Measure of asymmetric association for ordinal contingency tables via the bilinear extension copula

Partial Asymmetry Measures for Square Contingency Tables

In square contingency table analysis, we consider a partial measure that represents the degree of departure from symmetry for each of several pairs. It may be useful to pool the values of the measure into a single summary measure of partial asymmetry. We show that the estimator of partial measures is asymptotically mutually independent for a large sample size. The present paper proposes a symmetry measure in the class of weighted averages that is different from previous studies. The proposed measure is an approximation of the measure in the class of weighted averages that has the smallest variance.

The Role of Risk Forecast and Risk Tolerance in Portfolio Management: A Case Study of the Chinese Financial Sector

Portfolio decisions are affected by the volatility of financial markets and investors’ risk tolerance levels. To better allocate portfolios; we introduce risk tolerance into the portfolio management problem by considering the risk contribution of portfolio components. In this paper, portfolio weights are allocated to two stages. In the first stage, the portfolio risks and the risk contribution of each share are forecasted. In the second stage, we put forward three weighting techniques—“aggressive”, “moderate” and “conservative”, according to three standard levels of risk tolerance. In addition, a new risk measure called “joint extreme risk probability” (JERP), with risk tolerance taken into account, is proposed. A case study of the Chinese financial industry is conducted to verify the performance of our methods. The empirical results demonstrate that weighting techniques constrained by risk tolerance lead to higher gains in a normal market and less loss when a market is risky. Compared with risk-tolerance-adjusted strategies, the relationship between the performance of the traditional conditional value at risk (CVaR) minimization method and the market risk level is less obviously demonstrated. Viewed from the results, JERP functions as an effective signal that helps investors to deal with potential market risks.