bv_cvxbook_extra_exercises

E it is a sure win betting scheme in economics we say

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Risk-return trade-off in portfolio optimization. We consider the portfolio risk-return trade-off problem of page 185, with the following data: p= ¯ 0.12 0.10 0.07 0.03 , Σ= 0.0064 0.0008 −0.0011 0.0008 0.0025 0 −0.0011 0 0.0004 0 0 0 0 0 0 0 . (a) Solve the quadratic program minimize −pT x + µxT Σx ¯ subject to 1T x = 1, x 0 for a large number of positive values of µ (for example, 100 values logarithmically spaced between 1 and 107 ). Plot the optimal values of the expected return pT x versus the standard ¯ T Σx)1/2 . Also make an area plot of the optimal portfolios x versus the standard deviation (x deviation (as in figure 4.12). (b) Assume the price change vector p is a Gaussian random variable, with mean p and covariance ¯ Σ. Formulate the problem maximize pT x ¯ subject to prob(pT x ≤ 0) ≤ η 1T x = 1, x 0, as a convex optimization problem, where η < 1/2 is a parameter. In this problem we maximize the expected return subject to a constraint on the probability of a negative return. Solve the problem for a large number of values of η between 10−4 and...
View Full Document

This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at Berkeley.

Ask a homework question - tutors are online