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The premium of dynamic trading

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  • Chun Hung Chiu
  • Xun Yu Zhou

Abstract

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 Ito's 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, though 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 the 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.

Suggested Citation

  • Chun Hung Chiu & Xun Yu Zhou, 2009. "The premium of dynamic trading," Papers 0906.0999, arXiv.org.
    • Handle: RePEc:arx:papers:0906.0999
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    References listed on IDEAS

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    1. Duan Li & Wan‐Lung Ng, 2000. "Optimal Dynamic Portfolio Selection: Multiperiod Mean‐Variance Formulation," Mathematical Finance, Wiley Blackwell, vol. 10(3), pages 387-406, July.
    2. Andrew E. B. Lim, 2004. "Quadratic Hedging and Mean-Variance Portfolio Selection with Random Parameters in an Incomplete Market," Mathematics of Operations Research, INFORMS, vol. 29(1), pages 132-161, February.
    3. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    4. Henry R. Richardson, 1989. "A Minimum Variance Result in Continuous Trading Portfolio Optimization," Management Science, INFORMS, vol. 35(9), pages 1045-1055, September.
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    Cited by:

    1. Elena Vigna, 2009. "Mean-variance inefficiency of CRRA and CARA utility functions for portfolio selection in defined contribution pension schemes," Carlo Alberto Notebooks 108, Collegio Carlo Alberto, revised 2009.
    2. Elena Vigna, 2009. "Mean-variance inefficiency of CRRA and CARA utility functions for portfolio selection in defined contribution pension schemes," CeRP Working Papers 89, Center for Research on Pensions and Welfare Policies, Turin (Italy).

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