4 Quick CAPM derivation Deiive the CAPM formula fo F by usin

4. (Quick CAPM derivation) Deiive the CAPM formula fo F by using Equauon (6 9) in Chapter 6 lHint Noe thai Apply (6 9) bouh to asset k and to the market iself

Solution

Soln : r_k = return on asset and r_f is risk free return

For optimal portfolio/effiecient portfolio, we know that

r_k - r_f = ?*(?w_k* ?_1k ) ................. (I)

As it is given that ?w_k* ?1_k = Cov(r_k,r_m)

Also, we can write that r_m - r_f = ?*Cov(r_m, r_m)

or  ? = (r_m - r_f )/?_m²

Put the value of ? in eqn (I) here

r_k - r_f = (r_m - r_f )/?_m² *Cov.(r_k,r_m)

r_k - r_f = (r_m - r_f )* Cov.(r_k,r_m)/?_m²

But we should also know that Cov.(r_k,r_m)/?_m² = ?_k

Hence, we can say that  r_k - r_f = (r_m - r_f )*?_k

which is CAPM model equation.