Suppose that there is no risk free asset whatsoever. In addition I have a market portfolio which cosists of 4 stocks. How can I identify a zero beta portfolio? How do i find the y-intercept for the tangent needed for the graphical solution?

Suppose that there is no risk free asset whatsoever. In addition I have a market portfolio which cosists of 4 stocks. How can I identify a zero beta portfolio? How do i find the y-intercept for the tangent needed for the graphical solution?

 

 

answer:

The Zero-beta concept is invented by Fischer Black to overcome the situation when there is no risk free asset exist. Under this situation, the Zero-beta portfolio plays the similar role as the risk-free assets.

As you can see from the graph above, Z(P) is the given portfolio and Z(Q) is the risk-free asset. When the portfolio touches the tangent at P, it becomes as similar as the risk-free assets, which is touching at point Q. The risk-free asset Z(Q) has zero covariance with the portfolio Z(P), which indicates Z(P) is nowhere related to Z(Q). Hence, Z(P) is standalone without getting any impact from the market, and it considered as the zero-beta portfolio.

 

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