7_3-Measurement%20of%20Market%20Risk.pdf

7/28/2019 7_3-Measurement%20of%20Market%20Risk.pdf

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Market Risk

Directional risk

Relative value risk

Price risk

Liquidity risk

Type of measurements

scenario analysis

statistical analysis


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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.


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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


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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


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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


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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


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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


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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


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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.

(Profit/Loss Distribution)

5%

95%X

Value-at-Risk


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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


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Value-at-Risk Assumptions

1) Percentage change (return) of assets is Gaussian:

SdzSdtdS dzdtS

dS or

ztS

S

Normal Distribution


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Value-at-Risk Assumptions

2) Mean return m is zero:

ztS

S

Mean oft is.

)(~ tOt

Standard deviation of t is.

)(~ 2/1tOz

Time is measured in years, hence t or change intime is insignificant. Hence the mean is not taken

into consideration and the mean return is stated as:zSS


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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 a multiplication factor

(multiplication factor equals 3).


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Advantages of VaR

Captures an important aspect of risk in a single number

Easy to understand

Indicates the worst loss that could happen


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Daily Volatilities

Option pricing (volatility is express as volatility per year)

aR calculations (volatility is express as volatility per day)

yearyear

year

day

%6063.0252


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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


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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 = 3,794.733 (1,200 x )10V 10


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Example (continued)

Assume that the expected change in the value of the

banks share is zero

Assume that the change in the value of the banks share

is normally distributed

Since N(0.01)= -2.33, ({Z


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Example (continued)

VaR for one year (252 days) = 44,385.12

Banks Gross Income = 1,869,906

15% of Gross Income = 280,485.

Capital charge for operational risk = 280,097.

Banks current share capital will be related to risk weights

assessed by the capital charge.


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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


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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


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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


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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


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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 thestandard 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


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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


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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


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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


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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


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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


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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


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Back Testing

Backtests compare realized trading results with modelgenerated 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


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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


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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


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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


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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


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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


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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


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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


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Limitations of Stress Test

Stress tests are often neither transparent nor

straightforward

Depends on a large number of practitioner choices

Choice of risk factors to stress

Methods of combining factors stressed

Range of values considered


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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 banks risk-taking activities is subject to

interpretations

7_3-Measurement%20of%20Market%20Risk.pdf

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