SlideShare una empresa de Scribd logo
1 de 37
Descargar para leer sin conexión
Pristine Careers       www.pristinecareers.com | www.eneev.com




            FRM Trainings – VAR Webinar
            2009
System Requirements for Webinar

 • Operating System: Windows® 2000, XP, 2003 Server or Vista

 • Processor: Minimum of Pentium® class 1GHz CPU with 512 MB of RAM (Recommended) (2
   GB of RAM for Windows® Vista)

 • Connectivity: Cable modem, DSL or better Internet connection

 • Plug-ins : Internet Explorer® 6.0 or newer, Mozilla® Firefox® 2.0 or newer (JavaScriptTM and
   JavaTM enabled)

 • Other HARDWARE: Good Quality Microphone, speakers/headphones, Participants wishing to
   connect to audio using VoIP will need a fast Internet connection, a microphone and speakers (a
   USB headset is recommended).




                                                                                    www.pristinecareers.com
Agenda


         •   About Pristine
         •   Introduction to VaR
         •   Calculating Simple VaR
         •   VaR for Linear & Non-Linear Assets
         •   Marginal VaR
         •   Our Contact




                                                  www.pristinecareers.com
About Pristine


     • An institution started by graduates from premiere institutes like IIM/IITs with
        diversified experience in financial sector
     • An authorized "Course Provider" for the FRM Exam and provides trainings for
        preparation of the FRM & CFA Exam.
     • The faculty members are drawn from IIT/IIM's having relevant experience in risk
        management & Investment banking.
     • Pristine has developed relationships with various Investment Banks, Commercial
        Banks, Asset Management Firms, Insurance Companies, Securities Regulators,
        Hedge Funds, Large Corporations, Multinationals and Credit Rating Firms and is a
        source to these companies for FRM and CFA candidates.




© Neev Knowledge Management – Pristine Careers       4                        www.pristinecareers.com
Agenda


         •   About Pristine
         •   Introduction to VaR
         •   Calculating Simple VaR
         •   VaR for Linear & Non-Linear Assets
         •   Marginal VaR
         •   Our Contact




                                                  www.pristinecareers.com
Introduction To Various Risks

Risk can be broadly defined as the degree of uncertainty about future net returns

• Credit risk relates to the potential loss due to the inability of a counterpart to meet its
  obligations

• Operational risk takes into account the errors that can be made in instructing payments
  or settling transactions

• Liquidity risk is caused by an unexpected large and stressful negative cash flow over a
  short period

• Market risk estimates the uncertainty of future earnings, due to the changes in market
  conditions


                          Current Focus of Study is Market Risk


                                                                             www.pristinecareers.com
What 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.pristinecareers.com
VAR Benefits


  •   Aggregates all of the risks in a portfolio into a single number

  •   Suitable for use in the boardroom, reporting to regulators, or disclosure in annual
      report

  •   Provides an approach to arrive at economical capital.

  •   Relates capital with the expected losses

  •   Scaled to time




                                                                           www.pristinecareers.com
VaR Measurement

• Mark-to-market the portfolio



• Estimate the distribution of portfolio returns
  – VAR : a very challenging statistical problem



• Compute the VaR of the portfolio




                                                   www.pristinecareers.com
Distribution of returns : Three broad categories


• Parametric
 – RiskMetrics
 – GARCH


• Nonparametric
 – Historical Simulation
 – the Hybrid model


• Semiparametric
 – Extreme Value Theory
 – CAViaR
 – quasi-maximum likelihood GARCH




                                                   www.pristinecareers.com
Financial markets: empirical facts




• Financial return distributions are leptokurtotic,
  – that is they have heavier tails
  – a higher peak than a normal distribution



• Equity returns are typically negatively skewed



• Squared returns have significant autocorrelation
  – volatilities of market factors tend to cluster




                                                      www.pristinecareers.com
Agenda


         •   About Pristine
         •   Introduction to VaR
         •   Calculating Simple VaR
         •   VaR for Linear & Non-Linear Assets
         •   Marginal VaR
         •   Our Contact




                                                  www.pristinecareers.com
Visualizing VAR

                                                  V a lu e a t R is k

                  .0 2 2                                                                         433

                  .0 1 6                                                                         3 2 4 .7

                  .0 1 1                                                                         2 1 6 .5

