1. www.edupristine.com FRM Part I Quantitative Analysis 21st May 2011© Neev Knowledge Management – Pristine
2. Seminar Material Not for Sale Agenda • Introduction and context • Understanding the FRM Examination Structure • Introduction to Quantitative Analysis – Probability Distributions – Key Concept Checkers • Complete Offering & Registration • Next Seminar© Neev Knowledge Management – Pristine 2 www.edupristine.com
3. Pristine has been started by professionals with diverse experience in Seminar Material Not for Sale financial services, IT and Auto who are alumnus of IITs & IIMs Innovative content – To improve understanding & learning capability of students. VisualizeFRM, VisualizeCFA as one of the best selling products Topic Expert Model (TEM ) – Industry professionals bring invaluable industry perspective for students. Pool of 300+ working professionals as active faculty members with the likes of CFA regional directors, Presidents of various banks Pristine Classroom/ Online delivery (synchronous and Founded with an aim asynchronous) – To increase of creating world reach and improve efficiency of class professionals in learning. Conducted 15+ the area of finance – batches with over 300 hours of particularly risk recorded content management and Testimonial - 53% of the students join us on the investment banking basis of referral is a testimonial of the effective Effective training methodologies to improve the performance training methodologies of the students and enhance the employability© Neev Knowledge Management – Pristine 3 www.edupristine.com
4. Seminar Material Key Authorization Not for Sale GARP (2007-10) CFA Institute (2010-11) Authorized Training provider -FRM Authorized Training provider – CFA Largest player in India in the area of risk Pristine is now the authorized training provider management training. Trained 1000+ students for CFA Exam trainings . Pristine is largest in risk management training provider for CFA in India with presence across seven major cities. PRMIA (2009-10) FPSB India (2010-11) Authorized Training provider – PRM/ APRM Authorized Training provider -CFP Sole authorized training for PRM Training in An authorized Education Provider for India. Largest player in India in the area of risk Chartered Financial Planner Charter. management training. Trained 1000+ students in risk management© Neev Knowledge Management – Pristine www.edupristine.com
5. Seminar Material Key Associations* Not for Sale Bank Of America J. P. Morgan (2010) Mizuho (2010) Continuum Solutions (2010) Financial Modeling in Excel Financial Modeling in Excel Financial Modeling in Excel The Real Assets Group were trained in Bankers were using excel models that Associates were trained on valuation and Excel for infrastructure and real-estate they could not understand. Conducted mergers and acquisitions modeling financial modeling in Excel trainings to bridge the gap Franklin Templeton Credit-Suisse India (2009) HSBC (2008) CFA (2010) Risk Management and Quant. Analysis Risk Management and Quant. Analysis Students were facing a gap in the IT Professionals of Credit-Suisse India New joinees in HSBC had a gap in overall understanding of finance were trained on risk management. knowledge of Risk Management and topics like corporate finance, FSA and quantitative skills. Conducted trainings valuation. Provided training for over (On campus) to bridge the gap 100 hours to bridge the gap *Indicative List© Neev Knowledge Management – Pristine www.edupristine.com
6. Seminar Material …Key Associations Not for Sale FMS Delhi (2010-11) IIM Calcutta (2010-11) BITS Pilani (2009) Financial Modeling in Excel Financial Modeling in Excel Workshops on Basics of Finance Final Year MBA students of Faculty of Students about to go for internships and Management Studies, Delhi University Most of the students desire a career join jobs found a gap in their grasp of were trained in financial modeling so as knowledge of excel for financial in finance. Conducted training for to prepare them better for a job in modeling. Conducted training for 75+ 350+ students with an average rating finance. students with an average rating of 4.5+ of 4.5+ NISM (2008) Derivatives workshop for Hedging IIT Delhi (2009) Sydneham College (2009) Corporate in Ludhiana incurred huge Corporate finance Financial Modeling in Excel losses because of derivative trades Students get placed in finance Students about to join jobs found a (for hedging). Conducted trainings for companies (UBS, GS, MS, etc) with gap in their grasp of excel for financial directors and CFOs for better no understanding of the subject/ Job modeling. Conducted 40+ hours of understanding of derivative products Profile. Conducted workshop to training and helped students be ready bridge the gap for job© Neev Knowledge Management – Pristine www.edupristine.com
