VaR BackTesting

VaR Analysis:-

One of widely used risk metric in financial industry is VaR(Value At Risk) .VaR is a risk measure which will give a magical number about loss (for a given period D with probability p% loss will not exceed x%).

For effective backtesting, VaR should exhibit following desirable characters:-
                 1)  Unbiasedness   [Average of Indicator Variable should be x%].
                  2) Don'tBunchUp [VaR estimates do not bunch up over a particular state of economy].

Verification:-
Backtesting is used to verify VaR validity[accept or reject], Major concerns here is to balance following types of errors:-

                 1) Type-I Error  [Possiblity that an accurate risk model would be classified as inaccurate].
                 2) Type-II Error [Possiblity that an inaccurate model would not be classified as accurate].

There is no statistical way to handle both Type I & Type II error so Basel came up with zone based approach of handling VaR and deciding Risk Weight.

	Zone	Description	Exceptions Count	Scaling factor Increase	Cumulative Probability
	Green Zone	Test results are consistent with an accurate model, And the possibility of erroneously accepting an Inaccurate model is low.	0	0	8.11%
			1	0	28.58%
			2	0	54.32%
			3	0	75.81%
			4	0	89.22%
	Yellow Zone	Test results are either consistent with either accurate or Inaccurate models, and the supervisor should encourage A bank to present additional information about its model Before taking action.	5	0.4	95.88%
			6	0.5	98.63%
			7	0.65	99.60%
			8	0.75	99.89%
			9	0.85	99.97%
	Red Zone	Test results are extremely unlikely to have resulted From an accurate model, and the probability of Erroneously rejecting an accurate model on this Basis is remote.	10 or more	1	99.99%

SASImplementation

VaRData:-
Data table contains Observations  containing (Date,PredictedVaR and ActualLoss), as below:-

Obs	DATE	PredictedVaR	ActualLoss
1	13894	102232	400000
2	13895	496875	450000
3	13898	406250	393750
4	13899	306250	387500
5	13900	506250	387500
6	13901	506250	475000
7	13902	510938	475000
8	13905	515625	478906

Backtesting Result:-

Using below procedure we get ExceptionCount and Zone in which VaR lies.  

proc IML;

 use Work.VarData;

 read all var {"ActualLoss","PredictedVaR"};

 close Work.VarData;

 indicatorVar             =(ActualLoss>PredictedVar);

 excessLoss               =(ActualLoss-PredictedVar);

 ExceptionCount       = indicatorVar[+,1];

 ExcpetionPercentage=(ExceptionCount/nrow(indicatorVar));

 if ExceptionCount > =10 then do;

   Zone="Red Zone";

 end;

 else do;

    if ExceptionCount <= 4 then do;

      Zone="Green Zone";

    end;

    else do;    

      Zone="Yello Zone";

    end;

 end;

 print Zone ExceptionCount ExcpetionPercentage;

run; 

Zone	ExceptionCount	ExcpetionPercentage
Green Zone	2	0.25

Conclusion:-

After analysis of ActualLoss & PredictedVaR we calculated ExceptionCount and then found the VaR is in Yellow Zone.So not a big problem :). 

Based on 

Thanks & Regards,

Srinivasan