                  .0 0 5                                                                         1 0 8 .2

                  .0 0 0                                                                         0
                           1 .5         2 .9                 4 .3                5 .6     7 .0
                                  C e rta inty is 9 5 .0 0 % f ro m 2 .6 to + In finity


                                                                   Confidence (x%)                    ZX%

                                                                          90%                        1.28
                                                                          95%                        1.65
 The area under the normal curve for
 confidence value is:                                                   97.5%                        1.96
                                                                          99%                        2.32


                                                                                                 www.pristinecareers.com
VAR : Representations

 • A portfolio having a current value of say Rs.500,000- can be described to have
   a daily value at risk of US$ 5000- at a 99% confidence level,



 • which means there is a 1/100 chance of the loss exceeding US$ 5000/-
   considering no great paradigm shifts in the underlying factors.



 • A one day VAR of $10mm using a probability of 5% means that there is a 5%
   chance that the portfolio could lose more than $10mm in the next trading day.




                                                                    www.pristinecareers.com
How To Measure ?


• VaR (daily VaR) (in %) = ZX% * σ
    – ZX% : the normal distribution value for the given probability (x%) (normal
      distribution has mean as 0 and standard deviation as 1)
    – σ : standard deviation (volatility) of the asset (or portfolio)

• VaR (daily VaR) = VaR (in %) * asset value
    Or, VaR (daily VaR) = ZX% * σ * asset value




                                                                         www.pristinecareers.com
How To Measure ?


• VaR (n days) (in %) = VaR(daily VaR) (in %) * √n

• VaR (n days) = ZX% * σ * asset value * √n

• σport = √ wa2 σa2 + wb2 σb2+2wawb* σa* σb* σab

• VaRport (daily VaR) (in %) =

   √ wa2 (%VaRa)2 + wb2 (%VaRb)2+2wawb* (%VaRa)* (%VaRb)* σab




                                                                www.pristinecareers.com
Basic Problem #1


• Asset daily standard deviation is 1.6%

• Market Value is US $ 10 Mn

• What is VaR (%) at 99% confidence?




                                           www.pristinecareers.com
Basic Problem #2:

• What is the VaR value for 10 day VaR in the earlier case?




                                                              www.pristinecareers.com
Basic Problem #3:

• What is the daily portfolio VaR at 97.5% confidence level?
  – Investment in asset A is US$ 40 Mn
  – Investment in asset B is US$ 60 Mn

    – Volatility of asset A is 5.5% and asset B is 4.25%
    – Portfolio VaR if correlation between A and B is 20% ?




                                                               www.pristinecareers.com
Extended Problem #3.1

• Portfolio VaR if correlation between A and B is Zero?
  – What if correlation is 1 ?
  – Or -1 ?
  – What are the implications ?




                                                          www.pristinecareers.com
Basic Problem #4:


• Market Value of asset US$ 10 Mn

• Daily variance is 0.0005

• What is the annual VaR at 95% confidence with 250 trading days in a year?




                                                                    www.pristinecareers.com
Basic Problem #5:

• For an uncorrelated portfolio what is the VaR if:
   – VaR asset A is US$ 10 Mn
   – VaR asset B is US$ 20 Mn




                                                      www.pristinecareers.com
Agenda


         •   About Pristine
         •   Introduction to VaR
         •   Calculating Simple VaR
         •   VaR for Linear & Non-Linear Assets
         •   Marginal VaR
         •   Our Contact




                                                  www.pristinecareers.com
VaR for Linear and Non-Linear Assets


• When the value of the delta is constant for all changes in the underlying.



• Primarily in the case of fixed income securities we have linear assets



• When the value of the delta keeps on changing with the change in the underlying
   asset. It is seen in options




                                                                       www.pristinecareers.com
VaR for Linear Assets

• Linear Derivatives: Payoff diagrams that are linear or almost linear
  – Forwards, futures




                                                                         www.pristinecareers.com
VaR for Linear Derivatives


• Delta of Derivative
  – Change in price of Derivative to change in underlying asset

• For example,
  – The permitted lot size of S&P CNX Nifty futures contracts is 200 and multiples thereof. If

