Question

Risk and return 

You are considering an investment in the stock market and have identified two potential stocks, they are Rio Tinto (NYSE: RIO) and Amazon (NASDAQ: AMZN). The year-end historical prices for the years 2010 to 2018 are shown in the table below. 

Year	Rio Tinto	Amazon
2010	48.51	125.41
2011	69.48	169.64
2012	60.46	194.44
2013	56.47	264.27
2014	53.15	358.69
2015	44.13	354.53
2016	24.65	587.00
2017	44.79	823.48
2018	56.11	1450.89

1. Which stocks would you prefer to own? Would every rational investor make the same choice? Explain your answer(s). 

2. Calculate the covariance and correlation coefficient between the two stocks. Does it appear that a portfolio consisting of RIO and AMZN would provide good diversification? Explain your answer(s). 

3. Calculate the expected (annual) return and standard deviation if you owned a portfolio consisting of 70% in AMZN and 30% in RIO.

Answer 1

Standard deviation of portfolio is 22%

Answer 2

Excel worksheet for calculating returns, standard deviation and correlation of the given stocks:-

Book1 - Excel nitin arora - 0 X File Home Insert Page Layout Formulas Data Review View Help ? Tell me what you want to do & Share A1 x ✓ fix C A B D E F G H I I J K L M N O P Q R 0 1 3 Year Rio Tinto Returns 2010 48.51 2011 69.48 43.23% 2012 60.46 -12.98% 2013 56.47 -6.60% 2014 53.15 -5.88% 2015 44.13 -16.97% 2016 24.65 -44.14% 2017 44.79 81.70% 2018 56.11 25.27% Avg. Return 7.95% Std. deviation 39.93% Year Amazon Returns 2010 125.41 2011 169.64 35.27% 2012 194.44 14.62% 2013 264.27 35.91% 2014 358.69 35.73% 2015 354.53 -1.16% 2016 587 65.57% 2017 823.48 40.29% 2018 1450.89 76.19% Avg. Return 37.80% Std. deviation 24.84% Correlation 0.118759 Sheet1 Ready 0 0 -- - + 100% + 02:12 19-03-2020 O Type here to search o A 9 ? ^ . 1» (la 4 ENG 6

Formula Sheet of the above calculations:-

Book1 - Excel nitin arora - o X File Home Insert Page Layout Formulas Data Review View Help ? Tell me what you want to do & Share A1 X ✓ fix А В G H I Returns Returns 1 2 3 Year 4. 2010 5 2011 6 2012 7 2013 8 2014 9 2015 10 2016 11 2017 12 2018 Rio Tinto 48.51 69.48 60.46 56.47 53.15 44.13 24.65 44.79 56.11 Avg. Return Std. deviation =B5/B4-1 =B6/B5-1 =B7/B6-1 =B8/B7-1 =B9/B8-1 =B10/B9-1 =B11/B10-1 =B12/B11-1 =AVERAGE(C5:012) ESTDEVA(C5:C12) Year 2010 2011 2012 2013 2014 2015 2016 2017 2018 Amazon 125.41 169.64 194.44 264.27 358.69 354.53 587 823.48 1450.89 Avg. Return Std. deviation =F5/F4-1 =F6/F5-1 =F7/F6-1 =F8/F7-1 =F9/F8-1 =F10/F9-1 =F11/F10-1 =F12/F11-1 =AVERAGE(G5:G12) ESTDEVA(G5:612) Correlation =CORREL(C5:C12,65: Sheet1 0 0 -- - + 100% Ready 1 + 02:13 19-03-2020 0 Type here to search lo ? ^ . 1» (la 4 ENG 6

Formulas for calculating the expected return and standard deviation of the portfolio:-

- 09 10 _ Expected Return= WARA + B RB where WA = weight of stock a WB = weight of shock B RA= Retum on stock A RB = Return on stock B 102] _Standard deviation = J was con + cua că + 2x Pas X WAXWB ход хов where Wa= weight of Stock A wg weight of stock B OA = sid. deviation of stock a a B = Std. deviation of stock B Pag z correlation coefficient blaueen Choice Af ShekB cs Scanned with NotesamScanner

Calculating the expected return and standard deviation of the given portfolio:-

27 28 29 30 31 Using Data from 10) _above, Excel worksheet & formulas 11_Ans 3: Expected Return = 0.80 x 0.378 + 0.20% 0.0795 121 2.0.3183 or 31.83° (where weight of Amazon: 80% Return of Amazon = 37.80% weight of Rio Tinto = 20%. Return of Rio Tinto a 7.95% Standard deviakona (0.8)^(0.248)2 + (0.2)*(0.399)? + 2x 0.118 x 0.8x0.2 x 0.248 x 0.399 E 0.0494 = 0.2224 Notes 22.24% where std. deviction of Rio tinto = 39.93% Std. deviation of Amazon z 24.84% Scanned with correlation coefficient = 0:1187 --Eartscanner