Abstract
This note compares three different risk measures based on the same stock return data: (1) the portfolio variance as in Markowitz (1952), (2) the value at risk based on the historical return distribution, and (3) the value at risk based on a t copula. Unless return series follow a Normal distribution, Normal-based risk measures underestimate risk, particularly so during periods of market stress, when accurate risk measurement is essential. Based on these insights, we recommend that supervisors discontinue to accept Normal-based value at risk estimations. We are happy to share our commented R-code with practitioners who wish to implement our methodology. Risk measurement is the foundation of risk management and hence of vital importance in any financial institution. Supervisory capital requirements according to Basel III or Solvency II are also derived from risk measures. Investors are interested in ratings which are based on risk assessments. This note is therefore relevant to practitioners and supervisors alike.
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