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Question

  • Since CVaR is a concept that can be applied to all probability distribution, even if they do not follow normal distribution, I thought CVaR should be more concerned with median, not the mean of return of any asset.
  • However, I haven't heard any about 'Median - CVaR portfolio optimization technique', whereas we have a mean-CVaR portfolio optimization technique. You can read research papers like 'CVaR Robust Mean-CVaR Portfolio Optimization' to get more information about 'mean-CVaR portfolio'
  • I am wondering why there is no such thigs as 'median - CVaR portfolio optimization'.
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Mean-CVaR portfolio optimization is an alternative to the more widely known and simpler mean-variance model. Since there doesn't seem to be any median-variance model out there, the familiarity surrounding the traditional model stuck.

The mean is an actual equation with convenient properties in statistics, whereas the median is obtained through a counting procedure. The use of median asset returns is absent in finance, even though estimates of mean asset returns have been shown to be unreliable.

Does calculating median asset returns as an input drastically improve the portfolio solution enough from the usual mean asset returns to write a whole paper on the topic?

Robust statistics and resistant regression models often use estimators based on the median instead of the mean, and the absolute loss function instead of the widely used squared loss function, so you have a good point anyway.

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