Question

Hi there, for this question. I found the answer in excel sheet to be negative. is ther something wrong with my calculation:

Using the approach covered in your textbook calculate the geometric average annual rate of return over five years given the following annual rates, year 1 = 5.10%, year 2 = 4.95%, year 3 = 4.83%, year 4 = 4.75% and year 5 = 4.70% . What is the arithmetic average? Explain the difference.

(Rates as a percentage accurate to one basis point)

By adding and multiplying all 5 years of annual rates	1.27
5th root for the annual rates	-0.746369514
Year	Percentage	Adding 1 to avoid negative in Geometric Rate of Return)
1	0.0510	1.0510
2	0.0495	1.0495
3	0.0483	1.0483
4	0.0475	1.0475
5	0.0470	1.0470

Would like you to help me explain on this question

Answer 1

A	B	C	D	E	F	G	H	I	J
2
3		Year	Return
4		1	5.10%
5		2	4.95%
6		3	4.83%
7		4	4.75%
8		5	4.70%
9
10		Arithmetic average is the average of all the returns which is calculated as follows:
11
12		Arithmatic Average	=(5.1%+4.95%+4.83%+4.75%+4.70%) / 5
13			4.87%	=SUM(D4:D8)/5
14
15		Hence Arithmatic Average is	4.87%
16
17		Geometric mean of returns can be calculated as follows:
18		Geometric return over n year	=[(1+R1)*(1+R2)*(1+R3)*(1+R4)*(1+R5)*…*(1+Rn)](1/n)-1
19		Where R1, R2 … Rn are return in year 1, 2 …n respectively.
20
21		Geometric average return over 5 years	=[(1+R1)*(1+R2)*(1+R3)*(1+R4)*(1+R5)](1/5)-1
22
23		Year	Return	1+Return
24		1	5.10%	105.10%	=D24+1
25		2	4.95%	104.95%
26		3	4.83%	104.83%
27		4	4.75%	104.75%
28		5	4.70%	104.70%
29
30		Geometric average return over 5 years	=[(1+R1)*(1+R2)*(1+R3)*(1+R4)*(1+R5)](1/5)-1
31			4.87%	=((PRODUCT(E24:E28))^(1/5))-1
32
33		Hence geometric average return over 5 years is	4.87%
34