1 marks ii Show that the variance of the portfolio var n y can be written as w

# 1 marks ii show that the variance of the portfolio

• Homework Help
• 4

This preview shows page 2 - 4 out of 4 pages.

(1 marks) ii) Show that the variance of the portfolio )) ( var( n y can be written as w C w xx T n y )) ( var( , where JJ J J J J T xx n n E ... : : : : ... ... ] ) ( ) ( [ 2 1 2 22 12 1 21 11 x x C is the covariance of ) ( n x . x n n μ x x ) ( ) ( is the centered return. (0.5 marks) iii) The mean-variance portfolio optimization problem can be written as: 1 t subject to min 2 1 J T x T xx T 1 w μ w w C w w ,

Subscribe to view the full document.

where t is a specified/desired expected return of the portfolio. J 1 is a 1 J vector of ones. By differentiating the Lagrangian ) ( ) 1 ( ) , , ( 2 1 2 1 2 1 t L x T J T xx T μ w 1 w w C w w w.r.t. w , the Lagrange multipliers 1 , 2 and set the gradient to zero. Show that the optimum weight vector * w that minimizes the variance and reaching the target return is ) ( * 2 1 1 x J xx μ 1 C w . . (1 marks) iv) (*) By substituting ) ( * 2 1 1 x J xx μ 1 C w into the constraints t x T μ w and 1 J T 1 w , show that the optimal Lagrange multipliers are 2 1 * b ac bt c and 2 2 * b ac b at , where J xx T J a 1 C 1 1 , J xx T J b μ C 1 1 and J xx T J c μ C μ 1 . (0.5 marks) Part 2. MATLAB Implementation of Markowitz mean-variance portfolio b) Run the MATLAB® code “Ass2.m”. It contains three parts: 1. 200 time-instants of the return of 10 assets are randomly generated. They are assumed to be independent of each other and are normally distributed. 2. The autoregressive moving average and general autoregressive conditional heteroscedasticity (ARMA(P,Q)-GARCH(R,S)) is a time series model in which the mean and variance of the assets are modelled by the ARMA and the GARCH processes respectively. The mean and variance of the assets in future
• Fall '16

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern