bv_cvxbook_extra_exercises

# In the equilibrium positions the total force on each

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Unformatted text preview: is quasilinear in this case. (b) Blending initial investment only streams. Use the result in part (a) to show the following. Let x(i) ∈ Rn+1 , i = 1, . . . , k , be a set of k cash ﬂows over n periods, each of which satisﬁes the conditions above. Let w ∈ Rk , with 1T w = 1, and consider the blended cash ﬂow given + by x = w1 x(1) + · · · + wk x(k) . (We can think of this as investing a fraction wi in cash ﬂow i.) Show that IRR(x) ≤ maxi IRR(x(i) ). Thus, blending a set of cash ﬂows (with initial investment only) will not improve the IRR over the best individual IRR of the cash ﬂows. 13.14 Eﬃcient solution of basic portfolio optimization problem. This problem concerns the simplest possible portfolio optimization problem: maximize µT w − (λ/2)wT Σw subject to 1T w = 1, with variable w ∈ Rn (the normalized portfolio, with negative entries meaning short positions), and data µ (mean return), Σ ∈ Sn (return covariance), and λ > 0 (the risk aversion paramet...
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## This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.

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