CFA LEVEL 1 - QUANTITATIVE METHODS
I create this summary of knowledge related to CFA level 1 for my 2017 December exam. I got into the top 10% with this. Hope this can help you.
Please note that this does not guarantee for your pass, which requires dedication, hardwork and consistency. In case having trouble with any part, please refer to CFA notebook/Schwesser.
Routines to simulate correlated normal random variables
Introduce three algorithms for simulating correlated normal random variables from a specified covariance matrix Σ (Σ is square and symmetric). In Section E.2 we present the details of the Cholesky decomposition. E.1 Three algorithms to simulate correlated normal random variables This section describes the Cholesky decomposition (CD), eigenvalue decomposition (ED) and the singular value decomposition (SVD). CD is efficient when Σ is positive definite. However, CD is not applicable for positive semi-definite matrices. ED and SVD, while computationally more intensive, are useful when Σ is positive semi-definite. • Cholesky decomposition We begin by decomposing the covariance matrix as follows: [E.1] where P is an upper triangular matrix. To simulate random variables from a multivariate normal distribution with covariance matrix Σ we would perform the following steps: 1. Find the upper triangular matrix P. 2. Compute a vector of standard normal random variables denoted . In other words, has a covariance matrix I (identity matrix). 3. Compute the vector . The random vector y has a multivariate normal distribution with a covariance matrix Σ. Step 3 follows from the fact that [E.2] where V( ) and E( ) represent the variance and mathematical expectation, respectively. • Eigenvalue decomposition Applying spectral decomposition to Σ yields [E.3] where C is an NxN orthogonal matrix of eigenvectors, i.e., is an NxN matrix with the N-eigenvalues of X along its diagonal and zeros elsewhere [E.4] Σ = PTP ε ε y P = Tε V y ( ) = = = = PTE εεT P PTIP PTP Σ Σ = C∆CT= QTQ CTC I = ∆ Q = ∆1 2 ⁄ CT254 Appendix E. Routines to simulate correlated normal random variables RiskMetrics —Technical Document Fourth Edition To simulate random variables from a multivariate normal distribution with covariance matrix Σ we would perform the following steps: 1. Find the eigenvectors and eigenvalues of Σ. 2. Compute a vector of standard normal random variables denoted . In other words, has a covariance matrix I (identity matrix). 3. Compute the vector . The random vector y has a multivariate normal distribution with a covariance matrix Σ. Step 3 follows from the fact that [E.5] The final algorithm that is proposed is known as the singular value decomposition. • Singular Value decomposition We begin with the following representation of the covariance matrix [E.6] where U and V are NxN orthogonal matrices, i.e., , and D is an NxN matrix with the N singular values of Σ along its diagonal and zeros elsewhere. It follows directly from Takagi’s decomposition that for any square, symmetric matrix, . Therefore, to simulate random variables from a multivariate normal distribution with covariance matrix Σ we would perform the following steps: 1. Apply the singular value decomposition to Σ to get V and D. 2. Compute a vector of standard normal random variables denoted . In other words, has a covariance matrix I (identity matrix). 3. Compute the vector where . The random vector y has a multivariate normal distribution with a covariance matrix Σ. Step 3 follows from the fact that [E.7] E.2 Applying the Cholesky decomposition In this section we explain exactly how to create the A matrix which is necessary for simulating multivariate normal random variables from the covariance matrix Σ. In particular, Σ can be decomposed as: [E.8] If we simulate a vector of independent normal random variables X then we can create a vector of normal random variables with covariance matrix Σ by using the transformation Y=A’X. To show how to obtain the elements of the matrix A, we describe the Cholesky decomposition when the dimension of the covariance matrix is 3 x 3. After, we give the general recursive equations used to derive the elements of A from Σ
Fear, Anxiety and Related Disorders. Lecture 4: Social Anxiety Disorder
These are all notes of lecture 4 on social anxiety from the course Fear, Anxiety and Related Disorders at the RU in Nijmegen, third year psychology. These are all notes of lecture about social anxiety of the subject Fear, Anxiety and Related Disorders of the RU in Nijmegen, third year of psychology.
Dissertation/Project: Multicultural teams in Leeds University Business School: What is related to their performance and to the students’ skills acquisition? How cultural differences affect the students\' perceptions?
Multicultural teams in Leeds University Business School: What is related to their performance and to the students’ skills acquisition? How cultural differences affect the students\' perceptions?
Nowadays, the global marketplace requires employees with skills related to teamwork.
Multicultural teams are formed in Business Schools to supply the marketplace with skilful
graduates. The present work tries to provide to Business Schools guidance on achieving
their goal. It tests how the performance and the skills acquisition in the multicultural
teams is affected by multiple variables indicated by the literature (satisfaction, creativity,
openness, trust, conflict, language barriers, time available, groupthink, social loafing). In
addition, light is shed into the difference of the students’ perceptions that come from their
different cultural backgrounds.
