An Asset Allocation Model and Its Solving Method

Abstract

Abstract Asset allocation is an important issue in finance, and both risk and return are its fundamental ingredients. Rather than the return, the measure of the risk is complicated and of controversy. In this paper, we propose an appropriate risk measure which is precisely a convex combination of mean semi-deviation and conditional value-at-risk. Based on this risk measure, investors can trade-off flexibly between the volatility and the loss to tackle the incurring risk by choosing different convex coefficients. As the presented risk measure contains nonsmooth term, the asset allocation model based on it is nonsmooth. To employ traditional gradient algorithms, we develop a uniform smooth approximation of the plus function and convert the model into a smooth one. Finally, an illustrative empirical study is given. The results indicate that investors can control risk efficiently by adjusting the convex coefficient and the confidence level simultaneously according to their perceptions. Moreover, the effectiveness of the smoothing function proposed in the paper is verified.