Transcript 73-Measurement of Market Risk

Measurement of Market Risk
Market Risk
• Directional risk
• Relative value risk
• Price risk
• Liquidity risk
Type of measurements
– scenario analysis
– statistical analysis
Scenario Analysis
• A scenario analysis measures the change in market
value that would result if market factors were changed
from their current levels, in a specified way. No
assumption about probability of changes is made.
• A stress test is a measurement of the change in the
market value of a portfolio that would occur for a
specified unusually large change in a set of market
factors.
Value at Risk
• A single number that summarizes the likely loss in
value of a portfolio over a given time horizon with
specified probability.
• C-VaR states expected loss conditional on change in
value in the left tail of the distribution.
• Three approaches
– Historical simulation
– Model-building approach
– Monte Carlo simulation
Historical Simulation
• Identify market variables that determine the portfolio
value
• Collect data on movements in these variables for a
reasonable number of historical days
• Build scenarios that mimic changes over the
historical period
• For each scenario calculate the change in value of
the portfolio over the specified time horizon
• From this empirical distribution of value changes
calculate VaR
Model Building Approach
• Portfolio of n-assets
• Calculate mean and standard deviation of change in
the value of portfolio for one day
• Assume normality
• Calculate VaR
Monte Carlo Simulation
• Value of the portfolio today
• Draw samples from the probability distribution of
changes of the market variables
• Using the sampled changes calculate the new portfolio
value and its change
• From the simulated probability distribution of changes
in portfolio value calculate VaR
Pitfalls of Normal Distribution Based VaR
• Normality assumption may not be valid for tail part of the
distribution
• VaR of a portfolio is not less than weighted sum of VaR
of individual assets (not sub-additive)
• Expected shortfall conditional on the fact that loss is
more than VaR is a sub-additive measure of risk
Pitfalls of Value-at-Risk
• VaR is a statistical measurement of price risk
• VaR assumes a static portfolio. It does not take into
account
– Structural
change
in
the
portfolio
that
would
contractually occur during the period
– Dynamic hedging of the portfolio
• VaR calculation has two basic components
– Simulation of changes in market rates
– Calculation of resultant changes in the portfolio value
Value-at-Risk
VaR (Value-at-Risk) is a measure of the risk in a portfolio over
time.
Quoted in terms of a time horizon and a confidence level.
Example: 10 day 95% VaR is the size of loss X that will not
happen 95% of the time over the next 10 days.
Value-at-Risk
X
95%
5%
(Profit/Loss Distribution)
Value-at-Risk Levels
Two standard VaR levels are 95% and 99%.
95% is 1.645 standard deviations from the mean
99% is 2.33 standard deviations from the mean
mean
Value-at-Risk Assumptions
1) Percentage change (return) of assets is Gaussian:
dS  Sdt  Sdz
or
S
  t   z
S
dS
 dt  dz
S
Normal Distribution
Value-at-Risk Assumptions
2) Mean return m is zero:
S
  t   z
S
Mean of t is.
t ~ O(t )
Standard deviation of ∆t is.
z ~ O(t1/ 2 )
Time is measured in years, hence t or change in
time is insignificant. Hence the mean μ is not taken
into consideration and the mean return is stated as:
S  Sz
VaR and Regulatory Capital
Regulators require banks to keep capital for market risk
equal to the average of VaR estimates for past 60
trading days using confidence level of 99% and number
of
days
(N)
=10,
times
(multiplication factor equals 3).
a
multiplication
factor
Advantages of VaR
• Captures an important aspect of risk in a single number
• Easy to understand
• Indicates the worst loss that could happen
Daily Volatilities
• Option pricing (volatility is express as volatility per year)
• aR calculations (volatility is express as volatility per day)
 day 
 year
252
 0.063   year  6%   year
Daily Volatility
•
day
is defined as the standard deviation of the
continuously compounded return in one day
• In practice it is also assumed that it is the standard
deviation of the proportional change in one day
Example
• Based on 60 days prior trading data the following
computations have been made
• Volatility of a bank is 2% per day (about 32% per year)
• Assume N=10 and confidence level is 99 %
• Standard deviation of the change in the market price (₹
60,000) in 1 day is ₹ 1,200 (2% x 60,000)
• Standard deviation of the change in 10 days is
1,200 x V10 = 3,794.733 (1,200 x
10 )
Example (continued)
• Assume that the expected change in the value of the
bank’s share is zero
• Assume that the change in the value of the bank’s share
is normally distributed
• Since N(0.01)= -2.33, ({Z<-2.33}=0.01)
the VaR is
2.33 x 3,794.733 = ₹ 8,846.728.
Example (continued)
• VaR for one year (252 days) = ₹ 44,385.12
• Bank’s Gross Income = ₹ 1,869,906
• 15% of Gross Income = ₹ 280,485.
• Capital charge for operational risk = ₹ 280,097.
• Bank’s current share capital will be related to risk weights
assessed by the capital charge.
