Question

What are the arithmetic and geometric average returns for a stock with annual returns of 6.2%, 12.8%, ?7.7%, and 9.4%? (3 pts) Explain why the aggregate returns are different considering each of the 4 year returns are identical?

Answer #1

Arithmetic average return=(6.2+12.8-7.7+9.4)/4=5.175%

Geometric averfage return:

that is **4.78%**

Even though the 4 year returns are identical, in arithmetic average return we are considering sum of all returns divided by number of returns, while in geometric average return we are considering product of all returns raised to a power which is equal to 1/number of returns.

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___________________________________
Year Return
___________________________________
2016
–0.10 (or –10%)
2017
0.10 (or 10%)
2018
0.15 (or 15%)
2019
0.25 (or 25%)
__________________________________
a) Find the holding period return of the stock over the
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b) Compute the arithmetic average return of the stock over the
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years are provided below.
___________________________________
Year Return
___________________________________
2016
–0.10 (or –10%)
2017
0.10 (or 10%)
2018
0.15 (or 15%)
2019
0.25 (or 25%)
__________________________________
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Returns
Year
X
Y
1
11 %
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2
29
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3
18
-7
4
-19
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5
20
51
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