Question 3 (35 marks)

You are planning to invest in the following stocks:

Images above show the monthly closing prices of three stocks between 2012 and 2018. The data were collected from Yahoo Finance. When answering these questions, ignore dividends and assume all prices are in the same currency.

a. (3 marks) For each stock, show the monthly stock returns. b. (3 marks) Based on the responses in part (b), calculate the average monthly stock returns and standard deviation for each stock. c. (2 marks) Calculate the correlation of monthly stock returns between each pair of stocks. d. (4 marks) Suppose that you were to invest 65% in Apple Inc., 25% in Rio Tinto Ltd and 10% in Cathay Pacific Airlines. Calculate the portfolio expected return, variance and standard deviation. e. (4 marks) How would the expected return and standard deviation change if you decided to invest 20% in Rio Tinto Ltd, 25% in Apple Inc. and 55% in Cathay Pacific Airlines? Explain your answers. f. (5 marks) Find the weights of Apple Inc., Rio Tinto Ltd and Cathay Pacific Airlines that will provide a monthly return of greater than 0.8% with the lowest level of risk. There should be a minimum weighting of 10% for each stock. g. (5 marks) Plot a scatter diagram showing the portfolios from parts (e), (f) and (g), with the X-axis displaying standard deviation and the Y-axis displaying monthly returns. h. (4 marks) If the monthly risk-free rate is 0.12%, estimate the Sharpe ratio for the portfolios mentioned in parts (e), (f) and (g) and highlight the highest Sharpe ratio using conditional formatting.

Use screenshots in Excel if you can to explain calculations.

Apple Inc. (AAPL) Cathay Pacific Airlines (0293.HK) Rio Tinto Ltd Date (RIO.AX) Jul-2012 Aug-2012 Sep-2012 Oct-2012 Nov-2012 Dec-2012 Jan-2013 Feb-2013 Mar-2013 Apr-2013 May-2013 Jun-2013 Jul-2013 Aug-2013 Sep-2013 Oct-2013 Nov-2013 Dec-2013 Jan-2014 Feb-2014 Mar-2014 Apr-2014 May-2014 Jun-2014 Jul-2014 Aug-2014 Sep-2014 Oct-2014 Nov-2014 Dec-2014 Jan-2015 Feb-2015 Mar-2015 Apr-2015 May-2015 Jun-2015 Jul-2015 Aug-2015 Sep-2015 Oct-2015 Nov-2015 Dec-2015 Jan-2016 Feb-2016 49.24 2 58.75 85.46 84.81 15.06 67.05 65.59 62.57 2 63.49 3 52.37 57.51 58.30 61.74 63.99 66.06 68.18 13.56 14.36 1 15.20 68.35 74.86 16.10 66.84 63.55 61.70 76.82 84.57 90.57 93.52 103.06 100.59 58.00 118.81 118.05 129.25 124.82 126.10 130.28 126.90 121.50 110.15 109.07 120.80 118.75 102.61 96.47 97.65 5 5 3 5 19.98 19.86 19.06 58.20 9 48.60 14.52 45.91 40.28 42.69 Apple Inc. (AAPL) Cathay Pacific Airlines (0293.HK) Rio Tinto Ltd Date (RIO.AX) Jul-2012 Aug-2012 Sep-2012 Oct-2012 Nov-2012 Dec-2012 Jan-2013 Feb-2013 Mar-2013 Apr-2013 May-2013 Jun-2013 Jul-2013 Aug-2013 Sep-2013 Oct-2013 Nov-2013 Dec-2013 Jan-2014 Feb-2014 Mar-2014 Apr-2014 May-2014 Jun-2014 Jul-2014 Aug-2014 Sep-2014 Oct-2014 Nov-2014 Dec-2014 Jan-2015 Feb-2015 Mar-2015 Apr-2015 May-2015 Jun-2015 Jul-2015 Aug-2015 Sep-2015 Oct-2015 Nov-2015 Dec-2015 Jan-2016 Feb-2016 49.24 2 58.75 85.46 84.81 15.06 67.05 65.59 62.57 2 63.49 3 52.37 57.51 58.30 61.74 63.99 66.06 68.18 13.56 14.36 1 15.20 68.35 74.86 16.10 66.84 63.55 61.70 76.82 84.57 90.57 93.52 103.06 100.59 58.00 118.81 118.05 129.25 124.82 126.10 130.28 126.90 121.50 110.15 109.07 120.80 118.75 102.61 96.47 97.65 5 5 3 5 19.98 19.86 19.06 58.20 9 48.60 14.52 45.91 40.28 42.69