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:

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.  

(i) 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 11%, 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%, 11%, 11.5%, 12%, 12.5%, 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.