Modified Value at Risk

This Excel spreadsheet implements a Modified Value at Risk (or MVaR) calculation, which adjusts the standard deviation to account for skew and kurtosis in the returns distribution (greater negative skew and kurtosis act to increase VaR).

Value at Risk (VaR) is widely used in the risk management industry to quantify the risk of an investment.  However, the standard method for calculating VaR is not appropriate for returns distributions that are assymetric, or display fat tails (i.e. low-probability, high-impact returns).

Modified Value at Risk (or MVaR) calculation, however, adjusts the standard deviation to account for skew and kurtosis in the returns distribution (greater negative skew and kurtosis act to increase VaR).  MVaR is defined by the following equation.

where μ and σ are the mean and standard deviation, S is skew, K is kurtosis, z_c is the quantile of the distribution and Z is the Cornish-Fisher asymptotic expansion for the quantile of a non-gaussian distribution.

The mean, standard deviation, skew and  kurtosis are calculated from the observed returns.

MVaR has the same easy-to-understand basis as the standard VaR calculation, but still shares some of the same drawbacks as well, which I’ve described in a previous blog post. Additionally, Cavenaile & Lejeune (2010) conclude that confidence levels below 95.84% should not be used to calculate MVar so that investors’ risk preference for kurtosis are maintained (i.e.so that Z increases as kurtosis decreases)

Download Excel spreadsheet to calculate Modified Value at Risk