Profile Log-likelihood Function Gauss file(s) max_profile.g, apple.csv, ford.csv Matlab file(s) max_profile.m, diversify.mat The data files contain daily share prices of Apple and Ford from 2 January 2001 to 6 August 2010, a total of T = 2413 observations (see also Section 2.7.1 and Exercise 14 in Chapter 2). Let θ = {θ1, θ2} where θ1 contains the parameters of interest. The profile log-likelihood function is defined as ln LT (θ1, θb 2) = arg max θ2 ln LT (θ), where θb 2 is the maximum likelihood solution of θ2. A plot of ln LT (θ1, θb 2) over θ1 provides information on θ1. Assume that the returns on the two assets are iid drawings from a bivariate normal distribution with means µ1 and µ2, variances σ 2 1 and σ 2 2 , and correlation ρ. Define θ1 = {ρ} and θ2 =  µ1, µ2, σ2 1 , σ2 2 .

(a) Plot ln LT (θ1, θb 2) over (−1, 1), where θb 2 is the maximum likelihood estimate obtained from the returns data.

(b) Interpret the plot obtained in part (a).