Quantifying mortality risk in small defined-benefit pension schemes
  A risk of small defined-benefit pension schemes is that there are too few members to eliminate idiosyncratic mortality risk, that is there are too few members to effectively pool mortality risk. This means that when there are few members in the scheme, there is an increased risk of the liability value deviating significantly from the expected liability value, as compared to a large scheme.   We quantify this risk through examining the coefficient of variation of a scheme's liability value relative to its expected value. We examine how the coefficient of variation varies with the number of members and find that, even with a few hundred members in the scheme, idiosyncratic mortality risk may still be significant. Using a stochastic mortality model reduces the idiosyncratic mortality risk but at the cost of increasing the overall mortality risk in the scheme.   Next we quantify the amount of the mortality risk concentrated in the executive section of the scheme, where the executives receive a benefit that is higher than the non-executive benefit. We use the Euler capital allocation principle to allocate the total standard deviation of the liability value between the executive and non-executive sections. We find that the proportion of the standard deviation allocated to the executive section is higher than is suggested by an allocation based on the members' benefit amounts. While the results are sensitive to the choice of mortality model, they do suggest that the mortality risk of the scheme should be monitored and managed within the sections of a scheme, and not only on a scheme-wide basis. 
Catherine Donnelly
q-fin.RM