Reading 53: Security-Market Indices LOS a习题精选 2010, face, direction, contrast, discuss

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LOS a, (Part 1): Compare and contrast the characteristics of, and discuss the source and direction of bias exhibited by, each of the three predominant weighting schemes used in constructing stock market indices.

Assume a stock index consists of many firms who have recently split their stock. Which of the following weighting schemes will see a bias due to the impact of stock splits?

A) Unweighted price series.

B) Market value-weighted series.

C) Price-weighted series.

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Firms that split their stock price will have the identical weight before and after the split in both the unweighted and the market value-weighted series. However, in the price-weighted series, large successful firms will lose weight within the index due to simply splitting their stock. This creates a downward bias in a price-weighted series. Standard and Poor’s 500 Index is a market value-weighted index.

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Tamber Benz, CFA, recently joined Bay Area Investment Group as a personal financial planner. Today, she has a meeting with a client interested in equity index funds, with a particular interest in learning about the source and direction of biases. In preparation for this meeting, she makes some quick notes (relying on her memory). These notes are listed below. She then finds her well-worn CFA study notes and checks her memory. After reviewing her notes, which of the following choices does she determine is least accurate?

A) A market value-weighted index, such as the New York Stock Exchange Index, accurately reflects the impact of price changes on wealth.

B) The Dow Jones Industrial Index has a built-in downward bias.

C) An index such as the Valueline Composite Average is constructed by purchasing an equal number of shares of each stock in the index, and will have a downward bias when geometric averaging is used to compute the return.

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Although the latter part of this statement is correct, the first part is incorrect. The Valueline Composite Average is an unweighted price indicator series, and is constructed by maintaining an equal dollar investment in each stock in the index. The return of an unweighted index is usually calculated using a geometric average. Assuming the existence of volatility, the geometric average will always be lower than the arithmetic average.

The other statements are true. The Dow Jones Industrial Index is a price-weighted index and thus has a built-in downward bias because of the impact of stock splits. After a stock split, the denominator is adjusted downward to keep the index at the same level as before the split. Since high-growth companies tend to announce stock splits more frequently than low-growth companies, the larger, more successful firms lose influence on the index. The NYSE index, as well as the S& 500 index is a market-value weighted index. One problem with market-value weighted indexes is that firms with greater market capitalization have more impact than other firms. If these firms also have higher returns, the firms can dominate the index.

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Which of the following statements about indexes is TRUE?

A) A market weighted series must adjust the denominator to reflect stock splits in the sample over time.

B) A price-weighted index assumes an equal number of shares (one of each stock) represented in the index.

C) An unweighted index assumes a proportionate market value investment in each company in the index.

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The descriptions of value weighted and unweighted indexes are switched. The denominator of a price-weighted index must be adjusted to reflect stock splits and changes in the sample over time. A market value-weighted series assumes you make a proportionate market value investment in each company in the index.

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An index was recently begun with the following two stocks:

• Company A – 50 shares valued at $2 each.
• Company B – 10 shares valued at $10 each.

Given that the value-weighted index was originally set at 100 and Company A's stock is currently selling for $4 per share while Company B’s stock is still at $10 per share, what is the current value of the price-weighted index and the value-weighted index?

Price-weighted

Value-weighted

A) 8 150

B) 7 150

C) 7 300

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Price weight = [(4) + (10)] / 2 = 7

Value weight = [(4)(50) + (10)(10)] / [(2)(50) + (10)(10)](100) = 150

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Which of the following statements best describes the investment assumption used to calculate an unweighted price indicator series?

A) An equal number of shares of each stock are used in the index.

B) A proportionate market value investment is made for each stock in the index.

C) An equal dollar investment is made in each stock in the index.

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The unweighted price indicator series assumes that an equal dollar investment is made in each stock in the index. All stocks carry equal weight regardless of their price or market value.

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In a value-weighted index firms with:

A) greater market caps have greater impacts on the index.

B) higher stock prices have greater impacts on the index.

C) larger market caps have lesser impacts on the index.

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In a value weighted index, firms with greater market caps have a greater impact on the index than firms with lower market caps. A higher stock price does not necessarily mean a higher market cap.

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Assume a stock index consists of many firms who have recently split their stock. Which of the following weighting schemes will see a bias due to the impact of stock splits?

A) Unweighted price series.

B) Market value-weighted series.

C) Price-weighted series.

---

Firms that split their stock price will have the identical weight before and after the split in both the unweighted and the market value-weighted series. However, in the price-weighted series, large successful firms will lose weight within the index due to simply splitting their stock. This creates a downward bias in a price-weighted series. Standard and Poor’s 500 Index is a market value-weighted index.