7. Seminar Material Not for Sale Trainer Pawan Prabhat, Director and Faculty, Pristine Pawan has experience in the area of risk management and investment banking. He has worked in the area of risk management and investment banking. Pawan is a co-founder of Pristine and has earlier worked in senior management positions in Crisil – S&P and Standard Chartered Securities. He has also worked in the IT industry in companies like Geometric Software and Wipro. Pawan has successfully managed various IPOs worth more than 300 crores and has been the main point of contact with the promoters and the funds. Some of the IPOs in which has played instrumental roles are • Insecticide India • Nitin Fire • Nelcast • Barak Valley • Precision Pipes • Indowind Pawan has done his MBA from IIM Indore and is a B. Tech from IIT Bombay in mechanical engineering. Pawan has published research paper and has co-authored articles on risk management in national finance daily- Hindu Business Line He is an avid reader and has been involved in dramatics, quizzing and bridge.© Neev Knowledge Management – Pristine www.edupristine.com
8. Seminar Material Not for Sale Agenda • Introduction and context • Understanding the FRM Examination Structure • Introduction to Quantitative Analysis – Probability Distributions – Key Concept Checkers • Complete Offering & Registration • Next Seminar© Neev Knowledge Management – Pristine 8 www.edupristine.com
9. Seminar Material Not for Sale FRM 2011 Area Weight Foundations of Risk Management 20% Quantitative Analysis 20% Financial Markets and Products 30% Valuation and Risk Models 30% 100 MCQ, 4 hours test in pen and paper, May21, 2011© Neev Knowledge Management – Pristine Careers 9 www.edupristine.com
10. Seminar Material Not for Sale FRM Exam Statistics 2009 FRM Sample Paper 2010 FRM Sample Paper 12% Foundation of Risk 12% Foundation of Risk Management Management 28% 35% Quantitative Analysis Quantitative Analysis 23% 20% Financial Markets and Financial Markets and Products Products Valuation and Risk Models Valuation and Risk Models 30% 40% • From the trend seen in FRM exam, 65%-70% of the questions come from two topics, Financial Markets and Products, and Valuation and Risk Model. • In FRM Part-I, our estimate is that if a candidate manages to earn Quartile-1 scores in Financial Markets and Products, and Valuation and Risk Model, one should comfortably pass the exam even if the candidate does not do so well in QA and Foundation of Risk Management. Source: GARP Sample Paper© Neev Knowledge Management – Pristine 10 www.edupristine.com
11. Seminar Material Not for Sale Numerical vs Subjective Questions 2009 2010 9 12 8 10 7 6 8 5 6 4 3 4 2 2 1 0 0 Foundation of Financial Foundation of Financial Quantitative Valuation and Quantitative Valuation and Risk Markets and Risk Markets and Analysis Risk Models Analysis Risk Models Management Products Management Products Numerical 3 6 8 4 Numerical 1 4 5 11 Subjective 2 2 8 3 Subjective 4 5 7 3 • There is no fixed ratio of Numerical and subjective questions in any of the subject. • In valuation and risk models, numerical questions are favorite to GARP • To score in Quartile-1 in Financial Markets and Products, and Valuation and Risk Models you need to solve as many questions as you can. Source: GARP Sample Paper© Neev Knowledge Management – Pristine 11 www.edupristine.com
12. Seminar Material Not for Sale Number of Questions Year-wise 18 16 14 Number of Questions 12 10 8 2010 6 2009 4 2 0 Foundation of Quantitative Financial Valuation and Risk Analysis Markets and Risk Models Management Products Source: GARP Sample Paper© Neev Knowledge Management – Pristine 12 www.edupristine.com
