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FRM Part IQuantitative Analysis

21st May 2011

© Neev Knowledge Management – Pristine

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Seminar MaterialNot for Sale

© Neev Knowledge Management – Pristine

Agenda

• Introduction and context• Understanding the FRM Examination Structure• Introduction to Quantitative Analysis

– Probability Distributions– Key Concept Checkers

• Complete Offering & Registration• Next Seminar

2

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Seminar MaterialNot for Sale

Pristine has been started by professionals with diverse experience in financial services, IT and Auto who are alumnus of IITs & IIMs

PristineClassroom/ Online delivery (synchronous and asynchronous) – To increase reach and improve efficiency of learning. Conducted 15+ batches with over 300 hours of recorded content

Innovative content – To improve understanding & learning capability of students. VisualizeFRM, VisualizeCFA as one of the best selling products

Founded with an aim of creating world class professionals in the area of finance –particularly risk management and investment banking

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

Testimonial - 53% of the students join us on the basis of referral is a testimonial of the effective training methodologies

Effective training methodologies to improve the performance of the students and enhance the employability

© Neev Knowledge Management – Pristine 3

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Seminar MaterialNot for SaleKey Authorization

GARP (2007-10)Authorized Training provider -FRM

Largest player in India in the area of risk management training. Trained 1000+ students in risk management

PRMIA (2009-10)Authorized Training provider – PRM/ APRMSole authorized training for PRM Training in India. Largest player in India in the area of risk management training. Trained 1000+ students in risk management

CFA Institute (2010-11)Authorized Training provider – CFA

Pristine is now the authorized training provider for CFA Exam trainings . Pristine is largest training provider for CFA in India with presence across seven major cities.

FPSB India (2010-11)Authorized Training provider -CFP

An authorized Education Provider for Chartered Financial Planner Charter.

© Neev Knowledge Management – Pristine

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Seminar MaterialNot for SaleKey Associations*

HSBC (2008)Risk Management and Quant. AnalysisNew joinees in HSBC had a gap in knowledge of Risk Management and quantitative skills. Conducted trainings (On campus) to bridge the gap

*Indicative List

Mizuho (2010)Financial Modeling in Excel

Bankers were using excel models that they could not understand. Conducted financial modeling in Excel trainings to

bridge the gap

Bank Of America Continuum Solutions (2010)Financial Modeling in Excel

Associates were trained on valuation and mergers and acquisitions

J. P. Morgan (2010)Financial Modeling in Excel

The Real Assets Group were trained in Excel for infrastructure and real-estate

modeling

Franklin TempletonCFA (2010)

Students were facing a gap in the overall understanding of finance topics like corporate finance, FSA and valuation. Provided training for over 100 hours to bridge the gap

Credit-Suisse India (2009)Risk Management and Quant. AnalysisIT Professionals of Credit-Suisse India were trained on risk management.

© Neev Knowledge Management – Pristine

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Seminar MaterialNot for Sale…Key Associations

IIM Calcutta (2010-11) Financial Modeling in Excel

Students about to go for internships and join jobs found a gap in their grasp of

knowledge of excel for financial modeling. Conducted training for 75+

students with an average rating of 4.5+

BITS Pilani (2009)Workshops on Basics of Finance

Most of the students desire a career in finance. Conducted training for 350+ students with an average rating of 4.5+

IIT Delhi (2009)Corporate finance

Students get placed in finance companies (UBS, GS, MS, etc) with no understanding of the subject/ Job Profile. Conducted workshop to bridge the gap

Sydneham College (2009)Financial Modeling in Excel

Students about to join jobs found a gap in their grasp of excel for financial modeling. Conducted 40+ hours of training and helped students be ready for job

NISM (2008)Derivatives workshop for Hedging

Corporate in Ludhiana incurred huge losses because of derivative trades (for hedging). Conducted trainings for directors and CFOs for better understanding of derivative products

FMS Delhi (2010-11) Financial Modeling in Excel

Final Year MBA students of Faculty of Management Studies, Delhi University were trained in financial modeling so as

to prepare them better for a job in finance.

