Question

An investment returns for the years were 4% for year 1, 3% for year 2, 7% for year 3, and -2% for year 4.

1. What is the arithmetic mean and geometric mean of this investment’s returns?
2. If the year 1, year 2, and year 3 returns have 30%, 20% and 50% probabilities of happening, what is the expected return of this investment for the three years
3. What is the standard deviation for the investment’s returns in the first three years?

Answer 1

Answers

1. Calculation of arithmetic means

= Total of return of all the year/no. of years

= 4+3+7-2/4years

Arithmetic mean= 3%

2.Calculation of geometric mean

=4*3*7*-2

= -168

= -168^1/4

= -168^0.25

Geometric means= - 3.60%

3. Calculation of expected return of first 3 years

Year	Return(%) (a)	Probability (b)	Expected Return(%) (c=a*b)
1	4	0.3	1.20
2	3	0.2	0.60
3	7	0.5	3.50
	Total		5.30

4 Calculatiion of standard deviation of first 3 years

Year	Probability (a)	Return(%) (b)	Expected Return (c)	Calculation (b-c)2*a=d
1	0.3	4	5.30	0.507
2	0.2	3	5.30	1.058
3	0.5	7	5.30	1.445
				3.01

Standard deviation =

V3.01

= 1.73