13. Seminar Material Not for Sale Agenda • Introduction and context • Understanding the FRM Examination Structure • Introduction to Quantitative Analysis – Probability Distributions – Key Concept Checkers • Complete Offering & Registration • Next Seminar© Neev Knowledge Management – Pristine 13 www.edupristine.com
14. Seminar Material Not for Sale Quantitative Analysis Quantitative Analysis Statistics and Probability Sampling & Regression EWMA Probability Distributions Hyp. Testing Analysis GARCH • Basics of • Properties of • Standard • Linear • Estimating Probability Distributions Error Regression Volatility and • Population – Discrete/ • Formulating • Multiple Correlation and Sample Continuous Hypothesis Regressors • Monte Carlo Statistics • Binomial • Type I and II • OLS • Volatility Term Distribution Errors • Error Analysis Structures • Normal • Heteroscedac Distribution ity Reference Book - James Stock and Mark Watson, Introduction to Econometrics, Brief Edition (Boston: Pearson Education, 2008).© Neev Knowledge Management – Pristine www.edupristine.com
15. Seminar Material Not for Sale Probability Distribution • A Random Variable is a function, which assigns unique numerical values to all possible outcomes of a random experiment under fixed conditions. A random variable is not a variable but rather a function that maps events to numbers – Probability distribution describes the values and probabilities that a random event can take place. The values must cover all of the possible outcomes of the event, while the total probabilities must sum to exactly 1, or 100% • Example – Suppose you flip a coin twice. – There are four possible outcomes: HH, HT, TH, and TT. – Let the variable X represent the number of Heads that result from this experiment – It can take on the values 0, 1, or 2. – X is a random variable (its value is determined by the outcome of a statistical experiment) – A probability distribution is a table or an relation that links each outcome of a statistical experiment with its probability of occurrence Number of heads (X) Probability P(X=x) 0 0.25 1 0.50 2 0.25© Neev Knowledge Management – Pristine 15 www.edupristine.com
16. Seminar Material Not for Sale Continuous & Discrete Probability Distributions • If a variable can take on any value between two specified values, it is called a continuous variable – otherwise, it is called a discrete variable • If a random variable is a discrete variable, its probability distribution is called a discrete probability – For example, tossing of a coin & noting the number of heads (random variable) can take a discrete value – Binomial probability distribution, Poisson probability distribution • If a random variable is a continuous variable, its probability distribution is called a continuous probability distribution – The probability that a continuous random variable will assume a particular value is zero – A continuous probability distribution cannot be expressed in tabular form. – An equation or formula is used to describe a continuous probability distribution (called a probability density function or density function or PDF) – The area bounded by the curve of the density function and the x-axis is equal to 1, when computed over the domain of the variable – Normal probability distribution, Students t distribution are examples of continuous probability distributions© Neev Knowledge Management – Pristine 16 www.edupristine.com
17. Seminar Material Not for Sale Normal Distribution 68% of Data 95% of Data 99.7% of Data Only Mean and Standard Deviation is required to fully understand a distribution© Neev Knowledge Management – Pristine 17 www.edupristine.com
18. Seminar Material Not for Sale Normal (Gaussian) Distribution • The normal distribution is defined by first two moments, mean() and variance(2) • The probability density function P(x) of normally distributed variable is given by: 1  ( x   )2  P( x)  exp    2 2  2 2  • The probability of the value lying between a and b is given by: b P (a  X  b )   P ( x ). dx a • The expected value of a normally distributed variable: E[X]= , • The variance of normally distributed variable: Var(X)= 2 • If two variables are individually normally distributed, then the linear combination of the both is also normally distributed. – Lets take an example of two variable X1 and X2 which are normally distributed such that: – X1~N(1,1) and X2~N(2,2) – Then X= a.X1+ b.X2 is also normally distributed. The skewness of normal distribution is = 0 and the kurtosis is =3© Neev Knowledge Management – Pristine 18 www.edupristine.com
