A retail investor has collected data on different characteristics for three asset classes, namely the New York Stock Exchange (NYSE) index, gold (GOLD) and crude oil (WTI) spot prices, as illustrated in the table below.

I. The investor is interested in constructing a portfolio of the three assets. In the process, crude oil (WTI) is an asset that must be included in the portfolio at all times, irrespective of return and risk characteristics, and its weight is predetermined and set at 30 percent of the total available capital.

(a) Find the weights that will minimise the risk of the three-asset portfolio; leverage or short selling is not allowed.

(b) Show that the weights achieve a minimum; and calculate the portfolio standard deviation and expected return.