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Pristine www.edupristine.com FRM and PRM Exam : Analysis 2011

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Page 1: About FRM

Pristine www.edupristine.com

FRM and PRM Exam : Analysis2011

Page 2: About FRM

www.edupristine.com

Agenda

• About Pristine

• FRM and PRM Exams

• Resources

• Overall Exam Analysis

• Analysis of Quantitative Analysis

• Analysis of Market Products

• FAQs

• Contact Us

• Pristine FRM Offering

2Karuna - +91 8080 00 5533

Page 3: About FRM

www.edupristine.com

Pristine

Finance trainings for individuals/corporate/colleges

Trainings for

International

Certifications

Corporate

Trainings

Pristine

Certifications

- Authorized training providers for prestigious

international certifications like CFA*, FRM, PRM, CFP*

etc.

- Pan India class-room trainings and web-based live

online trainings for international students

- Advanced training in financial modeling, valuation, risk,

etc. to large corporate clients like HSBC, CSFB, IDBI,

Mizuho Bank etc.

- Own certification programs in financial modeling,

finance training for corporate lawyers, risk

management etc.

- Certification programs in Equity Research, Derivatives

being launched

3Karuna - +91 8080 00 5533

About Pristine

Page 4: About FRM

www.edupristine.com

Pristine Offerings

*All cities include Mumbai, Delhi, Kolkata, Chennai, Bangalore, Pune and Hyderabad ;

Course Classroom

Trainings

Online

Trainings

Content Crash Course/

Mock Test

Hours of

training

Accreditation Price

CFA Level I All* + Singapore Yes Original Yes 100 CFA Institute USD 595;

INR 17,950

CFA Level II Mumbai, Delhi Yes Original Yes 100 CFA Institute USD 595;

INR 16,950

FRM Level I All + Singapore Yes Original Yes 75 GARP USD 495;

INR 12,950

FRM Level II Mumbai Yes Original Yes 60 GARP USD 495,

INR 10,000

PRM All + Singapore Yes Original Yes 135 PRMIA USD 795,

INR 20,000

APRM Corporate Yes Original Yes 80 PRMIA INR 10,000

Financial

Modeling

Mumbai, Delhi,

Bangalore,

Pune, Hyd,

Chennai

Yes Original NA 50 - INR 10,000

Finance for

Lawyers

Mumbai No Original NA 50 - INR 45,000

CFP Mumbai, Delhi Yes Original NA 120 Under Process INR 20,000

4Karuna - +91 8080 00 5533

Page 5: About FRM

www.edupristine.com

GARP (2007-11)

Authorized Training provider -FRM

Largest player in India in the area of risk

management training. Trained 1000+ students

in risk management

PRMIA (2009-11)

Authorized Training provider – PRM/ APRM

Sole 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.

5Karuna - +91 8080 00 5533

Key Authorizations…

Page 6: About FRM

www.edupristine.com

HSBC (2008)

Risk Management and Quant.

Analysis

New 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)

Finance for Finance

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 Templeton

CFA (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.

Analysis

IT Professionals of Credit-

Suisse India were trained on

risk management.

Ernst & Young (2010)

Real Estate Modeling

Senior Associates were

trained on building

valuation models for real

estate

ING Vyasa (2010)

Infrastructure & Project

Finance

Bankers were trained on

making integrated

models for project

finance and

infrastructure.

6Karuna - +91 8080 00 5533

Key Associations*

Page 7: About FRM

www.edupristine.com

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

NUS Business School (2011)

Financial Modeling in Excel

Second year MBA students were

given a full 2-day workshop on

creating financial models. They

learnt how to create integrated

models of valuation.

NISM (2008-11)

Derivatives in Hedging (2008)

Financial Modeling (2011)

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.

IEMR Delhi (2010-11)

Financial Modeling in Excel

Final Year MBA students of IEMR

went through extensive financial

modeling workshop to acquire skills

of financial modeling.

SIMSREE (2010)

Final Year MBA students of

Sydenham MBA, Mumbai were

trained in financial modeling so as

to prepare them better for a job in

finance.

