Question

Look again at the data in problem 1. If you had invested $100 at the beginning of this period in this portfolio, what would be your ending balance? For your convenience, Problem 1 read as follows:

"Suppose in the past four years, the returns of your portfolio were 10%, 5%, -6%, and 12%. What was the standard deviation of the returns of your portfolio?"

Select one:

a. $105.25

b. $121.60

c. $122.71

d. $136.34

Answer 1

Standard deviation can be calculated with help of below formula-

Mean = Total of all years returns / No. of years

Returns are shown in below table-

No. of years	Return (%)	( Return - Mean return)	( Return - Mean return)2
1	10	4.75	22.5625
2	5	-0.25	0.0625
3	-6	-11.25	126.5625
4	12	6.75	45.5625
Total return	21	total	194.75
Mean 21/ 4=	5.25

S.d = 8.57 (approx)

Investment value at the beginning of the period = 100 $

Returns for 4 years = 10%, 5%, -6%, and 12%

Investment value will be increased by 10 % in 1st year.

At the end of 1st year investment value will be = 100 + 10% on 100

= 100 + 10

= 110 $

Investment value will be increased by 5 % in 2nd year.

At the end of 1st year investment value will be = 110 + 5 % on 110

= 110 + 5.5

= 115.5 $

Investment value will be decrease by 6 % in 3rd year.

At the end of 1st year investment value will be = 115.5 - 6 % of 115.5

= 115.5 - 6.93

= 108.57 $

Investment value will be decrease by 12 % in 4th year.

At the end of 1st year investment value will be = 108.57 + 12 % of 108.57

= 108.57 + 13.0284

= 121.5984 $

= 121.60 $ (approx)

Hence correct answer is b. $121.60.

Hope it helps!