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18 Feb 2021, 20:56
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D
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Difficulty:
95%
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Question Stats:
36% (02:11) correct
64%
(02:45)
wrong
based on 56
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The geometric mean is defined as the nth root of the product of n numbers. For example, the geometric mean of two numbers, say 2 and 8, is \(\sqrt{2 * 8}\). Consider a stock that grows by 10% in year one, declines by 20% in year two, and then grows by 30% in year three. What is the geometric mean of the return/loss?
A. 0.012
B. 0.026
C. 0.037
D. 0.046
E. 0.068
Vibrant Publishers
A. 0.012
B. 0.026
C. 0.037
D. 0.046
E. 0.068
Vibrant Publishers
09 Mar 2021, 09:20
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twobagels
We have 3 numbers to consider here because the changes happen over 3 years.
Growth of 10% is nothing but (1+0.1)x, where x is the original value of the stock
While a decline of 20% means (1-0.2)x
again, growth of 30% is (1+0.3)x
Geometric mean =\( \sqrt[3]{(1+0.1)*(1-0.2)*(1+0.3))}\) = 0.046 ------- > OPTION D
