# Practice Problems 8

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Published on March 6, 2014

Author: anhtuantran509

Source: slideshare.net

Mathematical Methods for Quantitative Finance Practice Problems 8 Write R programs to solve each of the following exercises. 1. Use Newton’s method to ﬁnd x ∈ (0, π ) such that 2 x− sin(x) = −x cos(x) What is the signiﬁcance of this particular value of x? Hint: slide 20 from slides 8. 2. Solve the maximum expected returns optimization exercise in section 7 of slides 8 (that is, reproduce the solution presented in the lecture). The last line of your R program should display the portfolio weights vector w. 3. Using the same expected returns vector µ and covariance matrix Σ from the previous exercise, solve the optimization problem minimize: wT Σw subject to: eT w = 1 µT w = µ2 where µ2 is the expected return computed in the previous exercise. Again, the last line of your R program should display the portfolio weights vector w. Compare with the previous answer. http://computational-finance.uw.edu

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