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The premium of dynamic trading in a discrete-time setting
Authors:Haixiang Yao  Xingyi Li
Institution:1. School of Finance, Guangdong University of Foreign Studies, Guangzhou, 510006China.;2. Warwick Business School, The University of Warwick, Coventry, CV4 7ALUK.
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.
Keywords:Premium of dynamic trading  Discrete-time setting  Efficient frontier  Sharpe ratio  Portfolio selection
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