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

B)   One problem with an index such as the S& 500 is that firms with greater market capitalization have more impact than other firms.

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

D)   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.

2.The table below lists information on price per share and shares outstanding for three companies–Lair Enterprises, Kurlew, Inc., and Mowe, Ltd.

Assume that at the beginning of the year, the value of the market-weighted index was 100. The one-year return on the market-weighted index is closest to:

A)   30.0%.

B)   8.33%.

C)   13.33%.

D)   7.14%.

3.If the stocks in the table above are used to create a stock market index, it is least likely that:

A)   a value-weighted index does not need any adjustment to reflect a stock split.

B)   a price-weighted index will have a downward bias compared to a value-weighted index.

C)   a 5% change in the price of Kurlew would have a greater impact on a value-weighted index than a 5% change in the prices of either Lair or Mowe.

D)   an investor creating a price-weighted index using these three stocks would need to rebalance his portfolio at year-end to reflect the price changes.

4.Which of the following statements about indexes is TRUE?

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

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

C)   A value weighted index assumes an investor makes and maintains an equal dollar investment in each stock in their portfolio.

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

5.Use the data below to determine which of the statements is TRUE?

A)   A 100% increase in the stock price of Company A will have a smaller impact on the price-weighted index than a 100% increase in the stock price of Company C.

B)   For a given percentage change in the stock price, Company A will have a greater impact on the market-value weighted index than Companies B or C.

C)   For a given percentage change in the stock price, Company B will have less of an impact on the market-value weighted index as Company C.

D)   A 100% increase in the stock price of Company A will have a greater impact on the price-weighted index than a 100% increase in the stock price of Company B.

答案和详解如下：

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

B)   One problem with an index such as the S& 500 is that firms with greater market capitalization have more impact than other firms.

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

D)   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.

The correct answer was D)

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 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.

2.The table below lists information on price per share and shares outstanding for three companies–Lair Enterprises, Kurlew, Inc., and Mowe, Ltd.

	As of Beginning of Year		As of End of Year
Stock	Price Per Share ($)	# Shares Outstanding	Price Per Share ($)	# Shares Outstanding
Lair	15	10,000	10	10,000
Kurlew	45	5,000	60	5,000
Mowe	90	500	110	500

Assume that at the beginning of the year, the value of the market-weighted index was 100. The one-year return on the market-weighted index is closest to:

A)   30.0%.

B)   8.33%.

C)   13.33%.

D)   7.14%.

The correct answer was B)

Expand the table as follows:

	As of Beginning of Year 1			As of End of Year 1
Stock	Price Per Share (in $)	# Shares Outstanding	Market Capitalization (in $)	Price Per Share (in $)	# Shares Outstanding	Market Capitalization (in $)
Lair	15	10,000	150,000	10	10,000	100,000
Kurlew	45	5,000	225,000	60	5,000	300,000
Mowe	90	500	45,000	110	500	55,000
Total	150		420,000	170		455,000

First, we will calculate the year-end market-weighted index value, then we will calculate the return percentage.

Value of market-weighted index = [(market capitalization_year-end) / (market capitalization_{beginning of year})]* Beginning index value
= (455,000 / 420,000) * 100 = 108.33

One-Year Return = [(Index value_year-end / Index value_{beginning of year}) -1]* 100
= [ (108.33 / 100) – 1] * 100 = 8.33%.

3.If the stocks in the table above are used to create a stock market index, it is least likely that:

A)   a value-weighted index does not need any adjustment to reflect a stock split.

B)   a price-weighted index will have a downward bias compared to a value-weighted index.

C)   a 5% change in the price of Kurlew would have a greater impact on a value-weighted index than a 5% change in the prices of either Lair or Mowe.

D)   an investor creating a price-weighted index using these three stocks would need to rebalance his portfolio at year-end to reflect the price changes.

The correct answer was 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 market value weighted index is most influenced by the stock with the largest market capitalization (Kurlew) and does not need to be adjusted for stock splits. A price-weighted index 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.

4.Which of the following statements about indexes is TRUE?

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

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

C)   A value weighted index assumes an investor makes and maintains an equal dollar investment in each stock in their portfolio.

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

The correct answer was A)

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.

5.Use the data below to determine which of the statements is TRUE?

As of December 31
Company	Stock Price	Shares Outstanding
A	$25	20,000
B	$50	20,000
C	$100	10,000

A)   A 100% increase in the stock price of Company A will have a smaller impact on the price-weighted index than a 100% increase in the stock price of Company C.

B)   For a given percentage change in the stock price, Company A will have a greater impact on the market-value weighted index than Companies B or C.

C)   For a given percentage change in the stock price, Company B will have less of an impact on the market-value weighted index as Company C.

D)   A 100% increase in the stock price of Company A will have a greater impact on the price-weighted index than a 100% increase in the stock price of Company B.

The correct answer was A)

A 100% change in the stock price of Company C will have a larger impact than a 100% change in either stocks A or B on the price-weighted index. A price-weighted index adds together the market price of each stock in the index and then divides this total by the number of stocks in the index. The price-weighted index assumes you purchase one share of each stock represented in the index. The price-weighted index is influenced most by given percentage changes in the higher priced stocks.