Problem 1020 Arithmetic and Geometric Returns LO 1 A stock h

Problem 10-20 Arithmetic and Geometric Returns [LO 1]

A stock has had returns of ?26 percent, 6 percent, 34 percent, ?5 percent, 28 percent, and 19 percent over the last six years.

Required:

What are the arithmetic and geometric returns for the stock? (Do not round intermediate calculations. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)

  Arithmetic average return

%

  Geometric average return

%

Solution

Arithmetic return=Total of returns/Total time period

=(-26+6+34-5+28+19)/6=9.33%(Approx)

Geometric return=[(1+rate1)(1+rate2)..........(1+rate6)]^(1/6)-1

=[(1-0.26)(1+0.06)(1+0.34)(1-0.05)(1+0.28)(1+0.19)]^(1/6)-1

=7.24%(Approx).