Optimizing Optimization: The Next Generation of Optimization Applications and Theory (Quantitative Finance)

164 Optimizing Optimization The user now has the option to change the location point of the distribution by shifting the mean to ...

Optimization and portfolio selection 165 7.2.2 Optimize or measure performance The model now allows the user to use the optimize ...

166 Optimizing Optimization Figure 7.6 shows one of five possible performance descriptions. Notice the pattern of the risk – ret ...

Optimization and portfolio selection 167 7.3 Part 2: The DTR optimizer No matter what kind of optimizer one uses to generate an ...

168 Optimizing Optimization Following the style analysis, the DTR optimizer solves for that combination of active and passive ma ...

Optimization and portfolio selection 169 0.12 0.1 0.08 0.06 0.04 0.02 –0.02 –5 (^0510) 5% 15 20 Passive distribution DTR distrib ...

170 Optimizing Optimization specified in the beginning is the asset allocation that one ends up with. This is the most important ...

Optimization and portfolio selection 171 Appendix: Formal definitions and procedures Overview Our portfolio selection is based o ...

172 Optimizing Optimization Upside Potential RatioUpside Potential/Downside Deviation     ()() ()() xTpx Txpx xT xT ∑ ∑ ...

Optimization and portfolio selection 173 the mean, the standard deviation, and the extreme value of annual returns. You are prob ...

174 Optimizing Optimization Some auxiliary parameters μ σ ln(Dif) 2 α πσ  1 () 2 β σ  1 () 2 2 Formula for the lognormal cu ...

Optimization and portfolio selection 175 If the extreme value is a maximum and x is less than the extreme value, then: Fx er c x ...

176 Optimizing Optimization And , of course: Upside Potential Ratio  Upside Potential/Downside Deviation Style analysis — deter ...

Optimization and portfolio selection 177 References Aitchison , J. , & Brown , J. A. C. ( 1957 ). The lognormal distribution ...

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© 2009 Elsevier Limited. All rights reserved. Doi:10.1016/B978-0-12-374952-9.00008-7. Computing optimal mean/downside risk front ...

180 Optimizing Optimization present some results in Section 8.2. These are a consequence of two results we present, Proposition ...

Computing optimal mean/downside risk frontiers: the role of ellipticity 181 where λ is a (2  1) vector of Lagrangians. The firs ...

182 Optimizing Optimization satisfies Equation (8.9) for any φ 1 and φ 2. This is because the right-hand side of Equation (8.9) ...

Computing optimal mean/downside risk frontiers: the role of ellipticity 183 and all portfolios from the joint pdf given by Equat ...