Var Presentation

Market Risk Management

Value-at-Risk


What is Risk ?

The possibility of suffering harm or, loss.

In financial parlance, risk is the chance that expected investment returns will not be materialised. Sources of risk are manifold

Market Risk is the risk of not realising the expected profit due to unfavourable market movements.


Market Risk: Definition

Market risk is the uncertainty resulting from changes in market prices

Market Risks arises due to movements in variables such as : Interest rates Currencies Equity Commodities

Arises due to directional risks from taking a net long/short position in a given asset class


Assessment of Market Risk

Important in terms of: Management information Setting limits Resource allocation (risk/return tradeoff) Performance evaluation Regulation


Measurement of Market Risk

Quantify the risk of losses due to movements in financial market variables

Various measures to assess market risk: Investment Limits Risk Factors ( PV01, Delta , Gamma etc) Value at Risk (VaR)


Value at Risk (VaR)

Statistical estimate of

The maximum amount of money

that may be lost on a portfolio

over a given period of time

with a given level of confidence

under normal market conditions


Definition Value-at-Risk is defined as a loss level that will

not be exceeded at some specified confidence level for a specified time horizon under normal market conditions “What loss level is such that we are X% confident

it will not be exceeded in N business days?”

If the VaR for one day horizon and at a confidence level of 95% is Rs.10 mn, that means: The likelihood that our losses will exceed Rs.10

mn over the next 24 hours is 5%

Concept of “Tail Risk”


VAR VAR asks “How bad things can get?”

VAR : Summarizes worst loss over a target horizon with a given level of confidence

VAR describes the down side quantile of the projected distribution of gains/losses over target horizon.

A single number ( currency amount) which estimates expected maximum loss (worst loss) over a given time horizon and at a given confidence level

Describes the probability boundary of potential losses

VAR an estimate of likely losses: Actual loss may differ

BIS accepted VAR as Market Risk measure & for provision of capital adequacy


VAR

Denotes impact of normal market risk events

Provides predictive, aggregate view of portfolio risk in terms of probable loss

Complements stop-loss limits and cumulative loss limits

Integrates risk management architecture

Intended to be used in future as primary input for capital allocation, risk adjusted performance measurement and creating a risk limit framework

VaR model validated by Back Testing

Complemented by Stress Testing.


BIS Guidelines

“…Each bank must meet, on a daily basis, a capital requirement expressed as the higher of (i) its previous day’s VaR number measured according to the parameters specified and (ii) an average of the daily VaR measures on each of the preceding sixty business days, multiplied by a multiplication factor.” This multiplying factor is minimum 3.


Why VaR is Popular(1) Representation through a single no.

Common measure across various products – helps in comparative analysis

It provides a control measure Limits can be set up based on VaR. VaR trends can be monitored and any unusual move

can act as a pointer for further examination

Leading Banks in US in 1998 and European Banks in 1997 were allowed to use internal models to calculate Capital Charge for Market Risk

Central banks have made it mandatory to their supervised banks for quantifying market risk through VaR and to maintain minimum required capital for this quantified risk


Why VaR is Popular(2)

Choosing appropriate VaR model Required capital charge for market risk is linked

to VaR estimates Higher VaR means higher Capital Charge

Banks may have a tendency/ preference towards a model that produces lower VaR Exposed to risk beyond their capacity and may be

vulnerable to the shocks arising out of market swings


Why VaR is Popular(3) Regulators provide certain norms (such as back

testing, data period and other factors for VaR estimations, etc.) to be satisfied by the VaR estimates.

