Var Presentation

Value-at-Risk

Market Risk Management

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 Management

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

Market Risk Management

Assessment of Market Risk 

Important in terms of:  Management

information

 Setting

limits  Resource allocation (risk/return tradeoff)  Performance evaluation  Regulation

Market Risk Management

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)

Market Risk Management

Value at Risk (VaR) The maximum amount of money that may be lost on a portfolio

Statistical estimate of

over a given period of time with a given level of confidence under normal market conditions

Market Risk Management

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 



If the VaR for one day horizon and at a confidence level of 95% is Rs.10 mn, that means: 



“What loss level is such that we are X% confident it will not be exceeded in N business days?”

The likelihood that our losses will exceed Rs.10 mn over the next 24 hours is 5%

Concept of “Tail Risk”

Market Risk Management

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

Market Risk Management

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.

Market Risk Management

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.

Market Risk Management

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



Market Risk Management

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

Market Risk Management

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

Market Risk Management

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 Market Risk Management

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

Market Risk Management

VaR computation approaches 

Historical Simulation



Analytic



Monte Carlo Simulation

Market Risk Management

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

Market Risk Management

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 vi

vm

vi −1

Market Risk Management

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

Market Risk Management

Example Historical Simulation Data for VaR historical simulation calculation Day

Market Variable 1

Market 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 Market Risk Management

Example Historical Simulation Contd. Scenarios generated for tomorrow (Day 501) Scenario Variabl Variabl Variabl … No. e1 e2 en

Portfolio Value ($ mn)

Change in value ($ mn)

1

26.42*

0.1375 … 61.66

23.71

0.21

2

26.67

0.1346 … 62.21

23.12

-0.38

.

.

.

…

.

.

.

.

.

.

…

.

.

.

.

.

.

…

.

.

.

499

25.88

0.1354 … 61.87

23.63

0.13

500

25.95

0.1363 … 62.21

22.87

-0.63

*25.85 × 20.78/20.33= 26.42 Market Risk Management

Exponential Smoothing 

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%. 0

(1 −λ) * λ



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

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.

Market Risk Management

Calculation under EWMA DATE

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

Market Risk Management

Calculation of VaR

Market Risk Management

•

Weights on Past Observations

0.06

Higher the Lambda the process of Information decay is lesser. Exponential Model Lambda =0.94

0.03

Exponential Model Lambda =0.97

1

75

50

25

0

Days in the Past Market Risk Management

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

Exponential Model Lambda =0.97

VaR

Exponential Model Lambda =0.94

Time Market Risk Management

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 Market Risk Management 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 Market Risk Management

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.

Market Risk Management

Advantages and Limitations Historical Simulation Advantages  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

Market Risk Management

Stress testing and Backtesting

Market Risk Management

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

Market Risk Management

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 P/L

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

VAR

(5,000,000)

(10,000,000)

(15,000,000)

95% 1 day VAR (20,000,000)

(25,000,000)

Market Risk Management

Back Testing CL – 95% Lambda = 0.94 Exceptions

Market Risk Management

Back Testing CL – 95% Lambda = 0.94

Market Risk Management

Backtesting and Assumptions Date

P&L

VaR 95/94

EXCEPT ION

VaR 95/97

EXCEPT ION

VaR 99/94

EXCEPT ION

VaR 99/97

EXCEPT ION

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

Market Risk Management

Stress Testing Objective

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 Scenarios To 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)

Market Risk Management

Setting VaR Limit

Market Risk Management

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

Market Risk Management

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.

Market Risk Management

Approaches Top Down Approach    

Set Set Set Set

the the the the

risk level from capital VaR Limit for the Enterprise Sub limits for the Business Groups 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. Market Risk Management

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. Market Risk Management

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.

Market Risk Management

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. Market Risk Management

Thank You

Market Risk Management