  – So VaR of Nifty Futures contract is 200 * VaR of Nifty

             VaRLinear Derivative = ∆ × VaR Underlying Risk Factor




                                                                                 www.pristinecareers.com
VaR for Non-Linear Assets




• Non-Linear Derivatives: Payoff diagrams
  that are highly non-linear
  – Non-linearity is due to the derivative either
    being an option or having an option
    embedded in its structure

  – Options, Credit Derivatives, Swaps




                                                    www.pristinecareers.com
VaR for Non-Linear Derivatives
• Main reason for difference is the shape of the payoff curve
                                                                                    Option
• For Delta Normal VaR                                                              price
  – A linear approximation is created
  – Approximation is an imperfect proxy for the portfolio
                                                                                                                         Slope = ∆
  – Computationally easy but may be less accurate.                             B
  – The delta-normal approach (generally) does not work for
    portfolios of nonlinear securities.                                                                  A         Stock price
  – Options Var = Delta of Option * (VaR at Zx%)
                                                                       f ( x ) ≈ f ( x0 ) + f ′( x0 )( x − x0 ) + 1 2 f ′′( x0 )( x − x0 )2


• Consider a portfolio of options dependent on a single stock price,
  S. Define        ∆P
              δ =
                   ∆S
                              ∆S
  – Approximately:     ∆x =
                               S

  – For Many Underlying variables:      ∆P = δ ∆S = Sδ ∆ x


                                       ∆P = ∑ S i δi ∆xi
                                              i



                                                                                                             www.pristinecareers.com
Problem #6 (Linear Assets)

•   If the daily VaR at 5%of Nikkie is 0.8 crores and you have 100 lots of Nikkie contract,
    Calculate annual VaR at 95% confidence for your portfolio assuming 250 days?
     • = 0.8*200*sqrt(250)
     • = 1264.911 crores




                                                                             www.pristinecareers.com
Problem #7 (Non-Linear Assets) :

•   If the value of stock is 100 and the value of the put option at 110 is 20. 10 units change
    in the underlying brings in change of 4 units change in the option premium. If the annual
    volatility is 0.25. Calculate daily VaR at 97.5% assuming 250 days?




                                                                              www.pristinecareers.com
Agenda


         •   About Pristine
         •   Introduction to VaR
         •   Calculating Simple VaR
         •   VaR for Linear & Non-Linear Assets
         •   Marginal VaR
         •   Our Contact




                                                  www.pristinecareers.com
What is the Total Risk?


  • Bonds
  • Stocks
  • Options
  • Credit
  • Forex




                          Total Risk??


                              32         www.pristinecareers.com
Marginal VaR



  • Suppose a portfolio has assets a, b and c. The Marginal VaR is the VaR of the
     portfolio – VaR of the respective asset.




  • Marginal VaR is for each unit and is the change in VaR of the portfolio with one
     unit change in the components




                                                                       www.pristinecareers.com
Problem #8 (Marginal VAR) :

•   Bank portfolio of stock has Reliance and Tata Steel with beta of 1.20 and 0.85. The VaR
    of the portfolio is Rs. 3,00,000 with the position of Reliance being Rs. 10,00,000 and
    Tata Steel as Rs, 5,00,000.


    What is the Marginal VaR for each?




                                                                             www.pristinecareers.com
Congratulations




                                                                                    u
                                                                                  yo
                                                                             a r,
                                                                         ebin xam
                                                                       W 9E
                                                                  n the 200
                                                               d i RM
                                                         lain e n F
                                                     ex p ns i
                                                  pts stio
                                               nce que
                                             co 7-8
                                        d the ast
                                      oo at le
                                  erst ve
                                nd sol
                           v e u to
                       u ha able
                  If yo ll be
                       wi


                                                                      www.pristinecareers.com
Agenda


         •   About Pristine
         •   Introduction to VaR
         •   Calculating Simple VaR
         •   VaR for Linear & Non-Linear Assets
         •   Marginal VaR
         •   Our Contact




                                                  www.pristinecareers.com
Contact




         Contact                                 Phone                          Email
         Atul Kumar                              +91 93221 94932                atul@eneev.com
         Pawan Prabhat                           +91 98676 25422                pawan@eneev.com
         Paramdeep Singh                         +91 93118 45000                paramdeep@eneev.com
         Sarita Chand                            +91 93427 34627                sarita@eneev.com

                                            Visit Us on: www.pristinecareers.com
                                            Visit our Blogs on: www.pristinecareers.com/blog




