Problem 12-15 Arithmetic and Geometric Returns [LO1] A stock has had returns of
ID: 2789724 • Letter: P
Question
Problem 12-15 Arithmetic and Geometric Returns [LO1]
A stock has had returns of 9 percent, 27 percent, 15 percent, 15 percent, 27 percent, and 6 percent over the last six years.
What are the arithmetic and geometric returns for the stock? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
Arithmetic return %
Geometric return %
A stock has had returns of 9 percent, 27 percent, 15 percent, 15 percent, 27 percent, and 6 percent over the last six years.
Explanation / Answer
Arithmetic return =Total returns/Total time period
=(9+27+15-15+27-6)/6=9.5%
Geometric return=[(1+rate1)(1+rate2)(1+rate3)(1+rate4)(1+rate5)(1+rate6)]^(1/6)-1
=[(1+0.09)(1+0.27)+(1+0.15)(1-0.15)(1+0.27)(1-0.06)]^(1/6)-1
=8.32%(Approx)