Heteroskedasticity

Heteroskedasticity occurs when the variance of the errors differs across observations i.e. variances are not constant.

Heteroskedasticity could of be two types:
1. Unconditional Heteroskedasticity: When variance does not systematically increase or decrease with changes in the value of independent variable. It is violation of assumption 4 but does not upholds any serious problems with regression.
2. Conditional Heteroskedasticiy: It exists when error variance changes with the value of independent variable and it is more problematic.

Consequences of (conditional) Heteroskedasticity:

• It does not affect consistency but it can lead to wrong inferences.
• Coefficient estimates are not affected.
• It causes the F-test for the overall significance to be unreliable.
• It introduces bias into estimators of the standard error of regression coefficients; thus t-tests for the significance of individual regression coefficients are unreliable.
• When Heteroskedasticity results in underestimated standard errors, t-statistics are inflated and probability of Type-1 error increases.
• When Heteroskedasticity results in overestimated standard errors, t-statistics are deflated and probability of Type-2 error increases.

Testing for Heteroskedasticity:

Heteroskedasticity can be tested by Plotting residuals on a graph and judging a relationship with respect to observations on the x-axis. A more stringent measure is the Breush-Pagan Test which involves regressing the squared residuals from the estimated regression equation on the independent variables in the regression. 

• Null Hypothesis = No conditional Heteroskedasticity exists.
• Alternative Hypothesis = Conditional Heteroskedasticity exists.

Test statistic = n x R²_Residuals

Critical value can be calculated from chi-square distribution table with degree of freedom = no. of independent variables (k)

If test statistic > critical value reject null hypothesis and conclude that conditional Heteroskedasticity exists in the regression model.

Correcting for Heteroskedasticity: 

Two different methods can be used to correct Heteroskedasticity.

1. Computing robust standard errors corrects the standard errors of the linear regression model's estimated coefficients to deal with conditional heteroskedasticity. 

2. Generalized least squares (GLS) method is used to modify the original equation in order to eliminate the heteroskedasticity.

Assumptions of the Multiple Linear Regression Model

The model is based on 6 assumptions. When these assumptions are hold the regression estimators are unbiased, efficient & consistent.

• Unbiased means that the expected value of the estimator is equal to the true value of the parameter.
• Efficient means that the estimator has a smaller variance.
• Consistent means that the bias and variance of the estimator approach zero as the sample size gets larger.

1. The relationship between the dependent variable, Y, and the independent variables, X1, X2... Xk, is linear.

2. The independent variables are not random & no exact linear relation (perfect 1) exists between two or more of the independent variables.

3. The expected value of the error term, conditional on the independent variables is 0.

4. The variance of the error term is constant for all observations. i.e. errors are Homoskedastic

5. The error term is uncorrelated across observations (i.e. no serial correlation).

6. The error term is normally distributed.

It is important to note that Linear regression can't be estimated when an exact linear relationship exists between two or more independent variables. But when two or more independent variables are highly correlated, although there is no exact relationship, then it leads to multicollinearity  problem. Even if independent variable is random but uncorrelated with the error term, regression results are reliable.

Why the CFA Program has Levels in it?

The day I got myself enrolled in the CFA Program, I started thinking why the program has levels in it? I did check the CFA Institute website but couldn't find the answer there. Thought of asking it from any official in the CFA institute but postponed the idea as I didn't find it material to be discussed. Time went on I appeared in the exam in June 2011 with quite a few friends and passed the exam. Unfortunately a few among those who accompanied me during my journey in Level I were not able to pass the exam and are either repeating or left the field. After meeting a few of them I tried to figure out the reasons of failure as they could help me out in making myself better in Level II as it is way more in-depth and harder than its predecessor.

Innumerable reasons came in front me. I used to sit in my leisure time and recall the behavior of my friends towards their studies and used to inquire from them the reasons why they failed. Surprisingly it was then in the quest of identifying the reasons of failure; I figured out my analogy of why the CFA exam has levels in it. 

As we all know that the exam does not have any prerequisite knowledge requirements related to field, though it does require 16 years of education or 14 years of education with 2 years experience, a few of my friends who failed had finance background and they had allegiance with what the curriculum was saying or the topics covered in Level I were elaborating.

