Question

Your portfolio had the values in the following table for the four years​ listed:

          Beginning Value   Ending Value
2016   60,261                  55,436
2017   55,436                  65,892
2018   65,892      68,750
2019   68,750      70,180

a. Calculate your return for each year over the​ 4-year period. Then calculate the average return over the​ 4-year period.

b. Calculate the portfolio standard deviation.

The return for 2016 is ______​%. ​ (Round to two decimal​ places.)

The return for 2017 is ______ ​%. ​ (Round to two decimal​ places.)

The return for 2018 is ______%​ (Round to two decimal​ places.)

The return for 2019 is ______​%.​ (Round to two decimal​ places.)

The average return is _______​%.​ (Round to two decimal​ places.)

The standard deviation is _____​%. ​(Round to two decimal​ places.)

Answer 1

a.

Periodic return = (Ending value – Beginning value)/ Beginning value

Return for 2016 = (55,436 - 60,261)/ 60,261 = (4,825)/ 60,261 = -0.080068369 or -8.01 %

Return for 2017 = (65,892 - 55,436)/ 55,436 = 10,456 / 55,436 = 0.1886139 or 18.86 %

Return for 2018 = (68,750 - 65,892)/ 65,892 = 2,858 / 65,892 = 0.04337401 or 4.34 %

Return for 2019 = (70,180 - 68,750)/ 68,750 = 1,430/ 68,750 = 0.0208 or 2.08 %

Average return = -8.01 % + 18.86 % + 4.34 % + 2.08 % = 17.27 % /4 = 4.3175 % or 4.32 %

b.

Year	Beginning Value (B)	Ending Value (E)	Return (E-B)/B	Return - Average	(Return - Average)2
2016	60,261	55,436	-8.01%	-12.32%	1.51901%
2017	55,436	65,892	18.86%	14.54%	2.11511%
2018	65,892	68,750	4.34%	0.02%	0.00000%
2019	68,750	70,180	2.08%	-2.24%	0.05009%
		Total return	17.27%		3.68421%
		Average return	4.32%

Standard deviation = √ [1/n-1 ∑ (Return - Average) ²]

                               = √ [1/4-1 x 3.68421%]

                               = √ (0.0368421/3)

                                = √ 0.0122807 = 0.11081832 or 11.08 %