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**The premium of dynamic trading.**
*(English)*
Zbl 1210.91119

Summary: It is well established that, in a market with inclusion of a risk-free asset, the single-period mean-variance efficient frontier is a straight line tangent to the risky region, a fact that is the very foundation of the classical CAPM. In this paper, it is shown that, in a continuous-time market where the risky prices are described by Itô processes and the investment opportunity set is deterministic (albeit time-varying), any efficient portfolio must involve allocation to the risk-free asset at any time. As a result, the dynamic mean-variance efficient frontier, although still a straight line, is strictly above the entire risky region. This in turn suggests a positive premium, in terms of the Sharpe ratio of the efficient frontier, arising from dynamic trading. Another implication is that the inclusion of a risk-free asset boosts the Sharpe ratio of the efficient frontier, which again contrasts sharply with the single-period case.

### MSC:

91G10 | Portfolio theory |

91B25 | Asset pricing models (MSC2010) |

91B30 | Risk theory, insurance (MSC2010) |

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\textit{C. H. Chiu} and \textit{X. Y. Zhou}, Quant. Finance 11, No. 1, 115--123 (2011; Zbl 1210.91119)

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