Which of the following situations are not suitable for applying parametric VaR:

I. Where the portfolio’s valuation is linearly dependent upon risk factors

II. Where the portfolio consists of non-linear products such as options and large moves are involved

III. Where the returns of risk factors are known to be not normally distributed

A . I and II

B . II and III

C . I and III

D . All of the above

**Answer: **B

Explanation:

Parametric VaR relies upon reducing a portfolio’s positions to risk factors, and estimating the first order changes in portfolio values from each of the risk factors. This is called the delta approximation approach. Risk factors include stock index values, or the PV01 for interest rate products, or volatility for options. This approach can be quite accurate and computationally efficient if the portfolio comprises products whose value behaves linearly to changes in risk factors. This includes long and short positions in equities, commodities and the like.

However, where non-linear products such as options are involved and large moves in the risk factors are anticipated, a delta approximation based valuation may not give accurate results, and the VaR may be misstated. Therefore in such situations parametric VaR is not advised (unless it is extended to include second and third level sensitivities which can bring its own share of problems).

Parametric VaR also assumes that the returns of risk factors are normally distributed – an assumption that is violated in times of market stress. So if it is known that the risk factor returns are not normally distributed, it is not advisable to use parametric VaR.