Selection of an appropriate VaR model in reality is important Produces as minimum VaR as possible and also

satisfy the regulatory requirements/norms prescribed by the regulators/Basle Committee

To minimise certain loss functions while making a choice of a VaR model from various alternatives


Drawbacks of VAR VAR system subject to

Model Risk:

Risk of errors arising from inappropriate assumptions on which models are based

Implementation Risk: risk of error arising from the manner n which the model has been implemented; common to all risk model

Assumptions : portfolio return normally distributed: existence of unusual or extreme events in market not captured by Normal Distribution

Some VAR models use historical return data: presumption that past is reliable guide to the future: Not always the case

A single VAR figure may give can give misleading information: two positions of same VAR (same confidence level and holding period


Drawbacks of VAR

Difficulties associated with capturing of reliable data

Some methods costly and difficult to set up Different method can give different VAR

estimates on daily basis for the same portfolio VAR itself is not risk management It is a tool for measuring market risk part of complete range of activities /duties of

involved in managing and minimizing financial institution’s risk exposure


VaR computation approaches

Historical Simulation

Analytic

Monte Carlo Simulation


Historical Simulation

Create a database of the daily movements in all market variables.

The first simulation trial assumes that the percentage changes in all market variables are as on the first day

The second simulation trial assumes that the percentage changes in all market variables are as on the second day

and so on


Historical Simulation continued

Suppose we use m days of historical data Let vi be the value of a market variable on

day i There are m-1 simulation trials The ith trial assumes that the value of

the market variable tomorrow (i.e., on day m+1) is

1i

im v

vv


Quantiles

Defined as values ‘q’ such that areas to their right (or left) represents a given probability “c”:

It is method of sorting the data and finding at any point how much data is their to the either side.

c=Prob (X≥q)=∫f(x).dx For normal distribution quantiles can be

found from statistical tables For a R.V Normal (0,1) : to find q for c=.95

we can use the table


Example Historical Simulation

Data for VaR historical simulation calculation

DayMarket

Variable 1Market

Variable 2…

Market Variable n

0 20.33 0.1132 … 65.37

1 20.78 0.1159 … 64.91

2 21.44 0.1162 … 65.02

. . . . .

. . . . .

499 25.75 0.1323 … 61.99

500 25.85 0.1343 … 62.1

Value of portfolio today is equal to $ 23.50 Mn


Example Historical Simulation Contd.Scenarios generated for tomorrow (Day

501)

Scenario No.

Variable 1

Variable 2

…Variab

le n

Portfolio

Value ($

mn)

Change in

value ($ mn)

1 26.42*0.137

5 … 61.66 23.71 0.21

2 26.670.134

6 … 62.21 23.12 -0.38

. . . … . . .

. . . … . . .

. . . … . . .

499 25.880.135

4 … 61.87 23.63 0.13

500 25.950.136

3 … 62.21 22.87 -0.63

*25.85 × 20.78/20.33= 26.42


Information Decay Give more weight to new information Referred as EWMA method Exponentially declining weights on historical data Smoothing is achieved by setting Lambda between

0 and 1 (Goes with our previous point) Weights totaled to be 1 Lambda at 0.97 means the weight given to the

latest price movement as 3% and declines at the rate of 97%.

JP Morgan document advocated the lambda to be at 0.94 for daily VaR and 0.97 for monthly var.

Exponential Smoothing

0*)1(


Calculation of VaR in EWMA

Apply the weight as per the lambda factor with a declining rate from recent to distant returns

Sort the returns from low to high Find the cumulative weight at any

simulated price The quintile has to be computed from the

cumulative of the weight.


Calculation under EWMADATE PRICE RETURN SIMULATED

PRICES (FOR 501)

WEIGHT (0.97) WEIGHT (0.94) Equal Weight

11/06/2008 741.20 1.40% 751.59 0.03000000 0.060000000 0.002

10/06/2008 730.95 -2.58% 722.08 0.02910000 0.056400000 0.002

09/06/2008 750.30 -2.48% 722.80 0.02822700 0.053016000 0.002

06/06/2008 769.40 -1.13% 732.82 0.02738019 0.049835040 0.002

05/06/2008 778.20 2.73% 761.40 0.02655878 0.046844938 0.002

04/06/2008 757.55 -0.39% 738.28 0.02576202 0.044034241 0.002

………. ………. ………. ………. ………. ………. ……….

