Reading 40

Equity Investments · Security Market Indexes

MODULE 40.1: INDEX CONSTRUCTION

LOS 40.a

Describe a security market index.

A security market index represents the performance of an asset class, security market, or segment of a market. Indexes are constructed from constituent securities selected from a target market. The performance of the market or segment over a period of time is represented by the percentage change in (i.e., the return on) the value of the index.

The price return of an index reflects only the prices of the constituent securities. The total return reflects both the prices of the constituent securities and any income they generate (such as dividends or interest).

中文翻譯

證券市場指數代表某資產類別、證券市場或市場某一區段的績效。指數由從目標市場挑選的成分證券（constituent securities）組成；某段期間市場或區段的表現以指數價值的百分比變動（即報酬率）來呈現。

價格報酬（price return）只反映成分證券的價格變動；總報酬（total return）同時反映價格變動與成分證券所產生的所得（如股利、利息）。

LOS 40.b

Calculate and interpret the value, price return, and total return of an index.

The price return is the percentage change in the index value over the period; the total return additionally includes any cash distributions (dividends or interest) earned over the period:

\[ \text{Price return} = \frac{V_1 - V_0}{V_0} \qquad \text{Total return} = \frac{V_1 - V_0 + \text{Income}_1}{V_0} \]

Once returns are calculated for each period, they then can be compounded together to arrive at the return for the measurement period:

\[ R_P = (1+R_{S1})(1+R_{S2})(1+R_{S3})(1+R_{S4})\cdots(1+R_{Sk}) - 1 \]

where:
$R_P$ = portfolio return during the measurement period
$k$ = total number of subperiods
$R_{Sk}$ = portfolio return during the subperiod $k$

For example, if the returns for the first two periods were 0.50% and 1.04%, they would be geometrically linked to produce 1.55%:

\[ R_P = (1+R_{S1})(1+R_{S2}) - 1 = (1.005)(1.0104) - 1 = 0.0155 \text{ or } 1.55\% \]

If the starting index value is 100, its value after two periods would be $100 \times 1.0155 = 101.55$.

中文翻譯

價格報酬＝期末指數值對期初的百分比變動；總報酬另加上期內現金分配（股利或利息）。

各子期間報酬計算後可幾何連乘得整段期間報酬：

$R_P = (1+R_{S1})(1+R_{S2})\cdots(1+R_{Sk}) - 1$

例：兩子期報酬分別為 0.50% 與 1.04%，幾何連乘後為 $(1.005)(1.0104)-1 = 1.55\%$。若起始指數＝100，兩期後＝$100 \times 1.0155 = 101.55$。

LOS 40.c

Describe the choices and issues in index construction and management.

Index providers must make several decisions:

What is the target market the index is intended to measure?
Which securities from the target market should be included?
How should the securities be weighted in the index?
How often should the index be rebalanced?
When should the selection and weighting of securities be re-examined?

The target market may be defined broadly (e.g., stocks in the United States) or narrowly (e.g., small-cap value stocks in the United States). It may also be defined by geographic region or by economic sector (e.g., cyclical stocks). The constituent stocks in the index could be all the stocks in that market or just a representative sample. The selection process may be determined by an objective rule or subjectively by a committee.

中文翻譯

編製指數時，提供者必須決定：

目標市場是什麼？
應納入哪些證券？
各證券的加權方式？
多久再平衡一次？
多久重新檢討一次成分與權重？

目標市場可廣定（如美國全市場股票）或窄定（如美國小型價值股），也可依地理區或產業（如景氣循環股）劃分。成分股可為市場全體或代表性樣本；選股流程可採客觀規則或由委員會主觀決定。

LOS 40.d

Compare the different weighting methods used in index construction.

Weighting schemes for stock indexes include price weighting, equal weighting, market capitalization weighting, float-adjusted market capitalization weighting, and fundamental weighting.

Price Weighting

A price-weighted index is simply an arithmetic average of the prices of the securities included in the index. The divisor of a price-weighted index is adjusted for stock splits and changes in the composition of the index when securities are added or deleted, such that the index value is unaffected by such changes.

Advantage: simple to compute. Disadvantages: a given percentage change in the price of a higher-priced stock has a greater impact on the index than the same percentage change in a lower-priced stock — i.e., higher-priced stocks have more weight. A stock's weight changes when the firm splits its stock, repurchases stock, or issues stock dividends. A portfolio with an equal number of shares in each constituent stock will match the index's price returns (ignoring dividends).

