Definition of different VaR types

[michael4129]

Could you please specify/summarize the explanation of the following types of VaR:
- Marginal VaR
- Component VaR
- Incremental VaR

Thank you!

Michael

 

[ShaktiRathore]

hi
Marginal var is the change in the portfolio var with a unit change in position of the portfolio. Thus MVar=dVaR/dw is the slope of tangent to the Var curve Vs the position w. Thus MVar=d(sigma(p)*z*Vp)/d(wi*Vp) =z*Vp*d(sigma(p))/Vp*d(wi)=z*d(sigma(p))/d(wi)=z*Beta(i)*sigma(p)=[z*Cov(i,p)/sigma(p)^2]*sigma(p)=z*Cov(i,p)/sigma(p)

Component Var is the Mvar*w can be seen as the approximate change in portfolio Var with the change in value of position w. For e.g. if the position has weight wi in the portfolio then it component Var is the (VaRp/Vp)*Beta*wi*Vp=VaRp*Beta*wi

Incremental Var is the change in portfolio Var once the position has been removed/added from portfolio. For e.g. if I remove or add some position to the portfolio than new Var of portfolio is Var2 and if the original Var was Var1 before the addition/deletion than the incremental Var due to the new position added/deleted from portfolio is the increase in Var= Var2-Var1

also refer to the links:
http://forum.bionicturtle.com/threa...al-value-at-risk-var-level-2.4961/#post-13451

thanks