            Pristine Careers is an official course provider of FRM Exam preparation
                                             from GARP


© Neev Knowledge Management – Pristine Careers               37                                www.pristinecareers.com

Más contenido relacionado

Similar a FRM VaR-preparation-pristine

Discounted Cash Flow Methodology for Banks and Credit Unions
Discounted Cash Flow Methodology for Banks and Credit UnionsDiscounted Cash Flow Methodology for Banks and Credit Unions
Discounted Cash Flow Methodology for Banks and Credit UnionsLibby Bierman
 
Fixed Income Derived Analytics Powered By BlackRock Solutions
Fixed Income Derived Analytics Powered By BlackRock SolutionsFixed Income Derived Analytics Powered By BlackRock Solutions
Fixed Income Derived Analytics Powered By BlackRock SolutionsConor Coughlan
 
(R)isk Revolution - Current trends and challenges in Credit & Operational Risk
(R)isk Revolution - Current trends and challenges in Credit & Operational Risk(R)isk Revolution - Current trends and challenges in Credit & Operational Risk
(R)isk Revolution - Current trends and challenges in Credit & Operational RiskMarkus Krebsz
 
Managing risk in financial sector
Managing risk in financial sectorManaging risk in financial sector
Managing risk in financial sectorMahrez Mohiuddin
 
Risk Management: Maximising Long-Term Growth Presentation
Risk Management: Maximising Long-Term Growth PresentationRisk Management: Maximising Long-Term Growth Presentation
Risk Management: Maximising Long-Term Growth PresentationQuantInsti
 
The Imperatives of Investment Suitability
The Imperatives of Investment SuitabilityThe Imperatives of Investment Suitability
The Imperatives of Investment Suitabilityfinametrica
 
Assets liability management
Assets liability managementAssets liability management
Assets liability managementUjjwal 'Shanu'
 
P&C Insurance case study
P&C Insurance case studyP&C Insurance case study
P&C Insurance case studyWayne Wilkins
 
Orc Trading For Risk Management
Orc Trading For Risk ManagementOrc Trading For Risk Management
Orc Trading For Risk ManagementLMessi10
 
Fair & Transparent in Pricing – The Equitas Model
Fair & Transparent in Pricing – The Equitas ModelFair & Transparent in Pricing – The Equitas Model
Fair & Transparent in Pricing – The Equitas ModelMicrocredit Summit Campaign
 
corporate finance
corporate financecorporate finance
corporate financeShrey Sao
 
Risky business: Guide to Risk Management
Risky business: Guide to Risk ManagementRisky business: Guide to Risk Management
Risky business: Guide to Risk ManagementMichael Le
 
Basel2 Seminar Credit Risk
Basel2 Seminar Credit RiskBasel2 Seminar Credit Risk
Basel2 Seminar Credit Riskukabuka
 
Forum asset liability_management
Forum asset liability_managementForum asset liability_management
Forum asset liability_managementMiguel Revilla
 
Quantopian is Launching a Crowd-sourced Hedge Fund
Quantopian is Launching a Crowd-sourced Hedge FundQuantopian is Launching a Crowd-sourced Hedge Fund
Quantopian is Launching a Crowd-sourced Hedge Fundkelmstrom
 

Similar a FRM VaR-preparation-pristine (20)

Discounted Cash Flow Methodology for Banks and Credit Unions
Discounted Cash Flow Methodology for Banks and Credit UnionsDiscounted Cash Flow Methodology for Banks and Credit Unions
Discounted Cash Flow Methodology for Banks and Credit Unions
 
Fixed Income Derived Analytics Powered By BlackRock Solutions
Fixed Income Derived Analytics Powered By BlackRock SolutionsFixed Income Derived Analytics Powered By BlackRock Solutions
Fixed Income Derived Analytics Powered By BlackRock Solutions
 
(R)isk Revolution - Current trends and challenges in Credit & Operational Risk
(R)isk Revolution - Current trends and challenges in Credit & Operational Risk(R)isk Revolution - Current trends and challenges in Credit & Operational Risk
(R)isk Revolution - Current trends and challenges in Credit & Operational Risk
 
Managing risk in financial sector
Managing risk in financial sectorManaging risk in financial sector
Managing risk in financial sector
 
