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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).

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Agenda

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


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.

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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


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


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


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


Distribution of returns : Three broad categories

• Parametric
– RiskMetrics
– GARCH

• Nonparametric
– Historical Simulation
– the Hybrid model

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


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


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


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.


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


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


Basic Problem #1

• Asset daily standard deviation is 1.6%

• Market Value is US $ 10 Mn

• What is VaR (%) at 99% confidence?


Basic Problem #2:

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


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% ?


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 ?


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?


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


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


VaR for Linear Assets

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


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


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


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


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


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?


What is the Total Risk?

• Bonds
• Stocks
• Options
• Credit
• Forex

Total Risk??

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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


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?


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Contact

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

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