Two major price-weighted indexes are the Dow Jones Industrial Average (DJIA) — based on 30 U.S. stocks — and the Nikkei Dow Jones Stock Average — built from 225 stocks on the first section of the Tokyo Stock Exchange.

Equal Weighting

An equal-weighted index is calculated as the arithmetic average return of the index stocks and, for a given time period, would be matched by the returns on a portfolio that had equal dollar amounts invested in each index stock.

Advantage: simplicity. Disadvantages: a matching portfolio must be periodically rebalanced as prices change, creating high transactions costs. The weights placed on the returns of smaller-cap firms are greater than their proportion of overall market value, while large-cap firms are underweighted relative to their proportion of overall market value.

The Value Line Composite Average and the Financial Times Ordinary Share Index are well-known examples of equal-weighted indexes.

Market Capitalization Weighting

A market capitalization-weighted index (or value-weighted index) has weights based on the market capitalization of each index stock (current stock price × number of shares outstanding) as a proportion of the total market capitalization of all the stocks in the index. A matching portfolio holds each security in the same proportion of total portfolio value as its market-cap weight in the index.

This weighting method more closely represents changes in aggregate investor wealth than price weighting. Because weights are based on market cap, the index does not need adjustment when a stock splits or pays a stock dividend.

Float-Adjusted Market Capitalization Weighting

An alternative is to use a firm's market float — the total value of shares actually available to the investing public, excluding shares held by controlling stockholders (who are unlikely to sell). For example, the float for Microsoft would exclude shares owned by Bill Gates, Paul Allen, and other large shareholders. Market float is often calculated excluding shares held by corporations or governments as well. Excluding shares not available to foreign buyers gives the free float.

A float-adjusted market capitalization-weighted index is constructed like a market capitalization-weighted index, except weights are based on the proportion of each firm's shares actually available to investors. Firms with relatively large percentages of shares held by controlling stockholders carry less weight than in an unadjusted market-cap index.

Advantage of market-cap indexes: security weights represent proportions of total market value. Disadvantage: the relative impact of a stock's return increases as its price rises and decreases as its price falls — so possibly overvalued stocks get disproportionately high weights and undervalued stocks low weights. Holding a value-weighted portfolio is therefore similar to following a momentum strategy.

The Standard and Poor's 500 (S&P 500) Index Composite is an example of a market capitalization-weighted index.

Fundamental Weighting

An index that uses fundamental weighting uses weights based on firm fundamentals such as earnings, dividends, or cash flow. In contrast to market-cap index weights, fundamental weights are unaffected by share prices (although related to them over the long term). Weights can be based on a single measure or some combination of fundamental measures.

Advantage: avoids the bias of market-cap-weighted indexes toward overvalued firms and away from undervalued firms. A fundamental-weighted index will have a value tilt, overweighting firms with high value-based metrics such as book-to-market ratios or earnings yields. A firm with a high earnings yield (total earnings ÷ total market value) will, by construction, have a higher weight in an earnings-weighted index.

中文翻譯

股票指數加權方式：價格加權、等權、市值加權、流通市值（float）加權、基本面加權。

價格加權：直接算術平均成分股價。除數會因股票分割或成分股變動而調整，以維持指數連續性。優點：計算簡單。缺點：高價股影響大；分割／回購／股票股利會改變權重。持有等量股數之投資組合可複製其價格報酬（不含股利）。代表：道瓊工業指數（DJIA, 30 檔）、日經 225。

等權：對所有成分股報酬給予相同權重。等金額投資每檔股票之投組可複製。優點：簡單。缺點：需頻繁再平衡，交易成本高；小型股相對被高配、大型股被低配。代表：Value Line Composite Average、FT Ordinary Share Index。

市值加權（value-weighted）：權重 = 個股市值 ÷ 全部成分股總市值。比價格加權更能反映整體投資人財富變動；分割或股票股利無須調整。代表：S&P 500。

流通市值（float）加權：以實際可供投資人交易的股份計算權重。Float 排除控制股東所持股份（如 Microsoft 排除 Gates、Allen 持股），亦常排除企業／政府持股。再排除外資不可購買者即自由流通（free float）。控股集中度高的公司權重較低。

市值加權之優點：權重等於市值占比。缺點：被高估股票權重相對被拉高、被低估者被壓低，類似動能策略。

基本面加權：以盈餘、股利、現金流等基本面項目為權重，不受股價直接影響。優點：避開市值加權偏向高估股的偏差，會呈價值傾斜，高 B/M 或高盈餘殖利率者權重較高。

LOS 40.e

Calculate and analyze the value and return of an index given its weighting method.

