Question

Ten annual returns are listed in the following table:

−19.8 %

16.1 %

17.9 %

−49.9 %

43.9 %

1.1 %

−16.9 %

45.6 %

44.8 %

−3.5 %

a. What is the arithmetic average return over the 10-year period? (Round to four decimal places.)

b. What is the geometric average return over the 10-year period? (Round to four decimal places.)

c. If you invested $100 at the beginning, how much would you have at the end?

Answer 1

1	2	3	4	5	6	7	8	9	10	Total
-19.80%	16.10%	17.90%	-49.90%	43.90%	1.10%	-16.90%	45.60%	44.80%	-3.50%	79.30%
										÷ 10
						a.	Arithmetic Average return =			7.93%
Geometric average return = [(1+r1)*(1+r2)….(1+rn)]^(1/n) - 1
1	2	3	4	5	6	7	8	9	10
-19.80%	16.10%	17.90%	-49.90%	43.90%	1.10%	-16.90%	45.60%	44.80%	-3.50%
1+r1	1+r2	1+r3	1+r4	1+r5	1+r6	1+r7	1+r8	1+r9	1+r10
80.20%	116.10%	117.90%	50.10%	143.90%	101.10%	83.10%	145.60%	144.80%	96.50%
Geometric Average return =
[(1+(-)19.80%)*(1+16.10%)*(1+17.90%)*(1+(-)49.90%)*(1+43.90%)*(1+1.10%)*(1+(-)16.90%)*(1+45.60%)*(1+44.80%)*(1+(-)3.50%)]^(1/10) - 1
1.030678 -1
3.07%	Ans b.
c.	$100 invested at beginning would be $100 x (1+3.07%)^10 = $135.31