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Friends or Foes : a Story of Value at Risk and Expected Tail Loss

Since the introduction by Artzner (1997, 1999) of coherent risk measures and the new dawn of measuring extreme losses it seems as if the academic community is willing to sacrifice and erase all the advances made in the field of measuring VaR. Expected tail loss (ETL) as a risk measure is superior to VaR since VaR is not a coherent risk measure, in that it does not encourage diversification and completely ignores extreme events. On the other hand, sophistication of VaR models has reached formidable levels, while ETL estimation is still in its beginnings and usually it is calculated via parametric approach based on Generalized extreme value distribution or nonparametric approaches such as fitting kernels to historical simulation. I propose using advanced VaR calculation techniques to produce superior ETL forecasts that are reactive to changes in volatility levels, do not presume any theoretical distribution of the tails and are not limited to the historical data set. The proposed ETL measure is semi-parametric in its nature and uses volatility transformed tail data. The paper also proposes a new loss function that relates tail losses to ETL forecasts. Testing of VaR and ETL models is performed on US and European stock indexes (DOW JONES, NASDAQ, S&P500 (US), FTSE (Great Britain), DAX (Germany) and CAC (France)).

coherent risk measures; expected tail loss; value at risk; extreme value theory; bootstrapping

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