If i have a vector of expected returns $A$, a covariance matrix $C$ and a vector of the corresponding weights $W$ for each investment, is it possible to generate the efficient frontier with vector algebra? I am sure I have seen the efficient frontier in matrix form somewhere but I cant remember it, something like $W^TACW$. I want to generate an efficient frontier in R by randomly selecting portfolio weights So I just need the matrix notation.
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1$\begingroup$ the formulas were derived by R. C. Merton in a famous paper "An Analytic Derivation of the Efficient Portfolio Frontier" which is available online. It is also in many books for ex Chi-Fu Huang: foundations for financial economics pages 64 and 67. $\endgroup$nbbo2– nbbo22020-08-10 00:23:13 +00:00Commented Aug 10, 2020 at 0:23
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$\begingroup$ adding to previous answer, only the unconstrained efficient frontier, where short selling is allowed, can be solved analytically with matrix algebra. The constrained efficient frontier cannot be solved analytically $\endgroup$develarist– develarist2020-08-10 03:26:27 +00:00Commented Aug 10, 2020 at 3:26
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