Assessing stochastic dominance of downside and upside financial risk profiles using the block maxima method in extreme value theory

This paper aims to assess the stochastic dominance of the extreme downside (negative return) and upside (positive return) risk profiles of three US stock market indices, namely NASDAQ Composite, S&P 500 and Dow Jones Industrial Average (DJIA) based on the block maxima method in extreme value theory. The extreme downside and upside risk profiles were developed using two datasets of 360 monthly minimum and maximum daily log returns respectively (from January 1992 to December 2021). Extreme losses beyond the 80th percentile (corresponding to a tail probability of less than 0.2) of the theoretical extreme risk profiles were adopted to investigate stochastic dominance. Pairwise comparisons show that the DJIA stochastically dominates the other two indices in both extreme negative and positive returns. Moreover, the extreme upside risk profile of the DJIA stochastically dominates its extreme downside risk profile. The paper finds that investment in short positions (encountering upside risk) provides the least extreme risk compared with long positions (encountering downside risk) for the DJIA, as well as both short and long positions for the S&P 500 and NASDAQ Composite.