Question

Ten annual returns are listed in the following table: −19.8 % 16.1 % 17.9 % −49.9...

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?

 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