Question

0.43 Portfolio return and standard deviation Jamie Wong is thinking of building an investment portfolio containing two stocks, L and M. Stock L will represent 40% of the dollar value of the portfolio, and stock M will account for the other 60%. The historical returns over the last 6 years, 2013-2018, for each of these stocks are shown in the following table. Year Expected return Stock L Stock M 14% 20% 14 16 2013 2014 2015 2016 2017 2018 a. Calculate the actual portfolio return, lp, for each of the 6 years. b. Calculate the average return for each stock and for the portfolio over the 6-year period. c. Calculate the standard deviation of returns for each asset and for the portfolio. How does the portfolio standard deviation compare to the standard deviations of the individual assets? d. How would you characterize the correlation of returns of the two stocks L and M? e. Discuss any benefits of diversification achieved by Jamie through creation of the portfolio.

Answer 1

Page - Anst- Portfolio % invested in stock L² weightage of stoon 2 2 40% Portfolio to invested in stock M: weightage of stock M: 60% 2 Wm Expected return Year stock (Re) stocum (Rm) Portfolio (86) 2013 207 12.6% 2014 14% 18%. 2015 16% 15.2%. 2012 I 2018 197 12.6% 2016 127. 14. 107 (a) Actual portrolio return for each of the 6 years. fp For 2013 - RiX WL + Rm x Wm= 14x 40% + 20x60% = 5.6+12 - 12.6% re for 2014 - Rixw, t Rm x Wm a luxyoy.+ 18 x 60% 2 5.6+ 10.8.16.4%. rp for 2015 - RexWL + RmxWm= 16 x uor + 16X60%. = 6.4+ 9.6= 16% rp for 2016 - RL x WDL + RmxWm= (2x 40% +14x60% 6.8+ 8.4 = 15.2%. ro for 2017 - R XWL+RmxWm= 12x40%. +12%.X60%. 6. 8+7,2 = 14% re for 2018 RLX WL +RmxWm= 19 x40%. + 0x60% = 7.6 + 6 = 13.6%. (6) Average RL = return {Re. for each stock over the N. 6-year period.! Re: Return on Stock Lper year No. No. of years Caverage return for stock L) & 14+ 14t 16 that 12 +14 2 16.11% Rim Erm Rm. Return of stoc per - No. of years 15t. (average return for stoc m) a 20+ 18+ 16 +14+12 to

Date Page 40%=w for Average return rpere 2 12.6 portfolio over the 6 year period e - r - return on portain perger 1.2 16 H15.2 E14 +13.6 - 15.49% (evende reported the ) Year 2013 1 2014 2015 2016 2017 2018 Stau (1-0) (L-2 Storum (m.m) (mm)2 (1) (mm) - 14 14-16.12=-2.17 9.91 20 5 25 10.85 14 14.16.17 = 2.17 4.71 18 3 9 - 6.51 16 16.-16.17... 17 .03 16 1 1 - 17 12 12-16.17.8 .69 14 - 1 17 17 -16.17.8 .69 12 - 9 -2.99 19 19-16.17. 2.83 8.01 10 -5 25 14.15 1. 16. 17. EL-W? 18.84 m2 154 {mm): 70 -35 Standard deviction stan: O: El-L² : 1864 = 1077 Standard deviation stocu M = Om som 9 - 3.42 V N Covariance between stocu: {(Return, - Average retum. ) x (Returnu - Averager retorn) nal 352-1. lovun Op = w: 8² + win om ²+2 W₂ Wm COULM 16.92(1.79)? +(6)?(3:40)?+26.4)(6) X(-a) - .50 + 4.21 $ - 3.36 11.35 - 1.16 The standard deviation of Portfolio is less than the Standard deviation of individual stock. Hence, less rish in the portfolio.

Date Pege. a. The correlation AS Covariance between the is stocu negative is also that is negative. Benefits of diversification • Reduce risu while go for J. Since the correlation between is less chance of loss. at portfolio. Stocu are negative her there