Portfolios - EDHEC-Risk

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Scientific Approaches: Towards the Efficient Frontier • Scientific diversification aims at reaching a high risk/return objective through portfolio construction techniques. • Two remarkable portfolios on the efficient frontier: – The MSR generates the highest reward per unit of portfolio volatility: needed optimization inputs are expected returns, correlations and volatilities. – The GMV generates the lowest possible portfolio volatility: needed optimization inputs are correlations and volatilities. • In what follows, we focus on these two approaches, and discuss some of the challenges involved in robust optimization. • Ad-hoc approaches can generally be regarded as specific cases under some particular assumptions. 12 12
MSR versus GMV Expected Return w −1 ( μ − re) ( μ − re) Σ = ≡ e' Σ ( μ , σ , ρ ) MSR −1 i i ij f Maximum Sharpe Ratio (MSR) Portfolio Global Minimum Variance (GMV) Portfolio ● −1 1 ● ● ( ) Σ e w GMV = ≡ g σ , 1 e' e i ρ − Σ ij ● Equally-weighted index Cap-weighted index Volatility 13
Page 2 and 3: EDHEC-Risk Days 2012 London, March
Page 4 and 5: Managing Investments t in Alternati
Page 6 and 7: • Alternatives to Cap-Weighted In
Page 8 and 9: Indices versus Benchmarks • The w
Page 10 and 11: Fundamental Weighting for Represent
Page 14 and 15: Implementing the Diversifiers • E
Page 16 and 17: Giving Up Smartly - MSR • How to
Page 18 and 19: Ad-Hoc Approaches: Maximum Diversif
Page 20 and 21: Selection Risk - Relative Returns
Page 22 and 23: Diversifying the Diversifiers - Lon
Page 24 and 25: Tracking Error Across Market Condit
Page 26 and 27: • Alternatives to Cap-Weighted In
Page 28 and 29: Tracking Error Constraints • If w
Page 30 and 31: What Separation Theorems Say and Do
Page 32 and 33: Impact of Relative Risk Control Pan

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