© Neev Knowledge Management – Pristine

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Seminar MaterialNot for SaleTrainer

Pawan Prabhat, Director and Faculty, Pristine

© Neev Knowledge Management – 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.

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Seminar MaterialNot for Sale

© Neev Knowledge Management – Pristine

Agenda

• Introduction and context• Understanding the FRM Examination Structure• Introduction to Quantitative Analysis

– Probability Distributions– Key Concept Checkers

• Complete Offering & Registration• Next Seminar

8

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© Neev Knowledge Management – Pristine Careers 9

FRM 2011

Area WeightFoundations 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

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© Neev Knowledge Management – Pristine 10

FRM Exam Statistics

12%

23%

30%

35%

2009 FRM Sample Paper

Foundation of Risk Management

Quantitative Analysis

Financial Markets and Products

Valuation and Risk Models

12%

20%

40%

28%

2010 FRM Sample Paper

Foundation of Risk Management

Quantitative Analysis

Financial Markets and Products

Valuation and Risk Models

• 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

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Foundation of Risk

Management

Quantitative Analysis

Financial Markets and

Products

Valuation and Risk Models

Numerical 1 4 5 11

Subjective 4 5 7 3

0

2

4

6

8

10

12

2010

Foundation of Risk

Management

Quantitative Analysis

Financial Markets and

Products

Valuation and Risk Models

Numerical 3 6 8 4

Subjective 2 2 8 3

0123456789

2009

Numerical vs Subjective Questions

• 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

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0

2

4

6

8

10

12

14

16

18

Foundation of Risk

Management

Quantitative Analysis

Financial Markets and

Products

Valuation and Risk Models

Num

ber o

f Que

stio

ns

2010

2009

Number of Questions Year-wise

Source: GARP Sample Paper

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Seminar MaterialNot for Sale

© Neev Knowledge Management – Pristine

Agenda

• Introduction and context• Understanding the FRM Examination Structure• Introduction to Quantitative Analysis

– Probability Distributions– Key Concept Checkers

• Complete Offering & Registration• Next Seminar

13

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Seminar MaterialNot for SaleQuantitative Analysis

© Neev Knowledge Management – Pristine

Quantitative Analysis

Statistics and Probability

Probability Distributions

Sampling & Hyp. Testing

Regression Analysis

EWMAGARCH

• Basics of Probability

• Population and Sample Statistics

• Properties of Distributions – Discrete/ Continuous

• Binomial Distribution

• Normal Distribution

• Standard Error

• Formulating Hypothesis

• Type I and II Errors

• Linear Regression

• Multiple Regressors

• OLS• Error Analysis• Heteroscedac

ity

• Estimating Volatility and Correlation

• Monte Carlo• Volatility Term

Structures

Reference Book - James Stock and Mark Watson, Introduction to Econometrics, Brief Edition (Boston: Pearson Education, 2008).

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© Neev Knowledge Management – Pristine 15

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

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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, Student's t distribution are examples of continuous probability

distributions

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Normal Distribution

Only Mean and Standard Deviation is required to fully understand a distribution

68% of Data

95% of Data

99.7% of Data

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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:

• The probability of the value lying between a and b is given by:

• 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.

2

2

2 2)(exp

21)(

xxP

b

a

dxxPbXaP ).()(

The skewness of normal distribution is = 0 and the kurtosis is =3

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© Neev Knowledge Management – Pristine 1919

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

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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

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

-4 -3 -2 -1 0 1 2 3 4

PlatykurticK<3Mesokurtic

K=3

LeptokuticK>3

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© Neev Knowledge Management – Pristine 2121

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.

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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.

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© Neev Knowledge Management – Pristine 2323

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:

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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.

-4 -3 -2 -1 0 1 2 3 4

68% of Data

95% of Data

99.7% of Data

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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. 0.083B. 0.2166C. 0.6826D. 0.7494

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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

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

-4 -3 -2 -1 0 1 2 3 4

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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.

