Question

Portfolio return and standard deviation Personal Finance Problem Jamie Wong is thinking of building an investment portfolio containing two stocks, Land M. Stock L will represent 65% of the dollar value of the porto, stock M will count for the other 35%. The historical returns over the next 6 years, 2013 - 2018, for each of these stocks are shown in the following table a. Calculate the actual portfolio return for each of the years. b. Calculate the expected value of portolo returns.p. Over the year period c. Calculate the standard deviation of expected portfolio retums, over the 6-year period. d. How would you characterize the correlation of returns of the two stocks Land ? e. Discuss any benefits of diversification achieved by Jamie through creation of the portfolio

Answer 1

a) Expected portfolio return for each of the 6 years
		WL = 65%	WM = 35%
				Formula = (WL* RL) + (WM * RM)
	Year	Stock L	Stock M	Portfolio return
	2013	15%	25%	18.50%
	2014	17%	24%	19.45%
	2015	18%	23%	19.75%
	2016	19%	22%	20.05%
	2017	20%	21%	20.35%
	2018	22%	20%	21.30%
Total				119.40%
b) Average Expected value of portfolio returns over the 6-year period = =(119.40%/6)	19.90%
c) Standard deviation of expected portfolio returns over the 6-year period	0.01%
	A	B
Year	Profolio Return	expected Return on portfolio	(A - B)^2
2013	18.50%	19.90%	0.000196
2014	19.45%	19.90%	2.025E-05
2015	19.75%	19.90%	2.25E-06
2016	20.05%	19.90%	2.25E-06
2017	20.35%	19.90%	2.025E-05
2018	21.30%	19.90%	0.000196
Total			0.000437
Variance			0.009%
Std Dev			0.935%
d) Correlation of returns of the two stocks L and M	-0.99
Stocks are negatively correlated.
e) With two negatively correlated stocks, over portfolio risk is reduced

А B с D E 18 WL = 65% WM = 35% 19 Formula = (WLRL) + (WMRM) 20 21 22 23 24 25 26 27 Total 28 Year 2013 2014 2015 2016 2017 2018 Stock L 0.15 0.17 0.18 0.19 0.2 0.22 Stock M 0.25 0.24 0.23 0.22 0.21 0.2 Portfolio return =(C21*65%)+(D21*35%) =(C22*65%)+(D22*35%) =(C23*65%)+(D23*35%) = (C24*65%)+(D24*35%) = (C25*65%)+(D25-35%) =(C26*65%)+(D26*35%) =SUM(E21:E26) b) Average Expected value of portfolio returns over the 6- 29 year period == (119.40%/6) 30 31 =SUM(E21:E26)/6 c) Standard deviation of expected portfolio returns over 32 the 6-year period 33 34 =((E21-B29)^2+(E22-B29) A B 35 Year 36 2013 37 2014 38 2015 39 2016 40 2017 41 2018 42 Total 43 Variance 44 Std Dev 45 Profolio Return =E21 =E22 =E23 =E24 =E25 =E26 expected Return on portfolio =B29 =C36 =C37 =C38 =C39 =C40 (A - B)^2 =(B36-C36)^2 =(B37-C37)^2 = (B38-C38)^2 = (B39-C39)^2 =(B40-C40)^2 =(B41-C41)^2 =SUM(D36:041) =D42/(6-1) =SQRT(D43)