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# delta Normal approach

#### [email protected]

##### Member
hi David
please can you help clarify this for me?

the delta -normal approachof VaR is applied to a portfolio with a linear distribution, assuming that an asset with nonlinear distribution like a mortgage backed security is added to the portfolio , this approach becomes extremely less accurate with the result that it will generate even if the following estimator is used .
ie. VaR= modified duration * (z-critical value*stand. dev.)*portfolio value
the above can't take care of the non linear exposure introduce to the portfolio by the mortgage backed security.

is it correct to adjust the above formular by multpling the estimate or result by convexity, just to capture the nonlinear section ignored by the modified duration or ignore it completely and resort to the full valuation methods?

in case, in practical terms, this adjustment holds, how accurate is the result with respect to the full valuation methods? is tthe full valuation methods are still more accurate than this adjustment.
thank you

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi baffour,

In general, the FRM answer is that full revaluation is required (this question is almost certainly sourced from Linda Allen). It is not the non-linearity per se that creates a problem: after all, a vanilla bond price/yield curve is non-linear. So, you are quite correct that we can add a term for convexity (i.e., extend the Taylor series) to account for the non-linearity of a fixed income bond/portfolio.

However, the issue here is what Linda Allen calls "extreme non-linearity" and the negative convexity in particular. In this case, the MBS introduces negative convexity and, under the Linda Allen view, renders the delta-normal inapplicable (analytically, also, it is likely the case that the portfolio disqualifies from a taylor series: delta normal is just the first two terms of a taylor approximation). In this way, the short answer is: full re-valuation is required.

(but, again, it is not b/c the portfolio instrument is non-linear. A bond, an option are already non-linear. It's the "extreme" nonlinearity [negative convexity] introduced by the embedded call option of the MBS). I hope that explains ...
... when in doubt, in the FRM, if there is portfolio "complexity" it is a good guess to go for full re-valuation!

Thanks, David

#### [email protected]

##### Member
thanks a lot for the clarification

ba4

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