Question

tock has had returns of 16 percent, 23 percent, 15 percent, −11 percent, 30 percent, and −5 percent over the last six years. What are the arithmetic and geometric average returns for the stock?

Answer 1

Answer:    arithmetic Average Return =11.33%

                  Geometric Average Return=10.33%

Explanation:

Returns per year

Year 1      16%

year 2       23%

year 3       15

year 4      -11%  

year 5     30 %

year 6      -5%

Total =    68%

Arithmetic Average = Total returns 0f ( year 1 -6) / number of years

= 68%/6 =11.33%

Geometric Average Return  is given as

= ((1 + R1) × (1 + R2) × ... × (1 +Rn))(1/n) - 1

((1 + 16%) × (1 + (23%)) × (1 + 15%) x (1+ -11%) x (1+30%)  x (1+ -5%))^1/6 - 1

((1.16 x 1.23 x 1.15 x 0.89 x 1.30  x (0.95)) ^1/6

((1.16 x 1.23 x 1.15 x 0.89 x 1.30   x 0.95)) ^1/6 -1

(1.8035073 )^1/6  - 1

= 1.10328 -1 = 0.10328 x 100 = 10.328%   =10.33%