Risk Management: Maximising Long-Term Growth Presentation
Risk Management: Maximising Long-Term Growth PresentationRisk Management: Maximising Long-Term Growth Presentation
Risk Management: Maximising Long-Term Growth Presentation
 
Value at risk
Value at risk Value at risk
Value at risk
 
The Imperatives of Investment Suitability
The Imperatives of Investment SuitabilityThe Imperatives of Investment Suitability
The Imperatives of Investment Suitability
 
VaR optimization
VaR optimizationVaR optimization
VaR optimization
 
Assets liability management
Assets liability managementAssets liability management
Assets liability management
 
P&C Insurance case study
P&C Insurance case studyP&C Insurance case study
P&C Insurance case study
 
Orc Trading For Risk Management
Orc Trading For Risk ManagementOrc Trading For Risk Management
Orc Trading For Risk Management
 
Fair & Transparent in Pricing – The Equitas Model
Fair & Transparent in Pricing – The Equitas ModelFair & Transparent in Pricing – The Equitas Model
Fair & Transparent in Pricing – The Equitas Model
 
corporate finance
corporate financecorporate finance
corporate finance
 
Risky business: Guide to Risk Management
Risky business: Guide to Risk ManagementRisky business: Guide to Risk Management
Risky business: Guide to Risk Management
 
Basel2 Seminar Credit Risk
Basel2 Seminar Credit RiskBasel2 Seminar Credit Risk
Basel2 Seminar Credit Risk
 
L02 definition of fm
L02 definition of fmL02 definition of fm
L02 definition of fm
 
Forum asset liability_management
Forum asset liability_managementForum asset liability_management
Forum asset liability_management
 
Act, 020212 final
Act, 020212 finalAct, 020212 final
Act, 020212 final
 
Lecture 4
Lecture 4Lecture 4
Lecture 4
 
Quantopian is Launching a Crowd-sourced Hedge Fund
Quantopian is Launching a Crowd-sourced Hedge FundQuantopian is Launching a Crowd-sourced Hedge Fund
Quantopian is Launching a Crowd-sourced Hedge Fund
 

Más de Pristine Careers

Financial Modeling Case on FMCG Sector
Financial Modeling Case on FMCG SectorFinancial Modeling Case on FMCG Sector
Financial Modeling Case on FMCG SectorPristine Careers
 
Pristine fra-participants-cfa-l1v5
Pristine fra-participants-cfa-l1v5Pristine fra-participants-cfa-l1v5
Pristine fra-participants-cfa-l1v5Pristine Careers
 
Pristine equity-participant-cfa-l2-v8
Pristine equity-participant-cfa-l2-v8Pristine equity-participant-cfa-l2-v8
Pristine equity-participant-cfa-l2-v8Pristine Careers
 
Frm va r-preparation-pristine-participants-v2
Frm va r-preparation-pristine-participants-v2Frm va r-preparation-pristine-participants-v2
Frm va r-preparation-pristine-participants-v2Pristine Careers
 
Pristine quant-frm demo-annotations
Pristine quant-frm demo-annotationsPristine quant-frm demo-annotations
Pristine quant-frm demo-annotationsPristine Careers
 
CFA II Quantitative Analysis
CFA II Quantitative AnalysisCFA II Quantitative Analysis
CFA II Quantitative AnalysisPristine Careers
 
FSA tips for CFA Preparation by Pristine (Annotated)
FSA tips for CFA Preparation by Pristine (Annotated)FSA tips for CFA Preparation by Pristine (Annotated)
FSA tips for CFA Preparation by Pristine (Annotated)Pristine Careers
 
FSA tips for CFA Preparation by Pristine
FSA tips for CFA Preparation by Pristine FSA tips for CFA Preparation by Pristine
FSA tips for CFA Preparation by Pristine Pristine Careers
 

Más de Pristine Careers (11)

Financial Modeling Case on FMCG Sector
Financial Modeling Case on FMCG SectorFinancial Modeling Case on FMCG Sector
Financial Modeling Case on FMCG Sector
 
Pristine fra-participants-cfa-l1v5
Pristine fra-participants-cfa-l1v5Pristine fra-participants-cfa-l1v5
Pristine fra-participants-cfa-l1v5
 