19. Seminar Material Not for Sale FRM Exam 2008 • Which type of distribution produces the lowest probability for a variable to exceed a specified extreme value ‘X’ which is greater than the mean assuming the distributions all have the same mean and variance? A. A leptokurtic distribution with a kurtosis of 4. B. A leptokurtic distribution with a kurtosis of 8. C. A normal distribution. D. A platykurtic distribution© Neev Knowledge Management – Pristine 19 www.edupristine.com
20. Seminar Material Not for Sale Answer • ANSWER: D – By definition, a platykurtic distribution has thinner tails than both the normal distribution and any leptokurtic distribution. Therefore, for an extreme value X, the lowest probability of exceeding it will be found in the distribution with the thinner tails. – A. Incorrect. A leptokurtic distribution has fatter tails than the normal distribution. The kurtosis indicates the level of fatness in the tails, the higher the kurtosis, the fatter the tails. Therefore, the probability of exceeding a specified extreme value will be higher . – B. Incorrect. Since answer A. has a lower kurtosis, a distribution with a kurtosis of 8 will necessarily produce a larger probability in the tails. – C. Incorrect. By definition, a normal distribution has thinner tails than a leptokurtic distribution and larger tails than a platykurtic distribution. 0.45 Platykurtic Mesokurtic 0.4 K<3 K=3 0.35 0.3 0.25 0.2 Leptokutic 0.15 K>3 0.1 0.05 0 -4 -3 -2 -1 0 1 2 3 4© Neev Knowledge Management – Pristine 20 www.edupristine.com
21. Seminar Material Not for Sale FRM Exam 2006 • Which of the following statements is the most accurate about the relationship between a normal distribution and a Student’s t-distribution that have the same mean and standard deviation? A. They have the same skewness and the same kurtosis. B. The Student’s t-distribution has larger skewness and larger kurtosis. C. The kurtosis of a Student’s t -distribution converges to that of the normal distribution as the number of degrees of freedom increases. D. The normal distribution is a good approximation for the Student’s t-distribution when the number of degrees of freedom is small.© Neev Knowledge Management – Pristine 21 www.edupristine.com
22. Seminar Material Not for Sale Answer • ANSWER: C – The skewness of both distributions is zero and the kurtosis of the Student’s t distribution converges to that of the normal distribution as the number of degrees of freedom increases.© Neev Knowledge Management – Pristine 22 www.edupristine.com
23. Seminar Material Not for Sale FRM Exam 2006 • Which one of the following statements about the normal distribution is NOT accurate? A. Kurtosis equals 3. B. Skewness equals 1. C. The entire distribution can be characterized by two moments, mean and variance. D. The normal density function has the following expression:© Neev Knowledge Management – Pristine 23 www.edupristine.com
24. Seminar Material Not for Sale Answer • ANSWER: B – The skewness of the normal distribution is 0, not 1. – The kurtosis of the normal distribution is 3, the normal distribution can be completely described by its mean and variance, and the density function of the normal distribution is as shown. 68% of Data 95% of Data 99.7% of Data -4 -3 -2 -1 0 1 2 3 4© Neev Knowledge Management – Pristine 24 www.edupristine.com
25. Seminar Material Not for Sale FRM Exam 2007 • Let Z be a standard normal random variable. An event X is defined to happen if either z takes a value between –1 and 1 or z takes any value greater than 1.5. What is the probability of event X happening if N(1) = 0.8413, N(0.5) = 0.6915 and N(-1.5) = 0.0668, where N() is the cumulative distribution function of a standard normal variable? A. 0.083 B. 0.2166 C. 0.6826 D. 0.7494© Neev Knowledge Management – Pristine 25 www.edupristine.com