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00.05

0.10.15

0.20.25

0.30.35

0.4

0 2 4 6 8 10 12 14 16 18 20 22 240

0.020.040.060.080.1

0.120.140.160.180.2

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28

0

0.02

0.04

0.06

0.08

0.1

0.12

0 2 4 6 8 10 12 14 16 18 20 22 240

0.010.020.030.040.050.060.070.080.09

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54

λ=1 λ=5

λ=25λ=15

Plots of Poisson Distribution

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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.

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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. 15.10B. 3.21C. 227.90D. 1

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• ANSWER: A

© Neev Knowledge Management – Pristine 3131

Answer

Lognormal Distribution

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Seminar MaterialNot 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

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Agenda

• Introduction and context• Understanding the FRM Examination Structure• Introduction to Quantitative Analysis

– Probability Distributions– Key Concept Checkers

• Complete Offering & Registration• Next Seminar

33

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Seminar MaterialNot 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

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Seminar MaterialNot for SaleAbout School for FRM Prep

School for FRM Prep is

a 100 Hrs extensive training program*

that can enable you

to prepare for and crack FRM Part I Exam

• Extensive 100 Hours coverage

• 10 days of regular classes

• 3 days of revision classes

• 2 Mock tests

• Extensive Question Bank to

prepare and Practice

• 2 Hrs of one-to-one doubt

clearing sessions*

• Qualified faculty with extensive

industry and teaching experience

=

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Seminar MaterialNot for SaleAbout School for FRM Prep

• Proven credentials in successfully

training FRM aspirants

• Actionable and Innovative Material

• Complete Slide Pack

• Each Session followed by Quiz

• Adaptive feedback based on Quiz

• Mock tests and feedback

• Individual doubt solving session

• FRM Visualized Formula Charts

• Summarized Recordings for

revision

=School for FRM Prep is

a 100 Hrs extensive training program*

that can enable you

to prepare for and crack FRM Part I Exam

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Seminar MaterialNot for SaleTentative Schedule – Feb-March

* Indicative list – Subject to Change

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 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

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Seminar MaterialNot 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

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Seminar MaterialNot for SaleHow it works?

1 2 3 4 5

Start Preparation with material and Live Interactive Class

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Seminar MaterialNot for SaleHow it works?

1 2 3 4 5

Work on the Problem sets/ Quizzes adapting preparation Style

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Seminar MaterialNot for SaleHow it works?

1 2 3 4 5

Give Mock Tests/ Ask Doubts/ Revise and Complete Preparation

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Seminar MaterialNot for SaleHow it works?

1 2 3 4 5

Plan and Achieve Success in FRM Part I Exam

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Seminar MaterialNot for SaleMethodology

Each topic will be explained through

Conceptual Discussion, Examples, Tests, Quizzes, Actionable

Presentations, Visualized Charts and Q&A

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Probability Distributions

Normal Distribution Binomial Distribution

Normal Distribution

• Described by mean & variance• Symmetric about its mean• Standard Normal Distribution

- Mean = 0; Variance =1

Z-Score Skewness and Kurtosis

No. of σ a givenobservation is awayfrom population mean.

Z=(x-µ)/σ

Q. At a particular time, the market valueof assets of the firm is $100 Mn and themarket value of debt is $80 Mn. Thestandard deviation of assets is $ 10 Mn.What is the distance to default?Ans. z = (A-K) / σA

= (100-80)/10= 2

If Z is a standard normal R.V. An event X is defined to happen if either -1< Z < 1 orZ > 1.5. What is the prob. of event X happening if N (1) =0.8413, N (0.5) = 0.6915and 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)

= N(1)-(1-N(1)) + N(-1.5)= 2*0.8413-1 + 0.0668= 0.7494

-1 +1 1.5

-4 -3 -2 -1 0 1 2 3 4

68% of Data

95% of Data

99.7% of Data

Q. Which of the following is likely to be a probability distributionfunction?For X=[1,2,3,4,5], Prob[Xi]= 49/(75-Xi

2)For X=[0,5,10,15], Prob[Xi]= Xi/30For X=[1,4,9,16,25], Prob[Xi]= [(X i)1/2 – 1]/5

Ans. The correct answer is For X=[0,5,10,15], Prob[Xi]= Xi/30For all values of X, probability lies within [0,1] and sum of all theprobabilities is equal to 1.

