In part 2 you are given the MATLAB codes Run Ass2m to generate the mean

# In part 2 you are given the matlab codes run ass2m to

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In part 2, you are given the MATLAB® codes. Run “Ass2.m” to generate the mean- variance portfolio. You will be asked questions related to the mean variance portfolio generated by “Ass2.m”.

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Part 1. Theory of Markowitz mean-variance portfolio a) A portfolio is a combination of different assets. In a portfolio optimization problem, one seeks to optimize the proportion of wealth allocated to different assets in order to reach certain specified target return. Since the return of the assets are often subjected to the randomness due to different kind of uncertainties, such as market risk, credit risk and etc., investors attempt to make more efficient choices. If there are two assets with same return, the one with lower variance is considered a better choice. Based on this concept, minimizing the variance of the portfolio is one of the investment strategies. More precisely, consider J risky assets, whose rates of return are given by the random variable T J x x x ] ,..., , [ 2 1 x . Suppose we are given N time-instants of the assets, denoted by ) ( n x , N n ,... 2 , 1 . In the Markowitz mean-variance portfolio, one seeks to construct a portfolio ) ( ) ( ) ( 0 n n x w n y T J j j j x w , and find the weight of wealth invested in asset j , denoted by j w , J j ,... 2 , 1 , 1 1 j J j w , which minimize the variance of the portfolio, i.e. )) ( var( n y , and reaching a target expected return t n y E )) ( ( at the same time. i) Show that the expected return )) ( ( n y E of the portfolio can be written as x T n y E μ w )) ( ( , where )] ( [ n E x x μ .
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