26. Seminar Material Not for Sale Answer • ANSWER: D – Let A be the event that z takes a value between 1 and –1 and B be the event that z takes a value greater than 11/2 . The probability of z being between 1 and –1 is the area under the standard normal curve between 1 and -1. From the properties of a standard normal distribution, we know that: N(-1) = 1.0 - N(1) = 1.0 – 0.8413 = 0.1587 – Therefore, the probability of z being between 1 and –1 = P(A) = N(1) - N(-1) = 0.6826 – The probability of z being greater than 11/2 = P(B) = 1 - N(11/2) = N(-11/2) = 0.0668 – Event X = A U B and P(X) = P(A) + P(B) since A and B are mutually exclusive. – Hence, P(X) = 0.7494 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 -4 -3 -2 -1 0 1 2 3 4© Neev Knowledge Management – Pristine 26 www.edupristine.com
27. Seminar Material Not for Sale FRM Exam 2007 • When can you use the Normal distribution to approximate the Poisson distribution, assuming you have "n" independent trials each with a probability of success of "p"? A. When the mean of the Poisson distribution is very small. B. When the variance of the Poisson distribution is very small. C. When the number of observations is very large and the success rate is close to 1. D. When the number of observations is very large and the success rate is close to 0.© Neev Knowledge Management – Pristine 27 www.edupristine.com
29. Seminar Material Not for Sale Answer • ANSWER: C – The Normal distribution can approximate the distribution of a Poisson random variable with a large lambda parameter (λ). This will be the case when both the number observations (n) is very large and the success rate (p) is close to 1 since λ = n*p. – INCORRECT: A, The mean of a Poisson distribution must be large to allow approximation with a Normal distribution. – INCORRECT: B, The variance of a Poisson distribution must be large to allow approximation with a Normal distribution. – INCORRECT: D, The Normal distribution can approximate the distribution of a Poisson random variable with a large lambda parameter (λ). But since λ = n*p, where n is the number observations and p is the success rate, λ will not be large if p is close to 0.© Neev Knowledge Management – Pristine 29 www.edupristine.com
30. Seminar Material Not for Sale Questions 14 – FRM Exam 2006 • If Y = ln(X) and Y is normally distributed with zero mean and 2.33 standard deviation. What is the expected value of X? A. 15.10 B. 3.21 C. 227.90 D. 1© Neev Knowledge Management – Pristine 30 www.edupristine.com
31. Seminar Material Not for Sale Answer • ANSWER: A Lognormal Distribution© Neev Knowledge Management – Pristine 31 www.edupristine.com
32. Seminar Material Not for SaleWhat is VaR ?• Value at Risk (VaR) has become the standard measure that financial analysts use to quantify this risk• VAR represents maximum potential loss in value of a portfolio of financial instruments with a given probability over a certain horizon• In simpler words, it is a number that indicates how much a financial institution can lose with probability θ over a given time horizon www.edupristine.com
33. Seminar Material Not for Sale Agenda • Introduction and context • Understanding the FRM Examination Structure • Introduction to Quantitative Analysis – Probability Distributions – Key Concept Checkers • Complete Offering & Registration • Next Seminar© Neev Knowledge Management – Pristine 33 www.edupristine.com
34. Seminar Material Not for SaleAbout FRM Prep School School for FRM Part I Prep is a 100 Hrs extensive training program* that can enable you to prepare for and crack FRM Part I Examination www.edupristine.com
35. Seminar Material Not for SaleAbout School for FRM Prep • Extensive 100 Hours coverage • 10 days of regular classes • 3 days of revision classes School for FRM Prep is • 2 Mock tests a 100 Hrs extensive training program* that can enable you = • Extensive Question Bank to prepare and Practice to prepare for and crack FRM Part I Exam • 2 Hrs of one-to-one doubt clearing sessions* • Qualified faculty with extensive industry and teaching experience www.edupristine.com
36. Seminar Material Not for SaleAbout School for FRM Prep • Proven credentials in successfully training FRM aspirants • Actionable and Innovative Material School for FRM Prep is • Complete Slide Pack a 100 Hrs extensive training program* that can enable you = • • Each Session followed by Quiz Adaptive feedback based on Quizto prepare for and crack FRM Part I Exam • Mock tests and feedback • Individual doubt solving session • FRM Visualized Formula Charts • Summarized Recordings for revision www.edupristine.com