Price Weighting

A price-weighted index adds the market prices of each stock in the index and divides this total by the number of stocks in the index. The divisor must be adjusted for stock splits and other changes to maintain continuity.

\[ \text{Price-weighted index} = \frac{\text{sum of stock prices}}{\text{number of stocks in index (adjusted for splits)}} \]

Example: Price-weighted index

Given the information for the three stocks presented in the following figure, calculate a price-weighted index return over a one-month period.

Index Firm Data

Stock	Share Price (Dec 31, 20X6)	Share Price (Jan 31, 20X7)
Stock X	$10	$20
Stock Y	$20	$15
Stock Z	$60	$40

Answer

The price-weighted index is $(10 + 20 + 60) / 3 = 30$ as of December 31, and $(20 + 15 + 40) / 3 = 25$ as of January 31. Hence, the price-weighted 1-month percentage return is:

\[ \frac{25 - 30}{30} = -16.7\% \]

Example: Adjusting a price-weighted index for stock splits

At the market close on Day 1, Stock A has a price of $10, Stock B has a price of $20, and Stock C has a price of $90. The value of a price-weighted index of these three stocks is $(10 + 20 + 90) / 3 = 40$ at the close of trading. If Stock C splits 2-for-1, effective on Day 2, what is the new denominator for the index?

Answer

The effect of the split on the price of Stock C, in the absence of any change from the price at the end of Day 1, would be to reduce it to $$90 / 2 = $45$. The index denominator will be adjusted so that the index value would remain at 40 if there were no other changes in stock prices. The new denominator $d$ must satisfy:

\[ \frac{10 + 20 + 45}{d} = 40 \quad \Rightarrow \quad d = \frac{75}{40} = 1.875 \]

The returns on a price-weighted index could be matched by purchasing an equal number of shares of each stock represented in the index. Because the index is price weighted, a percentage change in a high-priced stock has a relatively greater effect on the index than the same percentage change in a low-priced stock.

Market Capitalization Weighting

A market capitalization-weighted index is calculated by summing the total value (current stock price × number of shares outstanding) of all the stocks in the index. This sum is divided by a similar sum for the selected base period, then multiplied by the index's base value (typically 100).

\[ \text{Current index value} = \frac{\text{current total market value of index stocks}}{\text{base year total market value of index stocks}} \times \text{base year index value} \]

For example, if the total market values of the index portfolio on December 31 and January 31 are $80 million and $95 million, respectively, the index value at the end of January is:

\[ \frac{\$95\text{M}}{\$80\text{M}} \times 100 = 118.75 \]

The market capitalization-weighted index percentage return is $(118.75 / 100) - 1 = 18.75\%$.

Example: Price-weighted vs. market capitalization-weighted indexes

Consider the three firms described in the following table. Compare the effects on a price-weighted index and a market capitalization-weighted index if Stock A doubles in price or if Stock C doubles in price. Assume the period shown is the base period for the market capitalization-weighted index and that its base value is 100.

Index Firm Data

Company	Number of Shares Outstanding (000s)	Stock Price	Capitalization
A	100	$100	$10,000,000
B	1,000	$10	$10,000,000
C	20,000	$1	$20,000,000

Answer

Price-weighted index equals:

\[ \frac{100 + 10 + 1}{3} = 37.00 \]

If Stock A doubles to $200: $\frac{200 + 10 + 1}{3} = 70.33$.

If Stock C doubles to $2: $\frac{100 + 10 + 2}{3} = 37.33$.

If Stock A doubles, the index goes up 33.33 points; if Stock C doubles, the index only goes up 0.33 points. Changes in the value of the firm with the highest stock price have a disproportionately large influence on a price-weighted index.

Market capitalization-weighted index: base period market cap = $(100{,}000 \times \$100) + (1{,}000{,}000 \times \$10) + (20{,}000{,}000 \times \$1) = \$40{,}000{,}000$.