Pristine equity-participant-cfa-l2-v8
Pristine equity-participant-cfa-l2-v8Pristine equity-participant-cfa-l2-v8
Pristine equity-participant-cfa-l2-v8
 
Frm va r-preparation-pristine-participants-v2
Frm va r-preparation-pristine-participants-v2Frm va r-preparation-pristine-participants-v2
Frm va r-preparation-pristine-participants-v2
 
Pristine quant-frm demo-annotations
Pristine quant-frm demo-annotationsPristine quant-frm demo-annotations
Pristine quant-frm demo-annotations
 
Pristine quant-frm demo
Pristine quant-frm demoPristine quant-frm demo
Pristine quant-frm demo
 
Fcff fcfe
Fcff fcfeFcff fcfe
Fcff fcfe
 
Free cash flow to firm
Free cash flow to firmFree cash flow to firm
Free cash flow to firm
 
CFA II Quantitative Analysis
CFA II Quantitative AnalysisCFA II Quantitative Analysis
CFA II Quantitative Analysis
 
FSA tips for CFA Preparation by Pristine (Annotated)
FSA tips for CFA Preparation by Pristine (Annotated)FSA tips for CFA Preparation by Pristine (Annotated)
FSA tips for CFA Preparation by Pristine (Annotated)
 
FSA tips for CFA Preparation by Pristine
FSA tips for CFA Preparation by Pristine FSA tips for CFA Preparation by Pristine
FSA tips for CFA Preparation by Pristine
 