7Karuna - +91 8080 00 5533

…Key Associations

Page 8: About FRM

www.edupristine.com

Largest Authorized

FRM Course Provider in India

Trains 600+ FRM Aspirants each year

8Karuna - +91 8080 00 5533

Most Importantly

Page 9: About FRM

www.edupristine.com

About Pristine

• Founded by professionals and alumnus of Standard Chartered, Goldman Sachs, Reliance Private

Equity, SBI, Accenture, IBM and CRISIL, IIM, IIT and SIBM.

• Last Year Results: Have delivered trainings to more than 4,500+ candidates in last four

years with a success rate of 65% to 85% for various batches for CFA/ PRM/FRM exams.

• Training centers: in Delhi, Mumbai, Bangalore, Pune, Hyderabad, Chennai, Singapore & Online.

• Faculty : FRM/PRM Certified or working professional with significant experience in Finance

industry with education background of IIT/IIMs.

• Provided FRM/PRM Online trainings to 350+ professionals from US, Europe, Middle East, Asia

Pacific, Africa and Australia.

9Karuna - +91 8080 00 5533

Page 10: About FRM

www.edupristine.com

Agenda

• About Pristine

• FRM and PRM Exams

• Resources

• Overall Exam Analysis

• Analysis of Quantitative Analysis

• Analysis of Market Products

• FAQs

• Contact Us

• Pristine FRM Offering

10Karuna - +91 8080 00 5533

Page 11: About FRM

www.edupristine.com

CFA – Eligibility

• Minimum Eligibility

– FRM Part I exam : Even a undergraduate can appear for FRM Part I exam.

– FRM Part II exam : you should have cleared FRM Part I exam.

• FRM Certificate Requirements

– In order to be certified as a Financial Risk Manager (FRM®) and be able to use the FRM acronym after your name, the

following is required:

• A passing score in the FRM Part I and Part II Exams

• Active Fellow membership in the Global Association of Risk Professionals

• A minimum of two years experience in the area of financial risk management or another related field including, but not limited

to, trading, portfolio management, academic or industry research, economics, auditing, risk consulting, and/or risk technology

• About the Exam

– Administered by GARP Institute, USA

– Minimum time to pass the two exams: 6 months

– Average time: 1 year

• Benefits of FRM® designation

– Lucrative career options in Risk Management, Trading, Structuring, Modeling, etc. FRM holders have positions such as

Chief Risk Officer, Senior Risk Analyst, Head of Operational Risk, and Director, Investment Risk Management, to name a

few.

– Strong value addition to your skills, credentials and resume

– Complete coverage of risk management concepts

11Karuna - +91 8080 00 5533

Page 12: About FRM

www.edupristine.com

FRM : Exam pattern

– Each Part is 4 hours exam ( Two sessions of 2 hrs each)

• 100 multiple choice question exam for both Part I

• 80 multiple choice questions for Part II

• Necessary to Pass Part I before evaluation of Part II

• Both the parts are held in May and November

.

• Part I topics , test weights and question allocation is as follows:

– Foundations of Risk Management 20% 20 questions

– Quantitative Analysis 20% 20 questions

– Financial Markets and Products 30% 30 questions

– Valuation and Risk Models 30% 30 questions

The exam is a percentile based exam and there is a sectional cut-off for all the subjects,

thus it's necessary to pass in all the subjects separately and clear the cutoff overall as well.

12Karuna - +91 8080 00 5533

Page 13: About FRM

www.edupristine.com

FRM Exam Dates, Centers & Fees

• Exam Dates

– FRM Lev I & Lev II exam : 3rd Saturday of May & November month every year.

• Exam Centers

– Delhi, Mumbai, Chennai, Bangalore , Hyderabad, Calicut & Kolkata.

• Fees

Part I – For November Exam

• Early Registration Fees : Dec. 1, 2010 - July 31, 2011 : $650

• Standard Registration Fees : Aug. 1 - Aug. 31, 2011 : $775

• Late Registration Fees: Sept. 1 - Oct. 15, 2011: $950

Part II –For November Exam

• Early Registration Fees : Dec. 1, 2010 - July 31, 2011 : $350

• Standard Registration Fees : Aug. 1 - Aug. 31, 2011 : $475

• Late Registration Fees: Sept. 1 - Oct. 15, 2011: $650

13Karuna - +91 8080 00 5533

Page 14: About FRM

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FRM Exam Curriculum

Subjects Weightage

Quantitative Analysis 20%

Financial Market & Products 30%

Valuation & Risk Models 30%

Portfolio Theory & Performance measurement 20%

Market Risk Measurement & Management 25%

Credit Risk Measurement & Management 25%

Current Issues in financial markets 10%

Operational & Integrated risk Management 25%

Risk Management & Investment management 15%

Part I

Part II

14Karuna - +91 8080 00 5533

Page 15: About FRM

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PRM Exam

Exam I Finance Theory, Financial Instruments and Markets (120 minutes)

