  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.
