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I've read that, concerning the CAPM, in equilibrium all portfolio weights are strictly positive. Why is that? You can also go short in the risk free asset right? And then you're on the right of the Tangency Portfolio.
Furthermore, I read that by definition, the MVP can contain short positions. How does this relate to my first question?
Hope you can help out!
An equlibrium is a property of an entire market, not of any given investor's portfolio. The CAPM is an equilibrium theory.
In equilibrium, all (nontoxic!) assets must have non-negative prices. Hence, the weights of all assets in the market portfolio must be non-negative as well. The market portfolio weights will be strictly positive only if the assets have positive value, i.e., if their prices are strictly positive.
Within an equilibrium, it may be possible that some individual investors will find it optimal to be short some assets. But that does not imply that it's possible for market portfolio weights to be negative.