FRM VaR-preparation-pristine

  • 1. Pristine Careers www.pristinecareers.com | www.eneev.com FRM Trainings – VAR Webinar 2009
  • 2. System Requirements for Webinar • Operating System: Windows® 2000, XP, 2003 Server or Vista • Processor: Minimum of Pentium® class 1GHz CPU with 512 MB of RAM (Recommended) (2 GB of RAM for Windows® Vista) • Connectivity: Cable modem, DSL or better Internet connection • Plug-ins : Internet Explorer® 6.0 or newer, Mozilla® Firefox® 2.0 or newer (JavaScriptTM and JavaTM enabled) • Other HARDWARE: Good Quality Microphone, speakers/headphones, Participants wishing to connect to audio using VoIP will need a fast Internet connection, a microphone and speakers (a USB headset is recommended). www.pristinecareers.com
  • 3. Agenda • About Pristine • Introduction to VaR • Calculating Simple VaR • VaR for Linear & Non-Linear Assets • Marginal VaR • Our Contact www.pristinecareers.com
  • 4. About Pristine • An institution started by graduates from premiere institutes like IIM/IITs with diversified experience in financial sector • An authorized "Course Provider" for the FRM Exam and provides trainings for preparation of the FRM & CFA Exam. • The faculty members are drawn from IIT/IIM's having relevant experience in risk management & Investment banking. • Pristine has developed relationships with various Investment Banks, Commercial Banks, Asset Management Firms, Insurance Companies, Securities Regulators, Hedge Funds, Large Corporations, Multinationals and Credit Rating Firms and is a source to these companies for FRM and CFA candidates. © Neev Knowledge Management – Pristine Careers 4 www.pristinecareers.com
  • 5. Agenda • About Pristine • Introduction to VaR • Calculating Simple VaR • VaR for Linear & Non-Linear Assets • Marginal VaR • Our Contact www.pristinecareers.com
  • 6. Introduction To Various Risks Risk can be broadly defined as the degree of uncertainty about future net returns • Credit risk relates to the potential loss due to the inability of a counterpart to meet its obligations • Operational risk takes into account the errors that can be made in instructing payments or settling transactions • Liquidity risk is caused by an unexpected large and stressful negative cash flow over a short period • Market risk estimates the uncertainty of future earnings, due to the changes in market conditions Current Focus of Study is Market Risk www.pristinecareers.com
  • 7. What 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.pristinecareers.com
  • 8. VAR Benefits • Aggregates all of the risks in a portfolio into a single number • Suitable for use in the boardroom, reporting to regulators, or disclosure in annual report • Provides an approach to arrive at economical capital. • Relates capital with the expected losses • Scaled to time www.pristinecareers.com
  • 9. VaR Measurement • Mark-to-market the portfolio • Estimate the distribution of portfolio returns – VAR : a very challenging statistical problem • Compute the VaR of the portfolio www.pristinecareers.com
  • 10. Distribution of returns : Three broad categories • Parametric – RiskMetrics – GARCH • Nonparametric – Historical Simulation – the Hybrid model • Semiparametric – Extreme Value Theory – CAViaR – quasi-maximum likelihood GARCH www.pristinecareers.com
  • 11. Financial markets: empirical facts • Financial return distributions are leptokurtotic, – that is they have heavier tails – a higher peak than a normal distribution • Equity returns are typically negatively skewed • Squared returns have significant autocorrelation – volatilities of market factors tend to cluster www.pristinecareers.com
  • 12. Agenda • About Pristine • Introduction to VaR • Calculating Simple VaR • VaR for Linear & Non-Linear Assets • Marginal VaR • Our Contact www.pristinecareers.com
  • 13. Visualizing VAR V a lu e a t R is k .0 2 2 433 .0 1 6 3 2 4 .7 .0 1 1 2 1 6 .5 .0 0 5 1 0 8 .2 .0 0 0 0 1 .5 2 .9 4 .3 5 .6 7 .0 C e rta inty is 9 5 .0 0 % f ro m 2 .6 to + In finity Confidence (x%) ZX% 90% 1.28 95% 1.65 The area under the normal curve for confidence value is: 97.5% 1.96 99% 2.32 www.pristinecareers.com
  • 14. VAR : Representations • A portfolio having a current value of say Rs.500,000- can be described to have a daily value at risk of US$ 5000- at a 99% confidence level, • which means there is a 1/100 chance of the loss exceeding US$ 5000/- considering no great paradigm shifts in the underlying factors. • A one day VAR of $10mm using a probability of 5% means that there is a 5% chance that the portfolio could lose more than $10mm in the next trading day. www.pristinecareers.com
  • 15. How To Measure ? • VaR (daily VaR) (in %) = ZX% * σ – ZX% : the normal distribution value for the given probability (x%) (normal distribution has mean as 0 and standard deviation as 1) – σ : standard deviation (volatility) of the asset (or portfolio) • VaR (daily VaR) = VaR (in %) * asset value Or, VaR (daily VaR) = ZX% * σ * asset value www.pristinecareers.com
  • 16. How To Measure ? • VaR (n days) (in %) = VaR(daily VaR) (in %) * √n • VaR (n days) = ZX% * σ * asset value * √n • σport = √ wa2 σa2 + wb2 σb2+2wawb* σa* σb* σab • VaRport (daily VaR) (in %) = √ wa2 (%VaRa)2 + wb2 (%VaRb)2+2wawb* (%VaRa)* (%VaRb)* σab www.pristinecareers.com