According to the exam, when we enroll ourselves in the CFA program we are technically at Level 0. It is like an initial stage. We begin our journey by learning a lot of things and equip ourselves with both the knowledge and desired skills to jump to the next level and then there comes a combat - the exam, which eliminates some people with inadequate skills of knowledge and allow some to promote for the next level. It sounds quite simple but if we look into its depth, passing Level I does not only make you eligible for the Level II exam but also ensures you that you have attained certain level of expertise which make you eligible enough to explore the depth of Level II. Those who think the Level will fall to their conscious (knowledge + skill) stage most likely fail in the exam as due to excellence guaranteed by the exam it cannot afford to lower its level at the conscious stage of the candidate but it ensures that the ability of the candidate rises and matches the benchmark set by the exam. 

It seems philosophical but if we surrender ourselves before the curriculum and read it with core purpose of learning and getting its essence out of it, irrespective of what we already know, our chances of passing the exam rise significantly. The moment we feel that we already know this or at some other stage or class we had read this in some other way and that was more productive etc. we get distracted. So in order to get the best out of our efforts one prerequisite necessary to better understanding is that we must surrender ourselves at enrollment, consider ourselves at Level 0, begin the journey like we know nothing and learn the maximum out of the CFA Program and get ready for the combat. I think it will greatly improve the probability to pass the exam. Based on my personal experience, as I had no finance background, I can certainly exclaim that it really works well!

The CFA Exam: Developing Skills through Psychometric Testing

It was my first job interview. Interestingly the panel had promoted me to the 3rd level, where I was supposed to appear in an aptitude test, without appearing in the 2nd level. Being shortlisted in first ever performance in a multinational was superb. It had given me so much confidence that I felt like my wings had grown. I could foresee my career prospects developing in the largest organization in telecom sector. Everything was remarkably pleasing and charming. Days went on and on and I finally I got the test call. I appeared in the test and stood second among all candidates. It went on and I started waiting for my job letter.

It is said that whatever happens happens for good. I did get a letter but unfortunately, which later proved the most fortunate one, stated that due lack of experience I was not given the job. It shattered my confidence and tore me apart. It was then I started to figure out about why experience is so essential and what is the value addition which one gets through gaining experience. 

My quest to know about experience was going on when I found that it results in gaining of required skills which are necessary for the job. Organisations are systems which provide platform to their employees to work in order to accomplish their goals along with the goals of the organisations. They invest in their employees and people with existing skills, resulted through previous job experience, are better and attractive prospects. Based upon the prevailing market conditions when the economy is running through recession and organisations are downsizing it was almost impossible to get a job without any prior experience. 

After successive failures in almost 11 job interviews I decided to continue my studies. The question then was what to study? My graduation was broad based and it did not equip me with the required expertise in terms of knowledge to further nourish my skills specifically. To cut it short I somehow enrolled myself in the CFA program and passed the Level I exam. 

It was few days back when I found this amazing document over the CFA Institute website (link provided at the bottom). It stated that the CFA program testing has empirically proven that the students appearing in the exam are equipped with required knowledge and skills for competent professional practice. Really? I mean is that so? Appearing in CFA exam is not only about knowledge but it also inculcates in us the required skills for competency and professionalism? Isn't it against the 'norms'? The detailed report highlights several interesting aspects of the CFA examination, their credibility, the inculcation of psychometric tools while developing the testing material, the creation of the CFA curriculum and the standard setting. 

Since I am in Level II and have roughly covered two important study sessions; when I log into several financial websites I can sense the difference in my understanding and I find myself able to connect what I am studying with the real world. It is remarkable and overwhelming. Several strategies which are mentioned in the curriculum are so practical that one could not only learn from them but also earn from them. 

A day before yesterday I was offered a job from a renowned organization in our country. The executive responsible for hiring and recruitment himself offered me the job. It was not that he knew me but due to fact that I am enrolled in the CFA program and have passed the level I. He knows that I do not have any prior experience but yet he offered me the job. Like I said whatever happens, happens for good. Enrolling in CFA proved to be the best decision of my life because it has added immense value in me both in terms of knowledge and desired skills. There is so much to learn through this program that words can simply not encompass it. For those who want to pursue their careers in the amazing world of finance must consider the CFA program for its capabilities to develop a winning combination.

PS: CFA Program Detailed Report