………. ………. ………. ………. ………. ………. ……….

15/06/2006 482.55 6.95% 792.70 0.00000001 0.000000000 0.002

14/06/2006 451.20 -1.84% 727.57 0.00000001 0.000000000 0.002

13/06/2006 459.65 -3.07% 718.46 0.00000001 0.000000000 0.002

12/06/2006 474.20 1.05% 748.98 0.00000001 0.000000000 0.002


Calculation of VaR


Weights on Past Observations

100 75 50 25 0

Days in the Past

0.03

0.06

Exponential Model Lambda =0.94

Exponential Model Lambda =0.97

• Higher the Lambda the process of Information decay is lesser.


Lambda and VaR

Time

Va

R

Exponential Model Lambda =0.97Exponential Model

Lambda =0.94

Higher the lambda the impact of any sudden fall in the market will have long term effect on VaR.


Impact of Assumptions

Higher the confidence level higher will be the VaR

Advantage : lesser no of failure in backtesting. Disadvantage : Overestimated VaR will have

negative impact on capital adequacy. Higher the Lambda factor the VaR

movement will be low.Once there is a sudden crash in a market the

VaR will jump to higher level. This shift will stay for longer period if Lambda is high.

Lower Lambda can also cause for higher back testing failures.

Basel recommendation is to keep CI at 99%. No specification about lambda factor.


Effective Lambda

Keeping a higher lambda is defensive in nature Lower lambda may lead to frequent back

testing failures. Lambda should be in consistent with the

volatility and time taken by the market to become stabilise.

Higher lambda with short history and lower lambda with large history is a very good cushion.

JP Morgan technical doccument advocated 0.94 as the lambda for one day VaR and 0.97 for one month VaR


Effective Risk Model

If the history is 450 days then lambda should be kept at 0.94, So the chances more than 4 failures in a year is minimal.

10 day VaR should be computed from the time scaling method instead of moving window method.

The Back testing should be done with confidence level of 95% and lambda at 0.94. If the number of breaches is higher than one in a quarter the lambda should be increased to 0.95.

Monte-Carlo simulation should be done for the entire portfolio in order to expand the number of simulations and a better result.


Advantages and Limitations - Historical SimulationAdvantages

No need to assume normality No need to forecast volatility and

correlation Effective in measuring non-linear risks Based entirely on historical data, objective

Limitations Computationally more intensive vs.

variance-covariance Implied volatility and correlation can be

reversed in tail events


Stress testing and Back-testing


Back Testing Methodologies

Comparison of VaR model generated P/L against the actual P/L

Comparison of VaR model generated P/L against the theoretically calculated P/L based on the actual positions


Back-Testing A VAR Model Calculate 1-Day 95% VAR for a (changing) portfolio each day for

some substantial period of time (e.g., 100 Days) Compare the P/L on the succeeding trading day with the previous

close of business day’s VAR

Count the number of times the loss exceeds the VAR

(25,000,000)

(20,000,000)

(15,000,000)

(10,000,000)

(5,000,000)

