If risk free rate ($R_0$) is bigger than expected return on minimum variance portfolio ($\bar{\mu}$), so $R_0>\bar{\mu}$. I.e. the tanget portfolio is on the risky inefficient portfolio frontier and we want to short sell risky portfolio. Question 1: Why is this not consistent with CAPM? Question 2: Is it consistent with general notion of securities market equilibrium??

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    $\begingroup$ What do you think and why? $\endgroup$ – Matthew Gunn Jun 4 '18 at 19:22

This situation is not consistent with equilibrium at all because any investors should be hold always and only short position in risky assets. Who buy them? Note that in long only case, the usual, the firms sell their stock.

As a consequence also CAPM equilibrium not hold, even if CAPM equation can be derived yet. Read this related topic: Under the CAPM, how do I deal with market returns being below the risk-free rate?

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