VaR and BackTesting

[floyd2]

Hello, i'm new to this site, i really like it up to now. I have two questions if you can help me,

Why do we choose to do backtesting with a VaR with one day horizon and a VaR with ten days horizon when computing capital requirements for market risk?

what is the actual VaR calculated in a bank, i mean the one on which apply scaling to compute for other horizons?

Thank you for your answers!

 

[RiskNoob]

Welcome to the BT forum - It is great to see candidates preparing the exam in the new year already! I think it is suitable to post thread ‘P2.T5. Market Risk (25%)’ instead…

Briefly, for the first part of the first question, choosing one-day horizon VaR produces more data than other (longer) horizons. The reliability of (hypothesis) backtesting depends on the number of historical data.

For the other questions, I recommend you take a look at the section 1.2 new assigned Basel reading “Messages from the academic literature on risk measurement for the trading book”. The interesting points are…

-Is ten days an appropriate horizon?
... the appropriate horizon for VaR should depend on the characteristics of the position (e.g. liquidity)

-Is square-root of time scaling a good idea?
... scaling today's VaR by the sqaure root of time ignores time variation in the distribution of losses

RiskNoob

 

[floyd2]

Thank you so much for the quick and accurate answer!

Sorry, I didn't know that it wasn't the suitable place to post it.

Yes, i have got an exam of Risk Management next Thursday, i need to review my copula functions :/ the hardest part of all.

 

[RiskNoob]

Copulas are briefly mentioned in FRM P2 curriculum (Appendix from Dowd) so I think it is better to focus at the study material from your study. Good luck on the exam!

RiskNoob

 

[JayC]

Hello,
Could someone please help me on this calculation : I am trying to calculate a portfolio VaR (5 or 6 assets).
I have already done it for 2 assets using the following formula : VaR (asset 1 + asset 2) = sqrt (VaR asset1 ^2 + VaR asset2 ^2+ 2 * VaR asset1 * VaR asset 2 * correlation12).
What similar formula shoud I use for 5, 6 or n assets ?

 

[RiskNoob]

I am guessing you are referring to 'relative' VaR in Jorion Ch 7, where the drift (mean) is excluded in the calculation of VaR.

In that case, I recommend that you would review some linear algebra, since the (Jorion's Ch 7) Portfolio VaR is defined using inner product:

(Diversified portfolio) VaR= deviate * volatility_p * DollarValue_p,

where volatility_p * DollarValue_p is sqrt of inner product of dollar weights (of n assets) vector x and linear transformation of the covariance matrix (of n assets) and the dollar weights vector , or sigma * x.

In other words, volatility_p * DollarValue_p = sqrt ( x^transpose * sigma * x), where sigma = (covariance_ij), x = (xi)

Due to the curse of dimensionality so it would be very time consuming to do the calculation for 5,6 or n assets. For the exam purposes, I don't think it is a good idea to find the formula for more than 2 assets.

RiskNoob

 

[jonnblaze]

Thank you so much for the quick and accurate answer! you are amazing

 

[amal]

Hi every one plzzzz help me
i need to backtest VAR and ES , i dont know how to use kupiec test or the rolling window estimates!! they told me i should try to do it
usig R. backtesting package but i didn't find it!!
any one can help me plzzz

 

[ShaktiRathore]

Hi
Kupiec test is simple its use of loglikelihood ratio to determine whether the Var model is accurate or not.
See formula for LR ratio here:http://www.bizresearchpapers.com/2. Navneet Kaur.pdf page 17.
If the ration LR>3.84 then reject the model otherwise accept is its less than this value. Just use the LRpof formula for your data set over a period T, x the number of exceptions gave out by your model. I think in R you can carry out the operation: for different periods of time Var models test by computing LR for each period and then test for condition. And do it this way at a certain confidence level.
You just need to carry out these 2-3 tests given in the pdf by using the formulas given and get the ratios for your data as per the formula and conclude based on the ratio and the condition this is just what you have to do.No big task .
thanks

 

[amal]

hi thank you for your answer,
in fact the problem is not how to apply these formula, but how can i get a daily VAR etimates to compare it and then
get the number of exceptions!!
my problem is that i got only one VAR per confidence level for one day estimation , but a daily VAR!!!
that's my problem how can i get it??
thank you