Exam II Mathematical Foundations of Risk Measurement (120 minutes)

Exam III Risk Management Practices (90 minutes)

Exam IV Case Studies, PRMIA Standards of Best Practice, Conduct and

Ethics, Bylaws (60 minutes)

• The exams are computer-based and the

questions are all multiple choice.

• Extremely Flexible - Can take PRM exams any

business day of the year and in any order

• Passing marks 60% for each exam

Any one Exam USD 195

Full PRM Exam USD 500

Karuna - +91 8080 00 553315

Page 16: About FRM

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FRM vs PRM

FRM PRM

Conducted by GARP (www.garp.com) PRMIA (www.prmia.org)

Fee (Indicative and Overall) $1000 - 1350 $500-800

Pass rate ~60% ~50%

Incepted since 1997 2002

Parts/ Parts 2 4

Exam Dates May/ Nov Any day

Flexibility in giving Exam Either both in the same month or

different months

Either all modules on

same day or on different

days

Scheduling of Parts/

modules

Part I has to be cleared before

attempting the Part II

Any order

Course Structure 65% same as PRM 65% same as FRM

Kind of Questions Asked Case based long questions,

requiring calculations

Conceptual questions

Pristine Official Course

Provider-ship

Yes Yes

Karuna - +91 8080 00 553316

Page 17: About FRM

www.edupristine.com

Agenda

• About Pristine

• FRM and PRM Exams

• Resources

• Overall Exam Analysis

• Analysis of Quantitative Analysis

• Analysis of Market Products

• FAQs

• Contact Us

• Pristine FRM Offering

17Karuna - +91 8080 00 5533

Page 18: About FRM

www.edupristine.com

FRM Exam – Resources

• Core Reading : Approx 4000 Pages

• FRM Phillip Jorian Hand Book : 800 Pages

• Options Futures and Other Derivatives : 700 Pages

• Must haves

– GARP AIMS

– FRM Practice Papers

– Last year exam papers

Focused Study is the order of the Day

18Karuna - +91 8080 00 5533

Page 19: About FRM

www.edupristine.com

Agenda

• About Pristine

• FRM and PRM Exams

• Resources

• Overall Exam Analysis

• Analysis of Quantitative Analysis

• Analysis of Market Products

• FAQs

• Contact Us

• Pristine FRM Offering

19Karuna - +91 8080 00 5533

Page 20: About FRM

www.edupristine.com

FRM Exam : Question Pattern Analysis

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Credit R

isk

Fina

ncial M

arke

ts &

 Pro

ducts 

Foun

datio

ns o

f Risk Man

agem

ent 

Mar

ket R

isk

Ope

ratio

nal &

Inte

grat

ed R

isk

Qua

ntita

tive 

Analys

is

Risk &

 Inve

stm

ent M

anag

emen

Valua

tion 

and 

Risk

 Mod

els

Not Formula Based Formula Based

50% of the questions are purely formula based questions

20Karuna - +91 8080 00 5533

Page 21: About FRM

www.edupristine.com

FRM Exam : Question Pattern Analysis

• Most common question

– Calculating the portfolio VaR requires the calculation of portfolio volatility, for which we have the simple

formula:

VaR(Portfolio)= wa^2*σa^2 + wb^2*σb^2 + 2*wa*wb*σa*σb*Corelation(a,b)

• Similarly another common formula is calculating the annual VaR from daily VaR (or changing the time

duration of VaR) or calculating the significance intervals. These again use simple formulas:

VaR (for time period T) = VaR(Daily) * Sqrt(T)

• VaR (Significance Part alpha) = Z (Alpha) * Sigma

• Similarly Questions on Quantitative Analysis, which are formula based, are based on EWMA, GARCH

formulas, which are quite simple to calculate, if you know the formula and can apply it in the question.