-

5,000,000

10,000,000

15,000,000

20,000,000

25,000,000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49

P/L

VAR

95% 1 day VAR


Back Testing CL – 95% Lambda = 0.94 Exceptions


Back Testing CL – 95% Lambda = 0.94


Backtesting and AssumptionsDate P&L VaR

95/94EXCEPTION

VaR 95/97

EXCEPTION

VaR 99/94

EXCEPTION

VaR 99/97

EXCEPTION

28/07/2008 -540.59 330.50 -210.10 331.64 -208.95 409.39 -131.20 412.94 -127.65

02/07/2008 -357.27 341.41 -15.86 335.95 -21.32 434.04 76.77 432.11 74.84

30/06/2008 -352.13 261.84 -90.29 261.74 -90.39 435.40 83.27 433.14 81.01

19/06/2008 -453.58 236.43 -217.15 239.42 -214.16 242.12 -211.46 340.65 -112.93

18/06/2008 -239.42 197.41 -42.01 242.66 3.24 242.70 3.28 342.55 103.13

06/06/2008 -203.99 192.75 -11.23 244.00 40.01 276.08 72.09 354.24 150.25

21/05/2008 -221.63 136.33 -85.30 237.38 15.75 315.18 93.55 381.23 159.60

14/03/2008 -329.15 313.87 -15.29 286.97 -42.18 362.86 33.71 390.97 61.82

12/03/2008 -352.99 258.92 -94.08 258.73 -94.26 333.66 -19.33 391.41 38.42

29/02/2008 -266.16 241.34 -24.82 244.57 -21.59 400.82 134.66 447.15 180.99

21/01/2008 -402.25 352.27 -49.97 277.16 -125.09 581.81 179.56 524.44 122.19

18/01/2008 -627.90 268.17 -359.73 235.24 -392.66 283.00 -344.90 279.29 -348.61

17/01/2008 -284.75 191.55 -93.20 187.69 -97.06 250.59 -34.16 253.60 -31.15

09/01/2008 -253.15 149.58 -103.57 149.59 -103.56 182.25 -70.90 213.15 -40.00

08/01/2008 -211.11 117.26 -93.85 148.41 -62.70 184.26 -26.85 214.82 3.71

07/01/2008 -118.18 114.65 -3.53 151.38 33.20 186.10 67.92 216.21 98.03


Stress TestingObjective

To capture exposures of a portfolio to adverse discontinuous market events which are extreme but possible Historical Scenarios

To isolate exposures to the extreme historical events which exceeds the loss threshold determined based on statistical measures

Hypothetical ScenariosTo identify exposure to the extreme but possible future market events which have not yet occurred in the past

Performed at different levels (individual asset classes to portfolio level to Bank’s portfolio as a whole)


Setting VaR Limit


Evolution of VaR Applications

Passive

Defensive

Active

Reporting Risk

• Managing Reports• Disclosure to Share Holders• Regulatory Requirements

Controlling Risk

• Setting Risk Limits

Allocating Risk

• Performance Evaluation• Capital Allocation• Strategic Business decisions


Need For VaR limits

To complement other cut loss triggers. Comparing VaR Limit with stress testing. Accommodate the hedging benefits. Monitor performance of the Dealers. Capital Allocation. VaR limit is a part of the Advanced

measurement method under Basel – II Management information.


Approaches

Top Down Approach

Set the risk level from capital Set the VaR Limit for the Enterprise Set the Sub limits for the Business Groups Set the Limit for Individual Asset classes

Bottom up Approach

Set the VaR limit for individual asset class depending on volatility, current profit and unrealised profit

Analyse the correlation among scrips and asset classes

Apply the diversification benefits and set the limit for the entire enterprise.


Existing Policy

Overall VaR limit is set on the basis of the loss limit prescribed by the ALM.

The VaR limit is for the asset class is given after considering the diversification benefit

The allocation of VaR Limit is based on Volatility and maximum exposure. This limit is given in absolute amount.

Operating VaR limit is given as percentage of MTM expecting the actual exposure is less than the maximum exposure.


Performance of VaR limit

The Overall VaR limit has breached from 22nd January due to sharp decline in the Equity market. This had continued till 30th March 08.

The operative VaR limit breached from 21st January for equity and mutual funds.

The bond Market which was stable upto May started declining due to rising inflation and RBI policy to change the key rates.

Since operative VaR limit is in percentage only complete exit from the market can restore the VaR within the limit.

Bond Market is volatile and inclusion of long duration bond the effect was further worse.


Setting New Limit for VaR

Basis for the VaR Limit Capital of the bank

The capital of the bank has undergone a change so linking the VaR to overall Capital or the regulatory capital is a good measure

Volatility in the market. The allocation can be base on the volatility

of the indices and the volatility of the key securities in our portfolio.

Compare the VaR limit with the stress testing figures

Current realised and unrealised profit/loss of the portfolio.


Thank You

Documents

Var Presentation