Extreme Value-at-Risk of Bulgarian shares

Methodology: Extreme Value Theory (EVT) provides an alternative approach for the classical Value-at-Risk that is based on statistics as mean and standard deviation, as well as normal distribution assumption. Instead, EVT focuses not on the average numbers, but on extremes. And as such a background is the Generalized Extreme Value Distribution (GEV).

We collected daily close price series for a 2-year period: Sept 10, 2012 – Sept 10, 2014 (making 496 return series) for 7 stocks – Sopharma, Matlab, Advance Terrafund RETI, Fist Investment Bank, Chimimport, Eurohold and M+S Hydraulic. We then extract the worst 25 returns for each of the stocks, making 175 observations for the worst returns of all 7 stocks. Matlab’ gevfit function to the 175 worst returns is used to extract the three parameters - namely z, b, and a. Having the 3 parameters the approach for Extreme Value-at-Risk (EVaR) suggested by Quant at Risk is used, namely:

Data: The charts below present a hypothetical equally-weighted portfolio during the 2-year period. An interesting chart is the one showing the number of the standard deviations from the average, revealing how misleading could be the standard normal distribution assumption (we charted the absolute values of the standard deviations). There are too many extreme returns during the period that should not occur so often under the rules for normally distributed data. But they do, nonetheless and we should be prepared to such events.

1-day Extreme Value-at-Risk Results: We have a Fréchet distribution given the negative z as data was fit with negative signs (the daily losses). The resulted 1-day 95% confidence interval EVaR is -8.12%! This implies that among the 7 stocks at the specified significance level we should expect extreme loss of 8.12%. That’s really huge expected loss. But we have a 1-day 27.6% loss, the second and third worst losses are 17.2% and 15.2% respectively. So, it is a really period of extremes and normal distribution would hardly do a job here.

But how it compares with the VaR of the stocks we analyse? Below is a table of the results of VaR of the individual stocks based on two VaR approaches – one is based on empirical distribution and the second is based on normalised distribution (histogram):

This publication is for information purposes only and should not be construed as a solicitation or an offer to buy or sell any securities. 

Extreme acknowledgments are due to Pawel Lachowicz and his Quant at Risk!