• Typical formulas would be:

Return = ln(P(t)/P(t-1))

(Sigma(n))^2 = lambda * (Sigma(n-1))^2 + (1 – lambda) * U(n-1)^2

• Similarly the formula based questions from the rest of the parts are not very difficult. If you are

able to remember them and apply them in the FRM Exam, rest assured, your chances of

success would be very high.

21Karuna - +91 8080 00 5533

Page 22: About FRM

www.edupristine.com

Agenda

• About Pristine

• FRM and PRM Exams

• Resources

• Overall Exam Analysis

• Analysis of Quantitative Analysis

• Analysis of Market Products

• FAQs

• Contact Us

• Pristine FRM Offering

22Karuna - +91 8080 00 5533

Page 23: About FRM

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FRM Exam Question Pattern Analysis: Quant

• If we broadly divide the syllabus, it would consist of:

– Probability (Including Counting Principles and Joint Prob. Etc.)

– Probability Distributions

– Moments (Mean, Variance, Skewness, Kurtosis)

– Sampling Theorem

– Hypothesis Testing

– Correlation and Regression (And its Hypothesis testing)

– Volatility (Variance as a random variable)

– Monte Carlo Simulation

If you take a look at it, the syllabus is HUGE!

23Karuna - +91 8080 00 5533

Page 24: About FRM

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FRM Exam Question Pattern Analysis: Quant

• If we were to see the pattern for FRM Exam 2009, we find that more than 50% of the syllabus is

covered by non-quant and stats topics. These are essentially Estimating Volatility and Monte Carlo

Simulations. I will take them one by one:

• Estimating Volatility:

Return = ln(P(t)/P(t-1))

• EWMA:

(Sigma(n))^2 = lambda * (Sigma(n-1))^2 + (1 – lambda) * U(n-1)^2

• GARCH:

(Sigma(n))^2 = alpha * V(L) + Beta* (Sigma(n-1))^2 + Gamma * U(n-1)^2

Where, alpha + beta + gamma = 1

Another variant, alpha * V(L) = omega

• Monte Carlo is again simple! There is hardly any scope of a numerical question from simulation

• Correlation Regression: Again here, one of the easiest questions would be to find the %age variance

explained by your regression line. This is simple R^2, and the easiest thing to calculate:

– SST = SSR + SSE

– R^2 = SSR/SST

– SEE = (SSE/(n-2) )^1/2

24Karuna - +91 8080 00 5533

Page 25: About FRM

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FRM Exam Question Pattern Analysis: Quant

• The other kind of question can be based upon finding the significance of regression parameters. Again

this is simple – Look at the p-value in the table given, and find the parameters that are significant.

This is ONE question, you should not miss!!

• Portfolio Variance: Again questions (Usually multiple) from this concept have been coming in the

examination for the last so many years. Again something that you should not miss!!

VaR(Portfolio)= wa^2*σa^2 + wb^2*σb^2 + 2*wa*wb*σa*σb*Corelation(a,b)

• Probability Distributions: Usually there is either a question on Normal Distribution, where you have

to identify the rePartant area and find the value or you are given a binomial distribution, and you have

to find the chances of none-of the bonds defaulting!! If you have practiced well, you can get these

questions right!!

25Karuna - +91 8080 00 5533

Page 26: About FRM

www.edupristine.com

Agenda

• About Pristine

• FRM and PRM Exams

• Resources

• Overall Exam Analysis

• Analysis of Quantitative Analysis

• Analysis of Market Products

• FAQs

• Contact Us

• Pristine FRM Offering

26Karuna - +91 8080 00 5533

Page 27: About FRM

www.edupristine.com

FRM Exam Question Pattern Analysis: Market Products

• The broad classification of topics covered in Financial Markets and Products is:

– Financial Markets (Primarily defining the role of various players)

– Futures and forwards (Definitions, Valuation and Hedging)

– Interest Rate and Currency (Some part is included here,

– Fixed Income Instruments (Again part is covered in Valuation and Risk Models)

– Swaps

– Options (Again trading strategy is included here, some part is in Valuation and Risk Models)

– Commodities

If you take a look at it, the syllabus is HUGE!

