She has also realised that the 14% returning portfolio you have constructed is not as `efficient' as it might be because you have forgotten all about the risk-free asset… oops! Rather than a commodity, the risk-free asset should be added to the original portfolio of five asset classes. You quickly do some research and determine that the appropriate risk-free rate to use is 3% per annum. Perform the following tasks to adjust your portfolio weights from Question 1:

3. (a) Construct and plot the MVS (with short sales allowed) for the five asset classes plus a risk-free asset paying 3%. (Note: do not included your chosen commodity from Q2.)

(b) Identify the tangency portfolio, i.e. report its portfolio weights, expected return, and variance of returns. Furthermore, illustrate its tangency property graphically by plotting the MVS from 1.(e) on the same set of axes.

(c) Determine and report the new portfolio weights for the efficient portfolio with 14% expected return.

(d) Calculate and report the reduction in risk of the 14% returning efficient portfolio that can be achieved by adding the risk-free asset to the portfolio of five asset classes