Portfolio selection under higher moments using fuzzy multi-objective linear programming

Since asset returns have been recognized as not normally distributed, the avenue of research regarding portfolio higher moments soon emerged. To account for uncertainty and vagueness of portfolio returns as well as of higher moment risks, we proposed a new portfolio selection model employing fuzzy sets in this paper. A fuzzy multi-objective linear programming (MOLP) for portfolio optimization is formulated using marginal impacts of assets on portfolio higher moments, which are modelled by trapezoidal fuzzy numbers. Through a consistent centroid-based ranking of fuzzy numbers, the fuzzy MOLP is transformed into an MOLP that is then solved by the maximin method. By taking portfolio higher moments into account, the approach enables investors to optimize not only the normal risk (variance) but also the asymmetric risk (skewness) and the risk of fat-tails (kurtosis). An illustrative example demonstrates the efficiency of the proposed methodology comparing to previous portfolio optimization models.

Continuous and jump betas: implications for portfolio diversification

Using high-frequency data, we decompose the time-varying beta for stocks into beta for continuous systematic risk and beta for discontinuous systematic risk. Estimated discontinuous betas for S&P500 constituents between 2003 and 2011 generally exceed the corresponding continuous betas. We demonstrate how continuous and discontinuous betas decrease with portfolio diversification. Using an equiweighted broad market index, we assess the speed of convergence of continuous and discontinuous betas in portfolios of stocks as the number of holdings increase. We show that discontinuous risk dissipates faster with fewer stocks in a portfolio compared to its continuous counterpart.

Intraday return predictability, portfolio maximisation, and hedging

We examine whether intraday Chinese return predictability is linked to optimal portfolio holding and hedging. We find that: (1) S&P500 futures returns only predict Chinese spot market returns in up to 5-minute of trading with predictability disappearing at higher frequencies of trade; (2) the portfolio weight is maximised at the 5-minute trading frequency, when predictability is the strongest; and (3) when predictability is the strongest, significantly less shorting of the futures is required to minimise risk when a long position is taken in the Chinese market.