37. Seminar Material Not for SaleTentative Schedule – Feb-March Date Day Course Topic 26/Feb/11 Sat FRM-Part-I Quantitative Analysis - I 27/Feb/11 Sun FRM-Part-I Quantitative Analysis – II 05/Mar/11 Sat FRM-Part-I Quantitative Analysis – III 06/Mar/11 Sun FRM-Part-I Quantitative Analysis – IV 12/Mar/11 – Subject to Change * Indicative list Sat FRM-Part-I FMP -I 13/Mar/11 Sun FRM-Part-I FMP-II 26/Mar/11 Sat FRM-Part-I FMP-III 27/Mar/11 Sun FRM-Part-I FMP-IV 02/Apr/11 Sat FRM-Part-I VaR- I 03/Apr/11 Sun FRM-Part-I VaR- II www.edupristine.com
38. Seminar Material Not for SaleHow it works? 1 2 3 4 5 You signup for the program by making payment of USD 600* *Early Bird Discount of USD 100 for registrations before 10thFeb www.edupristine.com
39. Seminar Material Not for SaleHow it works? 1 2 3 4 5 Start Preparation with material and Live Interactive Class www.edupristine.com
40. Seminar Material Not for SaleHow it works? 1 2 3 4 5 Work on the Problem sets/ Quizzes adapting preparation Style www.edupristine.com
41. Seminar Material Not for SaleHow it works? 1 2 3 4 5 Give Mock Tests/ Ask Doubts/ Revise and Complete Preparation www.edupristine.com
42. Seminar Material Not for SaleHow it works? 1 2 3 4 5 Plan and Achieve Success in FRM Part I Exam www.edupristine.com
43. Seminar Material Not for SaleMethodology Each topic will be explained through Conceptual Discussion, Examples, Tests, Quizzes, Actionable Presentations, Visualized Charts and Q&A www.edupristine.com
44. Seminar Material Not for Sale Sample Innovative Material Probability Distributions Normal Distribution Binomial Distribution Normal Skewness and Z-Score Distribution Kurtosis • Described by mean & variance No. of σ a given • Symmetric about its mean observation is away • Standard Normal Distribution from population mean. - Mean = 0; Variance =1 Z=(x-µ)/σ Q. At a particular time, the market value of assets of the firm is $100 Mn and the market value of debt is $80 Mn. The 68% of Data standard deviation of assets is $ 10 Mn. What is the distance to default? Ans. z = (A-K) / σA 95% of Data = (100-80)/10 =2 99.7% of Data -4 -3 -2 -1 0 1 2 3 4 Q. Which of the following is likely to be a probability distribution function? For X=[1,2,3,4,5], Prob[Xi]= 49/(75-Xi2) If Z is a standard normal R.V. An event X is defined to happen if either -1< Z < 1 or For X=[0,5,10,15], Prob[Xi]= Xi/30 Z > 1.5. What is the prob. of event X happening if N (1) =0.8413, N (0.5) = 0.6915 For X=[1,4,9,16,25], Prob[Xi]= [(X i)1/2 – 1]/5 and N (-1.5) = 0.0668, where N is the CDF of a standard normal variable? Ans. P(X)= P(-1< Z < 1) + P(Z > 1.5) Ans. The correct answer is For X=[0,5,10,15], Prob[Xi]= Xi/30 = N(1)-(1-N(1)) + N(-1.5) = 2*0.8413-1 + 0.0668 For all values of X, probability lies within [0,1] and sum of all the = 0.7494 probabilities is equal to 1. -1 +1 1.5© Neev Knowledge Management – Pristine 44 www.edupristine.com
45. Seminar Material Not for Sale Sample Innovative Material Hypothesis Testing Null Alternative Confidence Intervals Hypothesis Tests One tailed Two Tailed test HYPOTHESIS:H0 Hypothesis: Ha (CI) for Variances Test Hypothesis that Concluded if there is Range of values within which Test if the value is greater Test if the value is the researcher significant evidence H0 Cannot be rejected (say than or less than K different from K wants to reject to reject H0 90% or 95%). H0; µ<=K vs. Ha: µ>K H0; µ=0 vs. Ha: µ≠ 0 Known variance, 2 Tailed test, Type 1 error: rejection of H0 when it CI is: X”± zα/2(σ/√t) 0.2 0.2 is actually true 0.15 0.15 Type 2 error :Fail to reject H0 when 0.1 α= 0.05 0.1 it is actually false α= 0.025 α= 0.025 0.05 0.05 Inference Real State of Affairs Based on 0 0 Sample Data H0 is True H0 is False -5 Z=0 0 Z=2.5 5 Reject H0 -5 Z=0 Reject H0 Do not Reject H0 Type II error Do not Reject H 0 Reject H0 Correct decision H0 is True Confidence level = 1-  P (Type II error) =  Correct decision Tests for a Single Tests for a two Type I error Population Variances Population Variances Q. If standard deviation of a H0 is False Significance level = * Power = 1- normal population