If Stock A doubles to $200:

\[ \frac{(100{,}000 \times \$200) + (1{,}000{,}000 \times \$10) + (20{,}000{,}000 \times \$1)}{\$40{,}000{,}000} \times 100 = 125 \]

If Stock C doubles to $2:

\[ \frac{(100{,}000 \times \$100) + (1{,}000{,}000 \times \$10) + (20{,}000{,}000 \times \$2)}{\$40{,}000{,}000} \times 100 = 150 \]

In the market capitalization-weighted index, the returns on Stock C have the greatest influence on the index return because Stock C's market capitalization is larger than that of Stock A or Stock B.

Equal Weighting

An equal-weighted index places an equal weight on the returns of all index stocks, regardless of their prices or market values. A $2 change in the price of a $20 stock has the same effect on the index as a $30 change in the price of a $300 stock regardless of the size of the company. The return of an equal-weighted index over a given period is often calculated as a simple average of the returns of the index stocks.

\[ \text{Equal-weighted index} = (1 + \text{average \% change in index stocks}) \times \text{initial index value} \]

Example: Equally weighted index

Calculate the equal-weighted index value for the three stocks described in the following table, assuming an initial index value of 131.

Equal-Weighted Index Data

Stock	Initial Price	Current Price	Price Change
A	$12	$15	+25.0%
B	$52	$48	−7.7%
C	$38	$45	+18.4%

Answer

\[ \text{Average change} = \frac{25.0\% + (-7.7\%) + 18.4\%}{3} = 11.9\% \]

\[ \text{New index value} = 131 \times (1 + 0.119) = 146.59 \]

Note that for a total return index, period returns would include any dividends paid over the period.

中文翻譯

價格加權指數＝成分股股價總和 ÷ 經分割調整後股票數。

例：12/31 三檔(10,20,60)→指數=30；1/31 (20,15,40)→指數=25；月報酬 = (25−30)/30 = −16.7%。

分割除數調整：原 (10+20+90)/3 = 40；C 由 90 分割為 45 後須維持 40，新除數 d = 75/40 = 1.875。

價格加權可用等股數投組複製；高價股影響較大。

市值加權指數＝（當期總市值 ÷ 基期總市值）× 基期指數值。例：80M→95M，指數＝95/80×100＝118.75，報酬＝18.75%。

價格加權 vs. 市值加權範例：A 翻倍→價權跳至 70.33（+33.33）但市值權僅至 125；C 翻倍→價權僅 37.33（+0.33）但市值權升至 150。最大市值股對市值加權指數影響最大。

等權指數＝(1 + 平均百分比變動) × 初始指數值。例：A +25%、B −7.7%、C +18.4%，平均=11.9%，初始 131 → 131×1.119 = 146.59。總報酬指數還需加入股利。

Module Quiz 40.1

1. Choices that must be made when constructing a security market index least likely include whether to:

A. use a nominal or interval scale.
B. measure the performance of an entire market or market segment.
C. weight the securities equally or by some firm-specific characteristic.

A — To be useful, a security market index must have a numerical value. Selecting the target market and determining the weighting method are among the choices that must be made when constructing a securities index. (LOS 40.a, 40.c)

Use the information in the following table to answer Questions 2 through 4.

	As of January 1		As of December 31
	Share Price	Number of Shares Outstanding (thousands)	Share Price	Number of Shares Outstanding (thousands)
Stock A	$22	1,500	$28	1,500
Stock B	$40	10,000	$50	10,000
Stock C	$34	3,000	$30	3,000

2. The 1-year return on a price-weighted index of these three stocks is closest to:

A. 12.5%.
B. 13.5%.
C. 18.0%.

A — $\frac{22+40+34}{3} = 32$; $\frac{28+50+30}{3} = 36$; $\frac{36}{32} - 1 = 0.125 = 12.5\%$. (LOS 40.b, 40.d, 40.e)

3. The 1-year return on an equal-weighted index of these three stocks is closest to:

A. 12.0%.
B. 12.5%.
C. 13.5%.

C — $\frac{1}{3}\left[\left(\frac{28}{22}-1\right)+\left(\frac{50}{40}-1\right)+\left(\frac{30}{34}-1\right)\right] = 0.135 = 13.5\%$. (LOS 40.b, 40.d, 40.e)

