Mean-Variance Optimization

Risk and portfolio management with econometrics ver

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Unformatted text preview: 2Aμ0 − 2B = =0 d μ0 Δ Therefore Aμ0 = B so γ = μ0A − B Δ = 0 and wg ∗ = λΣ−1ι C − μ0B −1 = Σι AC − B 2 C − μ02A −1 = Σι A(C − μ02A) Σ−1ι Σ−1ι = = A ι ′Σ−1ι RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 10/23/2012. © P. KOLM. 13 Recall, the resulting portfolio weights for the GMV are wg ∗ Σ−1ι = ι ′Σ−1ι • Note that they do not depend on the expected returns ! (For you: Where on the efficient frontier is the GMV portfolio?) RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 10/23/2012. © P. KOLM. 14 Example (1/3) RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 10/23/2012. © P. KOLM. 15 Example (2/3) RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 10/23/2012. © P. KOLM. 16 Example (3/3) RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 10/23/2012. © P. KOLM. 17 Example: What happens if we have more assets? RISK AND PORTFOLIO MANAGEMENT WITH ECONOMETRICS, VER. 10/23/2012. © P. KOLM. 18 Example: What happens if w...
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This document was uploaded on 02/17/2014 for the course COURANT G63.2751.0 at NYU.

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