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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 ItĂ´ 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.

91G10 Portfolio theory
91B25 Asset pricing models (MSC2010)
91B30 Risk theory, insurance (MSC2010)
Full Text: DOI
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