Suppose you are considering forming a portfolio with 10 assets. These assets are all identical in their characteristics, that is, they all have the same expected return E(R) 10%, the same standard deviation o(R) 10, and the same correlation with each other, 0.5. Remember that the correlation and covariance are related, so you can back out the covariance matrix from the information provided here (a) Find the minimum variance portfolio of these 10 assets (expected return and variance of the port- folio). Prove/show that this portfolio is an equal-weighted portfolio. Comment on this result. (b) Now, we want to plot the minimum variance frontier generated by these 10 assets. With the current values we cannot plot it because all assets are identical (if you try it you won't get anywhere because the solution won't be able to combine the identical assets in different ways). So, lets now assume that the expected return of each asset is given by E Ri-i, with i 1, .. 10. Thus, the vector E in Matlab is simply given by E [1:10]. Compute the minimum variance frontier for the following three cases (Note: you should use the formulas from the lecture notes on Topic 2, and use MATLAB to compute the values and create the plots): Case 1) Baseline case. Assume the correlation is the one given, that is, Case 2) Assume the correlation is 0 Case 3) Assume the correlation is =-0.1 0.5 Plot the three minimum variances frontiers on the same plot, and comment on the differences of the shape of the minimum variance frontier in the three cases. Suppose you are considering forming a portfolio with 10 assets. These assets are all identical in their characteristics, that is, they all have the same expected return E(R) 10%, the same standard deviation o(R) 10, and the same correlation with each other, 0.5. Remember that the correlation and covariance are related, so you can back out the covariance matrix from the information provided here (a) Find the minimum variance portfolio of these 10 assets (expected return and variance of the port- folio). Prove/show that this portfolio is an equal-weighted portfolio. Comment on this result. (b) Now, we want to plot the minimum variance frontier generated by these 10 assets. With the current values we cannot plot it because all assets are identical (if you try it you won't get anywhere because the solution won't be able to combine the identical assets in different ways). So, lets now assume that the expected return of each asset is given by E Ri-i, with i 1, .. 10. Thus, the vector E in Matlab is simply given by E [1:10]. Compute the minimum variance frontier for the following three cases (Note: you should use the formulas from the lecture notes on Topic 2, and use MATLAB to compute the values and create the plots): Case 1) Baseline case. Assume the correlation is the one given, that is, Case 2) Assume the correlation is 0 Case 3) Assume the correlation is =-0.1 0.5 Plot the three minimum variances frontiers on the same plot, and comment on the differences of the shape of the minimum variance frontier in the three cases
