1. Andrei Iulian Andreescu
Application of Value-at-Risk Methods for Measuring of the Financial Risk
Andrei Iulian Andreescu

2. Agenda Introduction Definition of the financial risk
Financial risk measurement techniques
The VaR concept
Application of VaR methods
Conclusion

3. Introduction
The need for an effective risk measurement system for companies and institutions
Worst case scenarios unlikely to happen, but very dramatical consequences for real economy
Most recently: Financial crisis from 2008
Negative effects: Spill over on the real economy
Andrei Andreescu

4. Risk Measurement Techniques
Year
Instrument
1938
Bond duration
1952
Markowitz mean-variance framework
1963
Sharpe‘s CAPM
1966
Multiple factors models
1973
Black-Scholes option pricing model „Greeks“
1988
Risk-weighted assets for banks (Basel)
1993
Value at Risk
1994
Risk metrics
1997
Credit metrics
1998
Integration of credit and market risk
Risk budgeting …
Andrei Andreescu

5. The VaR concept: Definition
The maximum expected loss for a portfolio for a specific time frame with a certain probability - Market price risiko model.
Parameters: holding period (1-30 days) and confidence level (90-99%)
Andrei Andreescu

6. The elements of a VaR system
Source: Jorion (2003), p. 256.
Model
Mapping
Risk factors
Portfolio
Historical data
Portfolio positions
VaR method
Distribution of risk factors
Exposures
Result
Andrei Andreescu

7. Overview of the VaR methods
Local valuation :
Linear models, Full covariance matrix, Factor models, Diagonal models
Non linear models: Gama, Convexity
Full valuation:
Historical Simulation
Monte Carlo Simulation
Andrei Andreescu

8. Application of VaR methods
A hypothetical portfolio consisting of assets in five different currencies USD, GBP, CHY, CHF, PLZ.
German exports in 2010 in non Euro zone
Source: German Statistical Bureau (2010), p. 2.
 Countries
Mio. € %
USA
65570
25% 25
Great Britain
59487
23% 23
China
53636
21% 21
Switzerland
41711
16% 16
Poland
38053
15% 15
Total
258457
100%
100
Andrei Andreescu

9.
Andrei Andreescu

10. Time frame from 01.01.2007 until 19.04.2011 Portfolio value 100 Mio. €
Source: Own calculations
Time frame from until
Portfolio value 100 Mio. €
Confidence level 90-99%
Time horizon 1-10 days
Andrei Andreescu

11. Delta-Normal method 1/2 Variance-covariance method Portfolio return
Portfolio variance
Value at Risk
Andrei Andreescu

12. Delta-Normal method 2/2 Step 1: Collect the historical data
Step 2: Potential mapping of the security positions
Step 3: Calculate weights, standard deviation, and correlation coefficient.
Step 4: Estimate the VaR by multiplying the portfolio standard deviation by the portfolio value and by the parameter specifically for the desired confidence level.
Pros: Easy to implement, small number of necessary data
Cons: Normal distribution of the returns, non suitable for non linear instruments
Andrei Andreescu

13. Comparison of VaR using Delta-Normal method
Time horizon
Confidence level
1 day
2 days
3 days
4 days
5 days
10 days
90%
0,46%
0,68%
0,85%
0,99%
1,12%
1,66%
95%
0,58%
0,87%
1,09%
1,27%
1,44%
2,14%
99%
0,83%
1,23%
1,54%
1,80%
2,03%
3,02%
Andrei Andreescu

14. Historical Simulation 1/2
No assumptions about the distribution of the risk parameters
Portfolio return
Step 1: Calculation of the daily returns
Step 2: Compute the market value of the assets and revaluating the portfolio.
Step 3: Sort the series of simulated profit and losses.
Step 4: For the desired confidence level, read the value of the simulated VaR.
Andrei Andreescu

15. Historical Simulation 2/2
Pros:
Easy to use and to communicate to the interested outsiders.
No estimation of volatility or correlation is necessary.
In the most case, the necessary past data are available.
Since there are no assumptions made regarding the distribution, tail, skewness and different non-normal features can be considered.
Cons:
If this time frame does not consider some likely market movements, than the calculated risk will probably be biased.
A very long data set leads to aged data and distortion of future results due to past events which are not longer likely to recur.
The news will have an underestimated impact on the VaR, due to their relatively low weight.
The volatility through time is assumed to be constant.
Andrei Andreescu

16. Comparison of VaR using historical simulation
Time horizon 
Confidence level
1 day
2 days
3 days
4 days
5 days
10 days
90%
0,44%
0,61%
0,81%
0,93%
1,07%
1,55%
95%
0,67%
0,85%
1,13%
1,24%
1,39%
2,08%
99%
2,15%
2,92%
4,07%
4,14%
4,21%
4,97%
Andrei Andreescu

