The effect of aggregation on extremes from asymptotically independent light-tailed risks

Portfolio risk diversification is a well established concept in finance. While aggregation of several risky assets generally reduces the overall investment risk due to diversification, the effectiveness of diversification depends on the stochastic behaviour of the returns of the assets comprising the portfolio. The paper proposes a new approach to quantifying the effect of portfolio tail diversification by looking at the asymptotic behaviour of the ratio of the largest loss on the portfolio to the sum of the largest losses on the individual investments held on the stand-alone basis. It is assumed that independent and identically distributed random vectors from the underlying distribution, describing the behaviour of returns on the assets in the portfolio, can be scaled to converge onto a deterministic limit set. This property is satisfied by a number of distributions commonly used in finance. Several analytical examples are given to illustrate the proposed asymptotic diversification index as a measure of the effect of risk aggregation on extremes as well as to quantify the impact of dimension on the diversification and as a tool in optimal portfolio selection.