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H0: σ2 = cHA: σ2 ≠ c

Inference Based on

Sample Data

Real State of Affairs

H0 is True H0 is False

H0 is True Correct decision Confidence level = 1-

Type II error

P (Type II error) =

H0 is False Type I error Significance level = *

Correct decision

Power = 1-

*Term represents the maximum probability of committing a Type I error

Null HYPOTHESIS:H0

Alternative Hypothesis: Ha

One tailed Test Two Tailed test

Hypothesis thatthe researcherwants to reject

Concluded if there issignificant evidenceto reject H0

Test if the value is greaterthan or less than KH0; µ<=K vs. Ha: µ>K

Test if the value isdifferent from KH0; µ=0 vs. Ha: µ≠ 0

Type 1 error: rejection of H0 when itis actually true

Type 2 error :Fail to reject H0 whenit is actually false

Q. Co. ABC would give bonus to employees, if they get arating higher than 7/10 from customers. A random sampleof 30 customers is conducted with rating of 7.1/10.Formulate Hypothesis?• Null Hypothesis: H0: Mean<=7• Alternate Hypothesis : H1: Mean>7• Statistic to be measured: t-statistic, with 29 DoF

Range of values within whichH0 Cannot be rejected (say90% or 95%).Known variance, 2 Tailed test,CI is: X”± zα/2(σ/√t)

Confidence Intervals (CI)

Do not reject H0 Reject H0

2

2

H0: σ2 ≤ σ02

HA: σ2 > σ02

Upper tail test:

2

22

σ1)s(n

F

/2

F/2Reject H0Do not

reject H0

H0: σ12 – σ2

2 = 0HA: σ1

2 – σ22 ≠ 0

Hypothesis Testsfor Variances

Tests for a SinglePopulation Variances

Tests for a twoPopulation Variances

F testChi-Square test

H0: σ12 – σ2

2 = 0HA: σ1

2 – σ22 ≠ 0

22

21

ssF

Q. If standard deviation of anormal population is known to be10 & the mean is hypothesizedto be 8. Suppose a sample sizeof 100 is considered. What is therange of sample means in whichhypothesis can be accepted atsignificance level of 0.05?Ans: SE = = 10/√100 =1

z = (x-µ)/ SE= (x-8)/1

At 95% -1.96<z<1.96Therefore 6.04<x<9.96

n

0

0.05

0.1

0.15

0.2

-5 0 5Z=0 Z=2.5

Do not Reject H0Reject H0

α= 0.05

Z=0

Do not Reject H0

Reject H0

α= 0.025

0

0.05

0.1

0.15

0.2

-5

α= 0.025

Reject H0

Hypothesis Testing

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Seminar MaterialNot 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

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Venue: Online

Starting Date: 26 Feb, 2011

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Seminar MaterialNot for SaleCost of the Program

USD 595For individual registrations

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USD 525For registrations before 10th February

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Questions & Doubts?

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or call +91 986 762 5422

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Course Classroom Trainings Online Trainings

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Accreditation

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Yes Original NA 50 -

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Colleges No Original NA 150 Not Required

*All cities include Mumbai, Delhi, Kolkata, Chennai, Bangalore, Pune and Hyderabad ; ** Singapore class room trainings to commence from June 2010

Other Pristine Offerings

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Agenda

• Introduction and context• Understanding the FRM Examination Structure• Introduction to Quantitative Analysis

– Descriptive Statistics– Key Concept Checkers

• Complete Offering & Registration• Next Seminar

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Value at Risk (VaR)13 Feb, 2011

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Contact Phone Email

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Paramdeep Singh +91 989 298 0608 [email protected]

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