Question

A stock had returns of 11.83 percent, −15.67 percent, 22.23 percent, 27.22 percent, and 10.88 percent...

A stock had returns of 11.83 percent, −15.67 percent, 22.23 percent, 27.22 percent, and 10.88 percent over the past five years. What was the geometric average return for this stock?

10.21%

11.75%

12.24%

11.30%

10.75%

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Answer #1

Answer: Correct answer is 10.21%
Geometric average return=[(1+r1)*(1+r2)*..*(1+rn)]^(1/n) -1
Here, r refers to the rate of return and n refers to the number of periods
Given that, r1=11.83%, r2=−15.67%, r3=22.23%, r4=27.22%, r5=10.88%
Here, the number of periods=5
So, geometric average return=[(1+11.83%)*(1−15.67%)*(1+22.23%)*(1+27.22%)*(1+10.88%)]^(1/5) -1
=[(1.1183)*(0.8433)*(1.2223)*(1.2722)*(1.1088)]^(1/5) -1
=(1.626023603)^(1/5) -1
=1.102111081-1
=0.102111081 or 10.21% (Rounded to two decimal places)

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