Part 2: Investment Allocations An investor has selected the following asset types in his portfolio. The expected return for each asset type has been estimated by using the historical data: Expected Returns Bonds 7% High tech stocks 12%% Foreign stocks 11 Call options 14% Put options 14%% Gold 9% Table 5: Expected returns of Investments The following table indicates the covariance matrix of the assets' returns. Each diagonal entry is the variance of an asset and non-diagonal entries are the covariances between any pairs of assets. Bonds High tech Foreign Call options Put options Gold stocks stocks Bonds 0.001 0.0003 0.0003 0.00035 -0.00035 0.0004 High tech stocks 0.009 0_0004 0.0016 -0.0016 10006 Foreign stocks 0.008 0.0015 0.0055 -0.0007 Call options 0.012 0.0005 0.0008 Put options 0.012 -0.0008 Gold 0.005 Table 6: The Covariance matrix of assets' returns Suppose that our investor wishes to invest $10.000 in this portfolio. Determine how he should allocate this investment to the individual assets in his portfolio in order to have a minimum baseline expected return of | 1%, and at the same time, at a minimum risk. (ii Let the solution pair be denoted by (r, e), where "r" denotes the minimized risk and "e" denotes the expected portfolio return after the problem is solved. Use successive values of 10%%. 10.5%%. 1 135, 10.5%%. 12%, 12.535, 13%% and 13.5%% as the baseline return values to obtain eight pairs of solutions (r, e). Plot "e" versus "r". Explain whether there exists a pattern in this plot. In other words. explain, in your opinion, the type of mathematical relationship that "r" and "e" may have