4. The 1-year return on a market capitalization-weighted index of these stocks is closest to:

A. 12.5%.
B. 13.5%.
C. 18.0%.

C — Total portfolio value Jan 1: $22(1{,}500) + 40(10{,}000) + 34(3{,}000) = \$535{,}000$. Total portfolio value Dec 31: $28(1{,}500) + 50(10{,}000) + 30(3{,}000) = \$632{,}000$. $\frac{632}{535} - 1 = 0.1813 \approx 18\%$. From a base value of 100, the December 31 index value would be $\frac{632}{535}\times 100 = 118.13$. (LOS 40.b, 40.d, 40.e)

5. Market float of a stock is best described as its:

A. total outstanding shares.
B. shares that are available to domestic investors.
C. outstanding shares, excluding those held by controlling shareholders.

C — Market float represents shares available to the investing public and excludes shares held by controlling shareholders. Free float is a narrower measure that also excludes shares that are not available to foreign investors. (LOS 40.d)

6. For which of the following indexes will rebalancing occur most frequently?

A. A price-weighted index.
B. An equal-weighted index.
C. A market capitalization-weighted index.

B — An equal-weighted index will be rebalanced most frequently because as stock prices change, their representation in the index needs to be adjusted. Price-weighted and market capitalization-weighted indexes do not usually need rebalancing. (LOS 40.d)

MODULE 40.2: USES AND TYPES OF INDEXES

LOS 40.f

Describe rebalancing and reconstitution of an index.

Rebalancing refers to adjusting the weights of securities in a portfolio to their target weights after price changes have affected the weights. For index calculations, rebalancing is done on a periodic basis, usually quarterly. Because the weights in price- and value-weighted indexes are adjusted to their correct values by changes in prices, rebalancing is an issue primarily for equal-weighted indexes. The weights on security returns in an (initially) equal-weighted portfolio are not equal as prices change over time, so rebalancing at the end of each period is necessary for the portfolio return to match the index return.

Index reconstitution refers to periodically adding and deleting securities that make up an index. Securities are deleted if they no longer meet the index criteria and are replaced by other securities that do. Indexes are reconstituted to reflect corporate events such as bankruptcy or delisting and are at the subjective judgment of a committee.

When a security is added to an index, its price tends to rise as portfolio managers seeking to track that index buy the security. The prices of deleted securities tend to fall as portfolio managers sell them. Additions and deletions also require that the weights on the returns of other index stocks be adjusted to conform to the desired weighting scheme.

中文翻譯

再平衡（rebalancing）：因價格變動使權重偏離目標後，將其調回目標權重。指數通常每季再平衡一次。價格加權與市值加權的權重會隨價格自動調整，再平衡主要是等權指數的問題。

重新組成（reconstitution）：定期新增／剔除成分證券。不符標準者剔除，反映破產、下市等公司事件，常由委員會主觀判斷。

新增證券價格通常會上漲（追蹤該指數的基金買入），剔除者下跌（基金賣出）。新增／剔除後，其他成分股權重也要重新調整。

LOS 40.g

Describe uses of security market indexes.

Security market indexes have several uses:

Reflection of market sentiment. Indexes provide a representative market return and thus reflect investor confidence. Although the DJIA is a popular index, it reflects the performance of only 30 stocks and thus may not be a good measure of sentiment with regard to the broader market.
Benchmark of manager performance. Used to evaluate the performance of an active manager. Because portfolio performance depends on chosen style, the benchmark should be consistent with the manager's investment approach. A value manager should be compared against a value index, not a broad market index.
Measure of market return and risk. In asset allocation, estimates of the expected return and standard deviation for various asset classes are based on historical returns for an index of securities representing that asset class.
Measure of beta and risk-adjusted return. The CAPM uses index portfolio returns as a proxy for the returns on the market portfolio, both in estimating a stock's beta and then in calculating its expected return. Expected returns can then be compared to actual stock returns to determine systematic risk-adjusted returns.
Model portfolio for index funds. Investors who wish to invest passively can invest in an index fund (mutual fund or ETF) that seeks to replicate the performance of a market index.

