentioned in previous article as follows:

1. All theorems in previous article denote to get the maximum and minimum for vectors in all directions but if we need to have the maximum and minimum of each point on surface or space exchanged by operators and transformations, all equations should be changed as follows:

Theorem (1): │V│max = (2^0.5).r1.r2              and              │V│min = 0

Theorem (4): │V│max = r2.max (z, r1)*(2^0.5)   and 

│V│min = r2.min (z, r1)*(2^0.5) 
 
Where:

r1 = radius in operator or transformation matrix

r2 = radius of each point on surface or space in accordance with its polar coordinates

2. In Theorem (4), if z = r1 then we can say this transformation matrix maps a random point on surface to a random point on a sphere with radius equal to:

  R = (2^0.5).r1.r2 

R = radius of the sphere           

An operator or transformation matrix formed by three points on circle


Suppose three points on a circle are rotating in which the distance among all three points are the same and equal just like below figure: 



For reaching to above conditions, below polar coordinates for each point should be established:

A:
x = r cos θ
y = r sin θ

B:
x = - r sin (θ + 30)
y = r cos (θ +30) 

C:
x = - r sin (30 – θ)
y = - r cos (30 – θ)

By considering any random number for “r” and “θ”, you can see not only all distances are equal but also all three points are on a circle. 

Example:

r = 23   and   θ = 41 degree

AO = BO = CO = 23
AB = BC = CA = 39. 83716857

Above polar coordinates give us a transformation matrix 3*2 as follows:


The properties of transformation matrix 3*2 for R^3 to R^2

By multiplying matrix M by any 3D vectors in the space, we can extract the properties of this transformation matrix as follows:

Theorem (6): The maximum magnitude among 2D vectors produced by three point’s transformation matrix M is calculated by using below equation:

│V│max = 0.5. (6^0.5).r1.r2 

Where:

r1 = radius in transformation matrix M
r2 = radius of each point in the space (3D) in accordance with its polar coordinates

The minimum magnitude is obtained by using below equation:

  │V│min = r1.r2 / Ф

Ф = the constant coefficient equal to 176.943266509085

Here is a very interesting property:

Theorem (7): Always there are six points or six 2D vectors produced by three point’s transformation matrix M which give us the maximum magnitude while there is only one point or one 2d vector which gives us the minimum magnitude in which the direction of all points or 2D vectors is between 0 degree to 180 degree.

The property of transformation matrix 2*3 for R^2 to R^3

It is transpose of above matrix in which we will have below matrix:





Theorem (8): This transformation matrix maps a random point on surface to a random point on a sphere with radius equal to:  R = 0.5. (6^0.5).r1.r2 

Where:

R = radius of the sphere           
r1 = radius in transformation matrix M
r2 = radius of each point on the surface (2D) in accordance with its polar coordinates



The properties of an operator 3*3 

If we want to study these three points in 3D space rotating on circle or sphere, we will have an operator 3*3. In this case, there are several statements where I have started three forms as follows:

1. I added a constant coordinate (z) for each point and matrix will be:




Theorem (9): Maximum and minimum magnitudes among 3D vectors produced by operator M are calculated by using below equations and conditions:

If    r1 /z > 2^0.5   Then   │V│max = 0.5. (6^0.5).r1.r2     and

│V│min = (3^0.5).r2 .min (z, r1)

If    r1 /z < 2^0.5   Then   │V│max = (3^0.5).r2 .max (z, r1)   and

│V│min = 0.5. (6^0.5).r1.r2     

Theorem (10): If r1 /z = 2^0.5 then this operator maps a random point in the space to a random point on a sphere with radius equal to:

 R = 0.5. (6^0.5).r1.r2       or

R = (3^0.5).r2 .min (z, r1)

Where:

R = radius of the sphere           
r1 = radius in operator M
r2 = radius of each point in the space (3D) in accordance with its polar coordinates



Theorem (11): If    r1 /z > 2^0.5   Then,   Always there are six points in the space or six 3D vectors produced by three point’s operator M which give us the maximum magnitude while there is only one point or one 3D vector which gives us the minimum magnitude.

If    r1 /z < 2^0.5   Then,  Always there are six points in the space or six 3D vectors produced by three point’s operator M which give us the minimum magnitude while there is only one point or one 3D vector which gives us the maximum magnitude.   

2. I replaced the constant coordinate (y) instead of (z):


The properties of this operator are similar to theorems (9), (10) and (11).

3. Suppose that three points in the space which have the same distance are rotating on a sphere. In this case, we will have below polar coordinates for all three points as follows:

 Point A:

x = r * cos β * cos θ
y = r * cos β * sin θ
z = r * sin β

Point B:

x = -r * cos (60 – β) * cos θ
y = -r * cos (60 – β) * sin θ
z = r * sin (60 – β)

Point C:

x = -r * cos (60 + β) * cos θ
y = -r * cos (60 + β) * sin θ
z = -r * sin (60 + β)

Example:

Assume θ = 56, β = 17 and    r = 31

According to above coordinates, we can calculate the distance among points and also the distance between points and center of sphere which answers are:

AO = BO = CO = 31
AB = BC = CA = 53.69358

The properties of operator 3*3

Above coordinates of points A and B and C make an operator 3*3 as follows:



Note: θ and β have been introduced in my previous article of “The Change Depends on the Direction of the Motion: Generating All Directions in 3D Space” posted on link: https://emfps.blogspot.com/2017/05/the-change-depends-on-direction-of.html

The property of this transformation matrix is similar to theorems (6) and (7).

An operator or transformation matrix formed by four points on circle


 To be continued….