is known to be 10 & the mean is hypothesized *Term  represents the maximum probability of committing a Type I error Chi-Square test F test to be 8. Suppose a sample size of 100 is considered. What is the range of sample means in which hypothesis can be accepted at Q. Co. ABC would give bonus to employees, if they get a H0: σ2 = c H0: σ12 – σ22 = 0 significance level of 0.05? HA: σ2 ≠ c HA: σ12 – σ22 ≠ 0 Ans: SE =  = 10/√100 =1 rating higher than 7/10 from customers. A random sample n of 30 customers is conducted with rating of 7.1/10. (n  1)s 2 s2 z = (x-µ)/ SE 2  F 1 Formulate Hypothesis? s2 = (x-8)/1 σ2 2 At 95% -1.96<z<1.96 • Null Hypothesis: H0: Mean<=7 Therefore 6.04<x<9.96 • Alternate Hypothesis : H1: Mean>7 Upper tail test: H0: σ12 – σ22 = 0 H0: σ2 ≤ σ02 HA: σ12 – σ22 ≠ 0 • Statistic to be measured: t-statistic, with 29 DoF HA: σ2 > σ02  /2 2 Do not reject H0 Reject H0 F 2 Do not Reject H0 reject H 0 F/2© Neev Knowledge Management – Pristine 45 www.edupristine.com
46. Seminar Material Not for SaleWhat to expect at the end? Towards the end of School for FRM Prep* You will be able to learn the topics related to FRM Part I Exam You will know how to solve the questions asked in FRM Part I Exam You will get an industry perspective of the topics *assuming you follow the program and practice www.edupristine.com
47. Seminar Material Not for SaleAbout the Program Venue: Online Starting Date: 26 Feb, 2011 www.edupristine.com
48. Seminar Material Not for SaleCost of the Program USD 475 For participants joining in groups of 5 or more USD 595 For individual registrations USD 525 For registrations before 10th February www.edupristine.com
49. Seminar Material Not for SaleContact Details Questions & Doubts? Please e-mail me at pawan@edupristine.com or visit http://www.edupristine.com or call +91 986 762 5422 www.edupristine.com
50. Seminar Material Not for Sale To Register • Wire Transfer – Bank Name: HDFC Bank – Country: India – Swift Code: HDFCINBB – Account Name: Neev Knowledge Management Pvt Ltd – Account Number: 00602560008449 • Paypal to Paypal (Preferred) – Create a Personal paypal account (it is free) – After Logging in, click on tab "My Account" and then on "Profile". Link Paypal account with your credit card or bank account – Click on the tab "Send Money" – In the "To" tab enter the email id – paypal@edupristine.com – Pay the fees as per package required. • Credit Card to Paypal – You can make the payment from your credit card to Paypal account. – Please make the payment to email id – paypal@edupristine.com© Neev Knowledge Management – Pristine www.edupristine.com
51. Seminar Material Not for Sale Other Pristine Offerings Course Classroom Trainings Online Content Crash Hours Accreditation Trainings Course/ of Mock Test Training CFA Level I All* + Singapore** Yes Original Yes 100 CFA Institute CFA Level II Mumbai, Delhi From 2010 Original From 2010 80 CFA Institute FRM Level I All + Singapore Yes Original Yes 75 GARP FRM Level II Mumbai, Delhi Yes Original Yes 60 GARP PRM All + Singapore Yes Original Yes 135 PRMIA APRM Corporate From 2010 Original Yes 80 PRMIA Financial Modeling Mumbai, Delhi, Yes Original NA 50 - Bangalore Finance for Lawyers Mumbai No Original NA 50 - CFP Mumbai, Delhi Yes Original NA 120 Under Process Placement Oriented Colleges No Original NA 150 Not Required Training *All cities include Mumbai, Delhi, Kolkata, Chennai, Bangalore, Pune and Hyderabad ; ** Singapore class room trainings to commence from June 2010© Neev Knowledge Management – Pristine www.edupristine.com
52. Seminar Material Not for Sale Agenda • Introduction and context • Understanding the FRM Examination Structure • Introduction to Quantitative Analysis – Descriptive Statistics – Key Concept Checkers • Complete Offering & Registration • Next Seminar© Neev Knowledge Management – Pristine 52 www.edupristine.com
53. Seminar Material Not for Sale Value at Risk (VaR) 13 Feb, 2011© Neev Knowledge Management – Pristine 53 www.edupristine.com
54. Seminar Material Not for Sale Contact Contact Phone Email Pawan Prabhat +91 986 762 5422 pawan@edupristine.com Paramdeep Singh +91 989 298 0608 paramdeep@edupristine.com© Neev Knowledge Management – Pristine www.edupristine.com
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