Modified VaR Adjusts for Skewness and Kurtosis, but Tail Estimates Remain Uncertain
Summary
The discussion compares ordinary Value at Risk with modified VaR at the same confidence level. Modified VaR adjusts an empirical estimate for skewness and kurtosis, addressing features of return distributions that a normality-based VaR calculation may miss. The replies therefore present it as a way to reflect non-normal empirical returns more directly.
The answers also caution against reading too much into equality between the measures: at very high confidence levels they may coincide despite skewness or kurtosis, and both estimates can be inaccurate in the tails. One response argues that modified VaR may perform worse because it relies on non-normality assumptions, while another notes that feasible bounds can be used to check whether a modified VaR calculation falls within an acceptable range. The document supplies no comparative data, uncertainty estimates, or decision rule for choosing between the measures. It raises the limitations of VaR-based tail assessment but does not establish that modified VaR is always preferable.
Key ideas
- Modified VaR incorporates skewness and kurtosis into an empirical VaR estimate.
- Ordinary and modified VaR can be equal even when returns are non-normal, particularly at extreme confidence levels.
- Both VaR measures may be inaccurate when used to estimate extreme tail losses.
- Modified VaR's distributional assumptions and feasible calculation bounds merit scrutiny.
- The discussion offers no empirical rule for deciding which measure is preferable in a given case.
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Full text
# comparing modified VaR to ordinary VaR # comparing modified VaR to ordinary VaR What inferences can one draw when given a modified VaR at x% confidence and an ordinary VaR at x% confidence level. If the two are equal one inference can be that returns are gaussian but that also depends on the confidence level. At extremely high confidence levels mVaR can be equal to VaR even with skewness and kurtosis. So how do risk managers look at these estimates? Is the uncertainty in the estimates a concern. What if VaR is lower than mVaR and also less uncertain than mVaR. What if VaR is higher than mVaR but less uncertain than mVaR. Is mVaR always preferable? By eyeballing the loss distribution it is easy to see if there is skewness and excess kurtosis and so mVaR may be preferable but is there a case where using mVaR can be a bad idea compared to using VaR. ## Answer by Rusan Kax (score 1) https://quant.stackexchange.com/a/15934 Using anything with "VaR" in the name, is basically a bad idea. But a modified VaR does not assume a normal distributed random variable. So maybe that makes people feel a little better. mVaR might look equal to VaR at "high confidence levels" but it is well-known that both measures are inaccurate at high confidence levels. mVaR may even be worse, given the non-normality assumptions. This is homework, right? ## Answer by emcor (score 1) https://quant.stackexchange.com/a/15935 As described on this link, mVaR represents an empirical expression adjusted for skewness and kurtosis of the empirical distribution. As we know, empirical returns are commonly skewed and peaked, such that assuming normal distribution is a bad fit to estimate VaR. Therefore, mVaR adjusts for skewness and kurtosis to better reflect the empirical VaR. ## Answer by purbani (score 1) https://quant.stackexchange.com/a/17045 In this presentation https://www.academia.edu/attachments/37039957/download_file?st=MTQyNjgyNTAxNCwyMDIuMTc0LjE3MC4xNjIsMTIyMTAxMg%3D%3D&s=work_strip I show the feasible bounds for the modified VaR calculation and provide a small test to show when it is outside those bounds.
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