27Karuna - +91 8080 00 5533

Page 28: About FRM

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FRM Exam Question Pattern Analysis: Market Products

• If we look closely at the last 3-4 years Sample papers, there are practically 2-3 questions from each of

the topics! So it is difficult to single out any topic, which is important!! Anyways.. lets analyze it closely

and give it a shot

• By default, remember to use continuous compounding, unless otherwise mentioned!! For example, if

you want to calculate returns, then use

– R = Ln(P(t)/P(t-1))

• If it is expressly mentioned that you have to use discrete compounding, then only use:

– R = {P(t) – P(t-1)}/P(t-1)

• Similarly to value futures/ other instruments, use:

– F(0,T) = S(0)*e^(rT) + C

• There are normally atleast two questions on converting rates based on different compounding

frequencies. It is one of the low hanging fruits as far as this section is concerned.

• Please learn the usage of the calculator. You should be a master in usage of calculator, to make

sure that you crack the exam.

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Page 29: About FRM

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FRM Exam Question Pattern Analysis: Market Products

• If we look closely at the last 2-3 years sample papers, the question that is always there relates to

finding duration and modified duration. Normally not a tough question and just a couple of formulae

to remember:

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Page 30: About FRM

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FRM Exam Question Pattern Analysis: Market Products

• FRM 2009 sample exam has a lot of questions on trading strategies.

• Can just draw curves of payoffs, and remember the various payoffs like

– Straddle,

– Strangle,

– Butterfly spreads, etc.

• you would have done 5 questions correct!

• Remember the Payoffs of

– Long Call,

– Short Call,

– Long Put,

– Short Put,

– Long Spot,

– Short Spot and similarly for futures.

• Apart from the above topics, there have been questions on Greeks.

• Delta Hedging of portfolio has been one of the favorites of the examiners because of its simplicity of

calculation and the concept checks on the understanding of the examinee about various aspects of

Options Pricing. For delta hedging,

Number of shares = (Number of calls) x (New delta – Old delta)

• Apart from this there is generally a question on relationship between delta of options and Black-

Scholes model.

30Karuna - +91 8080 00 5533

Page 31: About FRM

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Agenda

• About Pristine

• FRM and PRM Exams

• Resources

• Overall Exam Analysis

• Analysis of Quantitative Analysis

• Analysis of Market Products

• FAQs

• Contact Us

• Pristine FRM Offering

31Karuna - +91 8080 00 5533

Page 32: About FRM

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FAQs

• Will there be separate Study Guides for the FRM Exam Full and FRM Exam Part I and FRM Exam

Part II?

No, there will only be one Study Guide which will include the syllabus outline and recommended

reading materials for all FRM Exam formats (Full, Part I and Part II).

• Will there be separate Course Packs for the FRM Exam Full, FRM Exam Part I and FRM Exam

Part II?

Yes. The Course Packs will be customized according to the FRM Exam format and be made available

for purchase either in physical format or through the GARP Digital Library.

• How many hours of study are required to prepare for the FRM exams?

Approximately 150 to 200 hours for each Part of the exam. Since the last FRM Exam Full covers both

Parts, approximately 300 to 400 hours of preparation would be required.

• Is there any change to the format of the FRM Exam Full that would make it different from past

FRM Exams?

No, the FRM Exam Full will be offered in exactly the same way as past FRM exams.

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Page 33: About FRM

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FAQs

• What topics will be covered in the FRM Exam Part I and the FRM Exam Part II?

– The FRM Exam Part I will cover the following topics:

– Foundations of Risk Management

– Quantitative Analysis

– Financial Markets and Products

– Risk Modeling

• The FRM Exam Part II will cover the following topics:

– Market risk measurement and management

– Credit risk measurement and management

– Operational and integrated risk measurement and management

– Risk management and investment management

– Current issues in financial markets

• How many questions will there be on FRM Exam Part I and FRM Exam Part II?

• FRM Exam Part I will have 100 multiple-choice questions. FRM Exam Part II will have 80 multiple-

choice questions. The exact number of questions is subject to minimal change.

• How long are the test sessions for FRM Exam Part I and FRM Exam Part II?

• Both Parts will be 4 hours in length and broken down as follows: 2 hours for the morning session and

2 hours for the afternoon session with a 90 minute break in between.

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Page 34: About FRM

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FAQs

• Are there review courses I can take or study groups I can join?

