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MIT6_079F09_hw04

# MIT6_079F09_hw04 - 6.079/6.975 Fall 200910 S Boyd P Parrilo...

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6.079/6.975, Fall 2009–10 S. Boyd & P. Parrilo Homework 4 additional problems 1. Simple portfolio optimization. We consider a portfolio optimization problem as de- scribed on pages 155 and 185–186 of Convex Optimization , with data that can be found in the file simple_portfolio_data.m . (a) Find minimum-risk portfolios with the same expected return as the uniform port- folio ( x = (1 /n ) 1 ), with risk measured by portfolio return variance, and the following portfolio constraints (in addition to 1 T x = 1): No (additional) constraints. Long-only: x followsequal 0. Limit on total short position: 1 T ( x ) 0 . 5, where ( x ) i = max {− x i , 0 } . Compare the optimal risk in these portfolios with each other and the uniform portfolio. (b) Plot the optimal risk-return trade-off curves for the long-only portfolio, and for total short-position limited to 0 . 5, in the same figure. Follow the style of figure 4.12 (top), with horizontal axis showing standard deviation of portfolio return, and vertical axis showing mean return.

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MIT6_079F09_hw04 - 6.079/6.975 Fall 200910 S Boyd P Parrilo...

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