Quantile Risk–Return Trade-Off

Nektarios Aslanidis, Charlotte Christiansen*, Christos S. Savva

*Corresponding author for this work

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We investigate the risk–return trade-off on the US and European stock markets. We investigate the non-linear risk–return trade-off with a special eye to the tails of the stock returns using quantile regressions. We first consider the US stock market portfolio. We find that the risk–return trade-off is significantly positive at the upper tail (0.9 quantile), where the upper tail is large positive excess returns. The positive trade-off is as expected from asset pricing models. For the lower tail (0.1 quantile), that is for large negative stock returns, the trade-off is significantly negative. Additionally, for the median (0.5 quantile), the risk–return trade-off is insignificant. These results are recovered for the US industry portfolios and for Eurozone stock market portfolios.

Original languageEnglish
Article number249
JournalJournal of Risk and Financial Management
Number of pages14
Publication statusPublished - Jun 2021


  • VIX
  • quantile regressions
  • risk–return trade-off
  • stock markets


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