Question You are planning to invest in the following stocks: Rows 8 to 78 show the monthly closing prices of the stocks between 2010 and 2015.

The monthly data is collected from Yahoo Finance on 17th of December 2015. Ignore dividends for this question. Students used the prices that ignored dividends from Yahoo Finance

Date Rio Tinto Ltd (RIO.AX) Apple Inc. (AAPL) Cathay Pacific Airlines (0293.HK)

Jan-2010 68.00 27.44 12.80

Feb-2010 70.50 29.23 14.42

Mar-2010 78.40 33.57 16.36

Apr-2010 72.10 37.30 16.44

May-2010 67.14 36.70 15.42

Jun-2010 66.66 35.93 15.50

Jul-2010 70.61 36.75 17.30

Aug-2010 70.09 34.73 19.18

Sep-2010 76.77 40.54 21.05

Oct-2010 82.69 43.00 20.85

Nov-2010 82.21 44.45 22.65

Dec-2010 85.47 46.08 21.45

Jan-2011 84.05 48.47 19.64

Feb-2011 84.93 50.46 18.10

Mar-2011 84.75 49.79 18.64

Apr-2011 82.21 50.02 19.38

May-2011 81.50 49.69 18.64

Jun-2011 82.99 47.95 18.02

Jul-2011 80.00 55.78 18.06

Aug-2011 72.52 54.98 15.68

Sep-2011 61.80 54.47 12.80

Oct-2011 69.21 57.83 14.30

Nov-2011 62.95 54.60 13.56

Dec-2011 60.30 57.86 13.32

Jan-2012 69.16 65.21 15.36

Feb-2012 67.45 77.49 15.40

Mar-2012 65.40 85.65 14.38

Apr-2012 66.35 83.43 13.16

May-2012 56.86 82.53 11.98

Jun-2012 56.50 83.43 12.46

Jul-2012 53.20 87.25 12.84

Aug-2012 49.24 95.03 12.64

Sep-2012 53.36 95.30 12.62

Oct-2012 56.94 85.05 14.04

Nov-2012 58.75 83.61 13.62

Dec-2012 66.01 76.02 14.22

Jan-2013 66.36 65.07 15.06

Feb-2013 67.05 63.06 14.48

Mar-2013 57.20 63.24 13.28

Apr-2013 55.80 63.25 13.64

May-2013 55.18 64.25 14.48

Jun-2013 52.37 56.65 13.56

Jul-2013 57.51 64.65 14.36

Aug-2013 58.30 69.60 13.30

Sep-2013 61.74 68.11 15.20

Oct-2013 63.99 74.67 15.38

Nov-2013 66.06 79.44 16.42

Dec-2013 68.18 80.15 16.40

Jan-2014 65.64 71.51 16.10

Feb-2014 66.84 75.18 15.80

Mar-2014 63.55 76.68 14.46

Apr-2014 61.70 84.30 14.64

May-2014 59.30 90.43 14.12

Jun-2014 59.31 92.93 14.48

Jul-2014 66.38 95.60 14.72

Aug-2014 62.63 102.50 14.40

Sep-2014 59.58 100.75 14.30

Oct-2014 60.41 108.00 14.54

Nov-2014 59.10 118.93 17.08

Dec-2014 58.00 110.38 16.90

Jan-2015 57.56 117.16 18.10

Feb-2015 64.41 128.46 17.40

Mar-2015 57.23 124.43 17.94

Apr-2015 57.15 125.15 19.98

May-2015 58.20 130.28 19.86

Jun-2015 53.75 125.43 19.06

Jul-2015 52.86 121.30 18.34

Aug-2015 50.29 112.76 14.00

Sep-2015 48.60 110.30 14.52

Oct-2015 50.65 119.50 15.44

Nov-2015 45.91 118.30 13.68

b.For each stock, show the monthly stock returns.

c. Based on the responses in part (b), calculate the average monthly stock returns and standard deviation for each stock.

d. Calculate the correlation of monthly stock returns between each pair of stocks.

e. Suppose that you invest 20% in Apple Inc., 50% in Rio Tinto Ltd and 30% in Cathay Pacific Airlines. Calculate the portfolio expected return, variance and standard deviation.

f. How does the expected return and standard deviation change if you decide to invest 60% in Rio Tinto Ltd, 30% in Apple Inc. and 10% in Cathay Pacific Airlines? Explain your answers.

g. Find the weights of Apple Inc., Rio Tinto Ltd and Cathay Pacific Airlines that will provide a monthly return of 0.5% with the lowest level of risk.

h. 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.

i. If the monthly risk-free rate is 0.1%, estimate the Sharpe ratio for the portfolios mentioned in parts (e), (f) and (g) and highlight the highest Sharpe ratio using conditional formatting.