• GARP does not offer FRM preparation courses as the Association considers this to be a conflict of

interest. GARP also does not endorse any FRM review course or FRM course provider. However, as a

service to our FRM candidates GARP does provide a listing of FRM course providers on its

website. These Course Providers have asked to have their information posted for your review and

have not been preselected by GARP.

• GARP also facilitates the finding and development of local FRM study groups via its website. Click

here to see and post information about local study groups.

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Page 35: About FRM

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Agenda

• About Pristine

• FRM and PRM Exams

• Resources

• Overall Exam Analysis

• Analysis of Quantitative Analysis

• Analysis of Market Products

• FAQs

• Contact Us

• Pristine FRM Offering

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Page 36: About FRM

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Offering for FRM Part I Preparation

• FRM Part I Preparation

– FRM Certified Faculty from IIT/IIM’s with significant experience

– Training Offering

• 10 days of Comprehensive Classroom Trainings for all the subjects.

• 3 days revision classes FRM Practice papers (2006, 2007, 2008, 2009 and 2010) will be discussed and the important

concepts of all the subjects will be revised again

• 2 days - Mock Tests specially designed by our trainers based on AIMS 2010, to evaluate your relative performance

vis-à-vis other candidates

• 20 hrs of Online Tests ( topic wise) - 1500 + questions

• Free online classes for students who register for classroom trainings

– Material

• Free Pristine FRM Handbook and Visulized FRM Charts to all the FRM Training Participants

• Online access to all the presentations and practice tests

– Training timings: Saturday 2pm to 7.30pm ; Sunday 10am to 3.30pm

– Training Fees: Rs 12,950 per participant

• Visualize FRM

– Comprehensive Charts covering major concepts, formulas and questions

– Rs. 500* + Shipping Charges

• Pristine FRM Exam Instructor Notes

– Summarized handbook (~300 pages), covering all the learning objectives given by GARP

– Rs. 500 + courier charges

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Page 37: About FRM

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Quantitative Analysis

Random

variables

Measures of Central

tendencyProb. & Prob.

distribution

Hypothesis

TestingCorrelation & Regression

Mean: ∑xi/n

B

Mode:-Value that occurs more

frequently

Median:-Midpoint of data arranged

in ascending order

AC

Q. 25 observation are taken

from a sample of unknown

variance. Sample mean of 70

and σ = 60. You wish to conduct

a two - tailed test of null

hypothesis that the mean is

equal to 50. What is most

appropriate test statistic?

Ans. Standard Error of mean

(σx) = σ/ √(n)

= 60/sqrt(25) = 12

Degrees of freedom = 24

Use T statistic = (x - μ)/ σx =

(70 - 50)/12 = 1.67

Binomial Random Variable

E(X)=n*p

Var(X)=n*p*(1-p)=n*p*q

Standardized RV is normalized

mean = 0, σ = 1.

Z-score: # of σ a given

observation is from population

mean.

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 standard deviation of assets

is $ 10 Mn. What is the distance to

default?

Ans. z = (A-K)/ σA

= (100-80)/10

= 2

Standard Error

(SE)

SE (σx) of the sample mean is σ of the dist. of sample means

•Known pop. Var. σx= σ/ √(n)

•Unknown pop. var sx= s/ √(n)

Binomial Random Variable

E(X)=n*p

Var(X)=n*p*(1-p)=n*p*q

Standardized RV is normalized

mean = 0, σ = 1.

Z-score: # of σ a given

observation is from population

mean.

Z=(x-µ)/σ

Variance

D

Correlation Coefficient

(CC)

-1 < CC < 1

if CC = 0, X & Y are uncorrelated

rx,y=cov(x,y)/σxσy=√R2

C

Appropriate Test structure:

H0:b1=0; Ha:b1≠0

Test: tb1=(b^1-b1)/sb^1

Decision Rule:

reject H0 if t>+t critical or if t< -tcritical

Simple linear

regression

Regression

coefficient

Coefficient of

Determination(R2)

%age of total var. in Y explained by X

R2 =( SSR / SST )=1-( SSE / SST)

=explained variation/total variationLR model: Yi=b0+b1Xi+Ei

Yi = Dependent variable estimated value of

Yi, given value of Xi

Xi = independent variable

b0 =intercept term; represents

Y if X =0

b1 = slope coefficient; measures

change in Y for 1 unit change in X b^1=cov

(X,Y)/ σ2(X)

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