An online questionnaire was formed for the purpose of this research and students from
the Leeds University Business School were asked to complete the questionnaires.
The findings suggest that performance as well as skills acquisition in multicultural teams
in the Business School are related to most of the variables that have been tested for.
However, as it concerns the perceptions of the students, there were not found significant
differences, caused by their different cultural backgrounds, for most of the variables.
The generalisability of these results is subject to certain limitations. The sampling method
used, the small sample (N=72) collected as well as the fact that the students who
completed the questionnaire were all students from a single University reduce the
generalisability of the results to the whole Business school students population in the
The relationship between higher education and the labour market has been changing as
a result of globalisation (Tomlinson, 2010). It has been extensively indicated that
organisations have shifted towards narrower span of control (Groth and Nisen, 2013)
which offers to the employees more responsibilities as well as greater initiative and more
chances to shine and show their skills. This has created an increasing demand in workready graduates and Universities’ obligation is to supply them (Holmes, 2013; Tomlinson,
Teamwork is widely known from organisations but over the last two decades the increase
of work teams and the significance of the team skills has been rapidly growing (eg.,
Appelbaum and Batt, 1997). Adding to this, working in teams requires much more than
traditional business skills (Tarricone and Luca, 2002). Employers seek for graduates with
collaboration and teamwork skills as they believe that these are essential in all working
settings. Specifically, skills such as communication, time management, collaboration,
and interpersonal skills are considered to be the most preferable amongst employers
(Tarricone and Luca, 2002; Ritter et al., 2018). In more details, Hernandez (2002)
indicated that employers seek employees who know how to work effectively with others.
It is not surprising that Business Schools are targeting to enhance the teamwork skills of
their graduates. Because of the high demand for teamwork in business and the fact that
students will eventually become employees, employers have turned to Higher education
and Business Schools to incorporate the leaning of teamwork into the curriculum, with
the idea that students would learn from this process a lot of useful skills for their future
careers skills (Hansen, 2006; Ritter et al., 2018). More and more Business schools are
including teamwork exercises and group projects in their curriculums (Crossman and
Multinational businesses are increasing and now universities are progressively
encouraging students to get equipped with useful skills for their future employment in a
global environment (Green et al., 2009). The cultural diversity in Universities in the UK
reaches high percentages with some Universities having students from more than 150
countries (Mantle, 2018). As a result, students get to work in an environment similar to
that of a multinational business. Schworm et al. (2017) indicated that students that work2
in multicultural teams in University, gain international experience which can lead to
achieving a successful career. That is to indicate how significant is for students to
develop these skills successfully taking on account the modern global marketplace. In
the case that multicultural teams in Business Schools fail to achieve their potential, this
will result in graduates without the skills required from the employers.
However, teams and specifically multicultural teams are very complex, and their success
depends on multiple variables (West, 2012). Business schools need to take on account
multiple elements to facilitate the teams’ efficiency and the students’ skill learning. One
of the most complex part that is not easy to control are the cultural differences and
therefore the students’ different perceptions which depend on the country they are
coming from (Hofstede, 2011).
1.2 Research Aim
This research aims to indicate to Business Schools and their students the elements that
they should focus on to experience multicultural teams’ effectiveness and gain useful
skills for their future careers. In addition, to help universities make possible changes and
improvements on the way that student teams work, this research will look into how the
students evaluate the different cases in these diverse teams.
1.3 Research Questions
Hypothesis Group 1:
H1a: Satisfaction is positively correlated with the team performance in multicultural
teams in LUBS.
H1b: Creativity is positively correlated with the team performance in multicultural
teams in LUBS.
H1c: Openness is positively correlated with the team performance in multicultural
teams in LUBS.
H1d: Trust is positively correlated with the team performance in multicultural teams
H1e: Skill learning is positively correlated with the team performance in multicultural
teams in LUBS.
Hypothesis Group 2:
H2a: Conflict is negatively correlated with the team performance in multicultural
teams in LUBS
Summary FCH-21806 Food Related Allergies and Intolerances
Extensive summary of the course FCH-21806 Food Related Allergies and Intolerances. This summary contains all the lectures of both parts (Immunological aspects and Biochemical aspects) including my own notes and abstracts of articles referred to in lectures. The summary is written in English.
Anxiety, Obsessive Compulsive and Trauma Related Disorders
A comprehensive look at Anxiety, Obsessive Compulsive and Trauma Related Disorders with a 'flashcard' design.
Hoorcollege aantekeningen Fear, Anxiety and related disorders
Hoorcollege aantekeningen van Fear, Anxiety and related disorders. Bevat alle hoorcolleges.