A stock has had returns of 12 percent, 19 percent, 21 percent, −12 percent, 26 percent, and −5 percent over the last six years. What are the arithmetic and geometric average returns for the stock? (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e. g., 32.16.)

Average rate of return= 10.17 %

Geometric return = 9.23%

Explanation:

Geometric average return

This is compounded annual rate of return which is used to measure the performance of an asset over a certain number of years. It helps to measure the return generated by an investment taking into account the volatility .

Unlike the arithmetic average the geometric average gives an idea of the real rate taking into account of volatility

The formula below

Geometric Return =(1+r1) (1+r2) (1+rn)^1/n

Geometric Average return =  

(1.12× 1.19× 1.21× 0.88× 1.26× 0.95)^(1/6) - 1 =0.09233168

Geometric return =0.0923 × 100= 9.23%

Geometric return = 9.23%

Average rate of return

The average return is the sum of the returns over the years dividend by the Numbers of returns

Average return = sum of return / No of returns

(12% + 19% + 21% + (12%) + 26% + (5%))/6 =10.17 %

Average rate of return= 10.17 %

Geometric return = 9.23%