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Question 5.19: Show that the characteristic lines of all securities interse...

Show that the characteristic lines of all securities intersect at a common point in the CAPM. What are the coordinates of this point?

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The equation of the characteristic line is y = β_V x + α_V , where β_V is the beta factor of that security and α_V = μ_V −β_V μ_M. In the CAPM the equation μ_V = r_F +(μ_M −r_F )β_V of the security market line holds. Substitution into the formula for α_V gives  α_V = r_F −r_F β_V , so the equation of the characteristic line becomes y = β_V (x − r_F) + r_F . Clearly, the characteristic line of any security will pass through the point with coordinates r_F , r_F .

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