Question 2404 of 3960 from exam CFA® LEVEL 1: CFA® Level 1

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Question

The table below lists information on price per share and shares outstanding for three stocks "" Rocking, Payton, and Strand.

Using the information in the table, determine which of the following statements is FALSE?

Answers

A. The geometric return is less than 11.7%.

B. If the three stocks comprise an index, a change in Stock Payton would have the biggest impact if the index was market-value weighted.

C. An investor creating a price-weighted index of these three stocks would need to change his holdings at year-end to reflect the price changes.

D. If the three stocks comprise an index, a change in Stock Strand would have the biggest impact if the index was price-weighted.

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Explanations

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A. B. C. D.

A price-weighted index assumes that the investor holds an equal number of shares of each stock in the index. Since the number of stocks did not change, the investor would not need to change his holdings.

The other statements are true. A price-weighted index is most influenced by the stock with the highest per-share price (Strand). A market-value weighted index is most influenced by the stock with the largest market capitalization (Payton). The geometric return is always less than the arithmetic return (see calculation).

The arithmetic and geometric return are calculated as follows:

Arithmetic return = sum of: (1 + stock return) divided by the number of stocks minus 1, or

[(1.5 + 1.0 + 0.85) / 3] "" 1 = 0.117, or 11.7%. Thus, the geometric average must be less than 11.7%.

Check of geometric average: = product of (1+ stock return), all to the 1/n power (or nth root) minus 1.

= [(1.5)*(1.0)*(0.85)]1/3- 1 = 0.084, or 8.4%

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