Abstract
The paper deals with the second-order stochastic dominance relation and its necessary conditions. Assuming a discrete distribution with many atoms, the second-order stochastic dominance implementation in portfolio optimization is extremely computationally costly, especially if atoms are not equiprobable.
On the other hand, there exist necessary conditions for this relation (based on comparisons of mean and minimal realization) which are easy to apply. Therefore, this paper explores the strength of these necessary conditions when considering financial data.
In particular, daily returns of 49 industry portfolios from the Kenneth French library from the last 50 years are analysed. First, the number of pairs of portfolios fulfilling the necessary condition is calculated.
Second, the number of pairs obeying also the second-order stochastic dominance is identified. Finally, the dependence between the strenght of the necessary condition and correlation (average mean return) of portfolios is investigated.
The whole empirical analysis is performed using annual moving (non-overlapping) window approach.