  • 17. Basic Problem #1 • Asset daily standard deviation is 1.6% • Market Value is US $ 10 Mn • What is VaR (%) at 99% confidence? www.pristinecareers.com
  • 18. Basic Problem #2: • What is the VaR value for 10 day VaR in the earlier case? www.pristinecareers.com
  • 19. Basic Problem #3: • What is the daily portfolio VaR at 97.5% confidence level? – Investment in asset A is US$ 40 Mn – Investment in asset B is US$ 60 Mn – Volatility of asset A is 5.5% and asset B is 4.25% – Portfolio VaR if correlation between A and B is 20% ? www.pristinecareers.com
  • 20. Extended Problem #3.1 • Portfolio VaR if correlation between A and B is Zero? – What if correlation is 1 ? – Or -1 ? – What are the implications ? www.pristinecareers.com
  • 21. Basic Problem #4: • Market Value of asset US$ 10 Mn • Daily variance is 0.0005 • What is the annual VaR at 95% confidence with 250 trading days in a year? www.pristinecareers.com
  • 22. Basic Problem #5: • For an uncorrelated portfolio what is the VaR if: – VaR asset A is US$ 10 Mn – VaR asset B is US$ 20 Mn www.pristinecareers.com
  • 23. Agenda • About Pristine • Introduction to VaR • Calculating Simple VaR • VaR for Linear & Non-Linear Assets • Marginal VaR • Our Contact www.pristinecareers.com
  • 24. VaR for Linear and Non-Linear Assets • When the value of the delta is constant for all changes in the underlying. • Primarily in the case of fixed income securities we have linear assets • When the value of the delta keeps on changing with the change in the underlying asset. It is seen in options www.pristinecareers.com
  • 25. VaR for Linear Assets • Linear Derivatives: Payoff diagrams that are linear or almost linear – Forwards, futures www.pristinecareers.com
  • 26. VaR for Linear Derivatives • Delta of Derivative – Change in price of Derivative to change in underlying asset • For example, – The permitted lot size of S&P CNX Nifty futures contracts is 200 and multiples thereof. If – So VaR of Nifty Futures contract is 200 * VaR of Nifty VaRLinear Derivative = ∆ × VaR Underlying Risk Factor www.pristinecareers.com
  • 27. VaR for Non-Linear Assets • Non-Linear Derivatives: Payoff diagrams that are highly non-linear – Non-linearity is due to the derivative either being an option or having an option embedded in its structure – Options, Credit Derivatives, Swaps www.pristinecareers.com
  • 28. VaR for Non-Linear Derivatives • Main reason for difference is the shape of the payoff curve Option • For Delta Normal VaR price – A linear approximation is created – Approximation is an imperfect proxy for the portfolio Slope = ∆ – Computationally easy but may be less accurate. B – The delta-normal approach (generally) does not work for portfolios of nonlinear securities. A Stock price – Options Var = Delta of Option * (VaR at Zx%) f ( x ) ≈ f ( x0 ) + f ′( x0 )( x − x0 ) + 1 2 f ′′( x0 )( x − x0 )2 • Consider a portfolio of options dependent on a single stock price, S. Define ∆P δ = ∆S ∆S – Approximately: ∆x = S – For Many Underlying variables: ∆P = δ ∆S = Sδ ∆ x ∆P = ∑ S i δi ∆xi i www.pristinecareers.com
  • 29. Problem #6 (Linear Assets) • If the daily VaR at 5%of Nikkie is 0.8 crores and you have 100 lots of Nikkie contract, Calculate annual VaR at 95% confidence for your portfolio assuming 250 days? • = 0.8*200*sqrt(250) • = 1264.911 crores www.pristinecareers.com
  • 30. Problem #7 (Non-Linear Assets) : • If the value of stock is 100 and the value of the put option at 110 is 20. 10 units change in the underlying brings in change of 4 units change in the option premium. If the annual volatility is 0.25. Calculate daily VaR at 97.5% assuming 250 days? www.pristinecareers.com
  • 31. Agenda • About Pristine • Introduction to VaR • Calculating Simple VaR • VaR for Linear & Non-Linear Assets • Marginal VaR • Our Contact www.pristinecareers.com
  • 32. What is the Total Risk? • Bonds • Stocks • Options • Credit • Forex Total Risk?? 32 www.pristinecareers.com
  • 33. Marginal VaR • Suppose a portfolio has assets a, b and c. The Marginal VaR is the VaR of the portfolio – VaR of the respective asset. • Marginal VaR is for each unit and is the change in VaR of the portfolio with one unit change in the components www.pristinecareers.com
  • 34. Problem #8 (Marginal VAR) : • Bank portfolio of stock has Reliance and Tata Steel with beta of 1.20 and 0.85. The VaR of the portfolio is Rs. 3,00,000 with the position of Reliance being Rs. 10,00,000 and Tata Steel as Rs, 5,00,000. What is the Marginal VaR for each? www.pristinecareers.com
  • 35. Congratulations u yo a r, ebin xam W 9E n the 200 d i RM lain e n F ex p ns i pts stio nce que co 7-8 d the ast oo at le erst ve nd sol v e u to u ha able If yo ll be wi www.pristinecareers.com
  • 36. Agenda • About Pristine • Introduction to VaR • Calculating Simple VaR • VaR for Linear & Non-Linear Assets • Marginal VaR • Our Contact www.pristinecareers.com
  • 37. Contact Contact Phone Email Atul Kumar +91 93221 94932 atul@eneev.com Pawan Prabhat +91 98676 25422 pawan@eneev.com Paramdeep Singh +91 93118 45000 paramdeep@eneev.com Sarita Chand +91 93427 34627 sarita@eneev.com Visit Us on: www.pristinecareers.com Visit our Blogs on: www.pristinecareers.com/blog Pristine Careers is an official course provider of FRM Exam preparation from GARP © Neev Knowledge Management – Pristine Careers 37 www.pristinecareers.com