The premium of dynamic trading in a discrete-time setting. Issue 8 (2nd August 2016)

• Record Type: Journal Article
• Authors: Yao, Haixiang; Li, ZhongFei; Li, Xingyi
• Is Part Of: Quantitative finance. Volume 16:Issue 8(2016)
• Page Start: 1237
• Page End: 1257
• Publication Date: 2016-08-02
• Subjects: Premium of dynamic trading -- Discrete-time setting -- Efficient frontier -- Sharpe ratio -- Portfolio selection; Finance -- Periodicals; Business mathematics -- Periodicals; Finance -- Mathematical models -- Periodicals; Investments -- Mathematics -- Periodicals; Economics -- Periodicals; Finances -- Modèles mathématiques -- Périodiques; 332.015118
• DOI: 10.1080/14697688.2015.1136747
• Languages: English
• ISSNs: 1469-7688

Abstract

Abstract : Chiu and Zhou [ Quant. Finance, 2011, 11, 115–123] show that the inclusion of a risk-free asset strictly boosts the Sharpe ratio in a continuous-time setting, which is in sharp contrast to the static single-period case. In this paper, we extend their work to a discrete-time setting. Specifically, we prove that the multi-period mean-variance efficient frontier generated by both risky and risk-free assets is strictly separated from that generated by only risky assets. As a result, we demonstrate that the inclusion of a risk-free asset strictly enhances the best Sharpe ratio of the efficient frontier in a multi-period discrete-time setting. Furthermore, we offer an explicit expression for the enhancement of the best Sharpe ratio, which was referred to as the premium of dynamic trading by Chiu and Zhou [ op. cit. ], although they do not present a computational formula for it. Our results further show that, in the case with a risk-free asset, if an investor can extract some money from his initial wealth at time 0, the efficient frontier with a risk-free asset can be tangent to that without a risk-free asset. Finally, based on real data from the American market, a numerical example is provided to illustrate the results obtained in this paper; a numerical comparison between the discrete-time case and the continuous-time case is also provided. Our numerical results reveal that the continuous-time model can be considered to be a limit of the discrete-time model.