I know that the tangency point between the CAL line (drawn from risk-free asset's return) and the efficiency frontier is the optimal risky portfolio. But what if there is no risk free asset? Can I draw CAL line without risk free asset? How do I find the optimal risky portfolio on the efficient frontier?

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    $\begingroup$ I thought the original approach was to build your indifference curves and select the portfolio that lies on the intercept the most upper-left curve and the efficient frontier. $\endgroup$
    – ruslaniv
    Jun 2, 2020 at 7:32

1 Answer 1


"Fischer Black (1972) developed another version of CAPM, called Black CAPM or zero-beta CAPM, that does not assume the existence of a riskless asset" Source : Wikipedia

In this model there is no straight line CAL, but investors can choose a point on the (curved) efficient frontier that provides a suitable risk/return combination, by holding a mix of the Market Portfolio and the Zero Beta Portfolio, a portfolio orthogonal to the Market Portfolio. The chosen point is where the investor's iso-utility curve is tangent to the efficient frontier.

Look up Black CAPM or Zero Beta CAPM for more details.


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