17. Monte Carlo Simulation 1/2
A random generator of numbers for estimation of risk
Based on assumptions about distribution of the risk parameters
Step 1: A stochastic process including the distribution and the parameters of the portfolio positions must be chosen.
Step 2: A pseudo-sequence of variable must be generated. These means that pseudo future returns will be generated.
Step 3: The value of the portfolio will be calculated using the prices for the target time frame.
Step 4: Step 2 and 3 will be repeated for many times
Step 5: Rank the simulated prices and calculate VaR
Andrei Andreescu

18. Monte Carlo Simulation 2/2
Pros:
A wide range of market behavior can be captured and analyzed.
Complicated financial instrument such as mortgages, credit derivates, and nonlinear paths can also be successfully analyzed.
The impact of extreme scenarios can also be simulated.
Finally, extreme events do not influence the result as much as using the Historical Simulation method.
Cons:
The long computational time.
It is also costly to implement the necessary operational infrastructure, both in terms of hardware and in terms of employing highly skilled operators.
Finding a proper fitting of the joint distribution takes a lot of effort.
The stochastic models used for the risk modeling can be wrong.
Andrei Andreescu

19. Comparison of VaR using Monte Carlo Simulation
Time horizon
Confidence level
1 day
2 days
3 days
4 days
5 days
10 days
90%
0,35%
0,49%
0,68%
0,71%
0,81%
1,19%
95%
0,47%
0,67%
0,86%
0,87%
1,03%
1,57%
99%
1,09%
1,40%
2,17%
1,98%
2,01%
2,89%
@RISK Correlations UK
USA
Swiss
Zloty
Yuan 1 0, 0, 0, 0,
-0,
-0, 0, 0, 0,
-0,
Andrei Andreescu

20. Inputs (Monte Carlo Simulation for the 10 day Rate of Return
Dataset #19 hs
AF1136
RiskLogistic(0, ;0,010633;RiskName("Dataset #19");RiskCorrmat(NewMatrix7;1)) -∞ 0, +∞
Dataset #20
AG1136
RiskLogistic(0, ;0,012789;RiskName("Dataset #20");RiskCorrmat(NewMatrix7;2)) 0,
Dataset #21
AH1136
RiskLogistic(-0, ;0, ;RiskName("Dataset #21");RiskCorrmat(NewMatrix7;3))
-0,
Dataset #22
AI1136
RiskLoglogistic(-0,15731;0,15597;14,007;RiskName("Dataset #22");RiskCorrmat(NewMatrix7;4))
-24,61102
Dataset #23
AJ1136
RiskLogistic(-0, ;0,012073;RiskName("Dataset #23");RiskCorrmat(NewMatrix7;5))
-2,5645
Distribution Fitting (Dataset #19)
Correlation Matrix – 10 day Rate of Return
@RISK Correlations
Dataset #19 in $AF$1135
Dataset #20 in $AG$1135
Dataset #21 in $AH$1135
Dataset #22 in $AI$1135
Dataset #23 in $AJ$1135 1 0, 0, 0, 0,
-0,
-0, 0, 0, 0,
-0,

21. Criticism of VaR Pros: Cons:
Increased the quality of risk and corporate management / bank supervisory
Common risk measurement for different risk positions
Considers correlations between risk factors
Cons:
It is not subadditive, therefore no coherent
It is only quantitative and not qualitative
Inconsistent result by using different methods
Andrei Andreescu

22. Results of the VaR calculation
VaR depends positively on the confidence level and on the time horizon
The choice of the VaR method depends on many factors:
Legal constrains
Software tools and distribution assumptions
Accuracy of the calculation
Necessary effort and available data
Andrei Andreescu

23. Market Risk Amendment and VaR
The MRA specifies the dependence of the required capital on VaR
Standard calculation of VaR: 10 holding days, 99% confidence level
The multiplicator k depends on the time that bank daily losses exceed the estimated VaR in the last 250 trading days.
Wrong estimation of daily losses
Model accuracy and k value
≤ 4
Model is accurate, k=3
5≤9
Model is accurate, k increases
≥10
Model needs revision, k=4
Andrei Andreescu

24. Conclusion Definition, history of risk
Presentation of typical risk metrics
Popular VaR methods
Delta-Normal
Historical Simulation
Monte Carlo Simulation
Empirical part: Different VaR result using different VaR methods, consequences for the capital holding requirements
Andrei Andreescu

25. Thank you for your attention!
Andrei Andreescu