Value-at-Risk
• An estimate of potential loss in a
– Position
– Asset
– Liability
– Portfolio of assets
– Portfolio of liabilities
• During a given holding period at a given level of certainty
Value-at-Risk
• Probability of the unexpected happening
• Probability of suffering a loss
• Estimate of loss likely to be suffered
• VaR is not the actual loss
• VaR measures potential loss and not potential gain
• VaR measures the probability of loss for a given time
period over which the position is held
Bank for International Settlement (BIS)
• VaR is a measurement of market risk
• Provision of capital adequacy for market risk, subject to
approval by banks' supervisory authorities
• Computation of VaR changes based on the estimated
time period
– One day
– One week
– One month
– One year
Bank for International Settlement (BIS)
• Holding period for an instrument will depend on liquidity
of the instrument
• Varying degrees of certainty changes potential loss
• VaR estimates that the loss will not exceed a certain
amount
• VaR will change with different levels of certainty
VaR Methodology
• Computed as the expected loss on a position from an
adverse movement in identified market risk parameter(s)
• Specified probability over a nominated period of time
• Volatility in financial markets is calculated as the
standard deviation of the percentage changes in the
relevant asset price over a specified asset period
• Volatility for calculation of VaR is specified as the
standard deviation of the percentage change in the risk
factor over the relevant risk horizon
VaR Computation Method
• Correlation Method
– Variance – covariance method
– Deterministic approach
– Change in value of the position computed by combining
the sensitivity of each component to price changes in
the underlying assets
VaR Computation Method
• Historical Simulation
– Change in the value of a position using the actual
historical movements of the underlying assets
– Historical period has to be adequately long to capture
all possible events and relationships between the
various assets and within each asset class
– Dynamics of the risk factors captured since simulation
follows every historical move
VaR Computation Method
• Monte Carlo Simulation
– Calculates the change in the value of a portfolio using a
sample of randomly generated price scenarios
– Assumptions on market structures, correlations
between risk factors and the volatility of these factors
VaR Application
• Basic parameters
– Holding period
– Confidence interval
– Historical time period (observed asset prices)
• Closer the models fit economic reality, more accurate the
estimated
• There is no guarantee that the numbers returned by
each VaR method will be near each other
VaR Application
• VaR is used as a Management Information System (MIS)
tool in the trading portfolio
• Risk by levels
• Products
• Geography
• Level of organisation
• VaR is used to set risk limits
• VaR is used to decide the next business
VaR Limitation
• VaR does not substitute
– Management judgement
– Internal control
• VaR measures market risk
– Trading portfolio
– Investment portfolio
• VaR is helpful subject to the extent of
– Measurement parameters
Back Testing
• Backtests compare realized trading results with model
generated risk measures
• Evaluate a new model
• Reassess the accuracy of existing models
• Banks using internal VaR models for market risk capital
requirements must backtest their models on a regular
basis
Back Testing
• Banks back test risk models on a monthly or quarterly
basis to verify accuracy
• Observe whether trading results fall within pre-specified
confidence bands as predicted by the VaR models
• If the models perform poorly establish cause for poor
performance
– Check integrity of position
– Check market data
– Check model parameters
– Check methodology
Stress Testing
• Banks gauge their potential vulnerability to exceptional,
but plausible, events
• Stress testing addresses the large moves in key market
variables that lie beyond day to day risk monitoring but
that could potentially occur
Stress Testing
• Process of stress testing involves
– Identifying potential movements
– Market variables to stress
– How much to stress them
– What time frame to run the stress analysis
– Shocks are applied to the portfolio
• Revaluing the portfolios
– Effect of a particular market movement on the value of
the portfolio
– Profit and Loss
– Effects of different shocks of different magnitudes
Stress Testing Technique
• Scenario analysis
• Evaluating the portfolios
– under various expectations
– evaluating the impact
• changing evaluation models
• volatilities and correlations
•
Scenarios requiring no simulations
– analyzing large past losses
Stress Testing Technique
• Scenarios requiring simulations
– Running simulations of the current portfolio subject to
large historical shocks
• Bank specific scenario
– Driven by the current position of the bank rather than
historical simulation
• Subjective than VaR
• Identify undetected weakness in the bank's portfolio
Efficiency of a Stress Test
• Relevant to the current market position
• Consider changes in all relevant market rates
• Examine potential regime shifts (whether the current risk
parameters will hold or break down)
• Consider market illiquidity
• Consider the interrelationship between market and credit
risk
Application of Stress Tests
• Stress tests produce information summarising the bank’s
exposure to extreme but possible circumstances
• Role of risk managers in the bank is gathering and
summarising information to enable senior management
to understand the strategic relationship between the
bank’s risk taking
– Extent and character of financial leverage employed
– Risk appetite
– Stress scenarios created on a regular basis
– Stress scenarios monitored over time
Application of Stress Tests
• Influence decision-making
• Manage funding risk
• Provide a check on modelling assumptions
• Set limits for traders
• Determine capital charges on trading desks’ positions
Limitations of Stress Test
• Stress
tests
are
often
neither
transparent
straightforward
• Depends on a large number of practitioner choices
• Choice of risk factors to stress
• Methods of combining factors stressed
• Range of values considered
nor
Limitations of Stress Test
• Time frame to analyse
• Risk manager is faced with the considerable tasks of
analyzing the results and identifying implications
• Stress test results interpretation for the bank is based on
qualitative criteria
• Manage bank’s risk-taking activities is subject to
interpretations