How the Risk Measures Play Important Roles for Tail Risk Management and Diversification

Abstract

In the world of investment, the subject of building a portfolio concerning tail risk is still one of the frequently discussed subjects and unquestionably vital for investors. This paper seeks to examine how the risk measures, lower tail-dependence based on the copulas approach and Conditional Value-at-Risk (CVaR), affect the portfolio strategies and play important roles for tail risk management and diversify the portfolio. By using these two risk measures mentioned above, two different types of risk-based portfolios are proposed that consider for the tail risks: 1) Minimum-lower tail-dependence portfolio (RMTP) and 2) Risk Parity Portfolio based on Conditional Value-at-Risk (CRPP). The simulation results showed how those two risk-based portfolios, RMTP and CRPP, work effectively in multi-asset allocation framework with 6 assets: stocks and sovereign bonds of Japan, United States and Germany, based on the monthly rebalance rule, using 2004-2018 sample period. One of the key findings were that both RMTP and CRPP strategies delivered better performances compared with the traditional portfolio strategies in terms of sharp ratio: 1) RMTP yielded 0.92 and 2) CRPP yielded 0.99 (by adding an appropriate risk reduction to this portfolio, the sharp ratio went up to 1.76). In addition, both of these two strategies also worked effectively in terms of the average of maximum monthly drawdown related to the effect of the tail risk: 1) RMTP by 1.80% and 2) CRPP by 1.74% (by adding an appropriate risk reduction to this portfolio, maximum drawdown decreased to 0.78%). Furthermore, this paper also studies an enhancement strategy based on Risk Parity Portfolios (RPP) focusing on and using co-integration relationship (co-integration approach). According to the simulation result, this proposed enhancement strategy has a potential to yield roughly 4.5% return. Finally, this paper presents the explicit derivation of lower tail-dependence and co-integration approach.