Which of the following statements is true in respect of different approaches to calculating
VaR?
I. Linear or parametric VaR does not take correlations into account
II. For large portfolios with little or no optionality or other non-linear attributes, parametric
VaR is an efficient approach to calculating VaR
III. For large portfolios with complex sources of risk and embedded optionalities, the fullrevaluation method of calculating VaR should be preferred
IV. Delta normal local revaluation based VaR is suitable for fixed income and optionportfolios only
Select an option, then click Submit answer.
Reference / correct answer:
: This question is different in that it uses terminology you will not find in the PRMIA handbook. Yet it is important to understand these as there may be a question based on this slightly different terminology. (It is only the terminology that is different, the concepts are the same.)
If you read the PRMIA handbook, there are three methods of calculating VaR: Analytical or parametric, historical simulation and Monte Carlo simulations. There is one more way of categorizing the methods of calculating VaR, and these are as follows:
1. Local valuation: This refers to analytical or parametric VaR. This relies upon a neat statistical formula to calculate VaR and assumes a normal distribution. It also relies upon a known covariance matrix between the different components of VaR. Local valuation based VaR is further subdivided into two types:
a. Linear VaR: Linear VaR is calculated assuming the portfolio is linear, and its valuechanges just based upon the delta of the portfolio. In such cases, once a change (eg, in stock values) is known, that change is multiplied by the delta alone to get the VaR. Second order effects, such as gamma or convexity are ignored.
b. Non-linear VaR: Non linear analytical VaR is calculated using both delta and the secondderivative, ie gamma or the convexity. This is more accurate if the portfolio is non-linear. The key thing about 'local revaluation' VaR is that it does not require us to reprice or completely value all instruments in the portfolio. All we have to know is the delta (or the gamma and convexity as well) and multiply that with the number of standard deviations of change in the risk factor that we are interested in. So if we are considering a bond, we don't have to recalculate the new value of the bond as we can just use the delta. This can be a significant computational advantage for a large financial institution where there may be a large number of positions.
2. Full revaluation: This refers to a VaR method where the asset in question is fully repriced based on the new value of the risk factor - and this includes both historical and Monte Carlo based VaR methods.
Local revaluation, or analytical method based VaR is computationally easier to calculate, specially if based on just the delta-normal method (ie ignoring second order effects from convexity or gamma). But it will give incorrect results if the portfolio includes substantial non-linearity or other complexities. The full revaluation methods will always give the correct results, but they can be computationally difficult to arrive at.
Statement I is completely inaccurate - local revaluation methods do take correlations into account through the correlation or covariance matrices. Statement IV is false too - the 'delta normal' VaR refers to Var calculations based upon just the delta and do not account for the convexity or optionality. Statements II and III are correct. Therefore Choice 'c' is the correct answer.