中文翻譯

指數的用途：

反映市場情緒：但 DJIA 僅 30 檔，未必能代表整體市場。
績效基準：基準應與經理人風格一致，價值型應比價值指數，不可比廣泛市場指數。
市場報酬與風險衡量：資產配置時用以估計各資產類別的期望報酬與標準差。
估計 β 與風險調整後報酬：CAPM 以指數作為市場投組代理。
指數型基金的模板：被動投資人可購買指數型共同基金或 ETF 複製指數表現。

LOS 40.h

Describe types of equity indexes.

Equity indexes can be classified as follows:

Broad market index. Provides a measure of a market's overall performance and usually contains more than 90% of the market's total value. The Wilshire 5000 Index contains more than 6,000 equity securities and is a good representation of the overall U.S. equity market.
Multi-market index. Constructed from the indexes of markets in several countries. Used to measure equity returns of a geographic region (e.g., Latin America), markets based on stage of economic development (e.g., emerging markets), or the entire world (e.g., MSCI World Index).
Multi-market index with fundamental weighting. Uses market-cap weighting for the country indexes but then weights the country index returns in the global index by a fundamental factor (e.g., GDP). This prevents a country with previously high stock returns from being overweighted.
Sector index. Measures returns for an industry sector such as health care, financial, or consumer goods firms. Investors use these in cyclical analysis because some sectors do better in different phases of the business cycle. Can be country-specific or global.
Style index. Measures returns to market capitalization and value or growth strategies. Some indexes reflect a combination (e.g., small-cap value). Different indexes use different definitions of large/mid/small-cap (specified market-cap values, or relative — e.g., the largest 500 firms). Value vs. growth typically uses P/E or dividend yield. Stocks can migrate between classifications, so style indexes typically have higher turnover than broad market indexes.

中文翻譯

股票指數類型：

廣泛市場指數：通常涵蓋市場 90% 以上總市值，如 Wilshire 5000（含 6000+ 檔，代表美國股市）。
多市場指數：跨國組成，用以衡量地區（拉美）、經濟階段（新興市場）或全球（MSCI World）。
基本面加權多市場指數：國別指數內以市值加權，國別在全球指數中以基本面因子（如 GDP）加權，避免高報酬國權重過大。
產業指數：衡量單一產業（醫療、金融、消費）。可用於景氣循環分析。
風格指數：依市值（大／中／小）、價值／成長分類。各指數定義不一，常用 P/E 或股利殖利率區分價值／成長。股票會在類別間移動，故風格指數成分週轉率高於廣泛市場指數。

LOS 40.i

Compare types of security market indexes.

The following table summarizes characteristics of various global indexes. Most security market indexes are market capitalization-weighted and often adjusted for the float. The number of securities in many indexes can vary.

Index	Reflects	Number of Constituent Securities	Weighting Method	Notes
Dow Jones Industrial Average	Large U.S. stocks	30	Price	Stocks are chosen by Wall Street Journal editors
Nikkei Stock Average	Large Japanese stocks	225	Modified price	Price weighted and adjusted for high-priced shares
TOPIX	All stocks on Tokyo Stock Exchange First Section	Variable	Market cap, float-adjusted	Has many small illiquid stocks; hard to replicate. Contains 93% of Japanese equities by cap.
MSCI All Country World Index	Stocks in 23 developed and 24 emerging markets	Variable	Market cap, float-adjusted	Available in both U.S. dollars and local currency
S&P Developed Ex-U.S. BMI Energy Sector Index	Global energy stocks outside the U.S.	Variable	Market cap, float-adjusted	Model portfolio for an ETF
Barclays Capital Global Aggregate Bond Index	Global investment-grade bonds	Variable	Market cap	Formerly compiled by Lehman Brothers
Markit iBoxx Euro High-Yield Bond Indexes	Below investment-grade bonds	Variable	Market cap	Represents liquid portion of market; rebalanced monthly
FTSE EPRA/NAREIT Global Real Estate Index	Global real estate	Variable	Market cap, float-adjusted	Represents publicly traded REITs
HFRX Global Hedge Fund Index	Global hedge funds	Variable	Asset weighted	Various hedge fund strategies; weighted by amount invested
HFRX Equal Weighted Strategies EUR Index	Global hedge funds	Variable	Equal weighted	Same strategy funds as HFRX Global, but equal weighted
Morningstar Style Indexes	U.S. stocks grouped by value/growth and market cap	Variable	Market cap, float-adjusted	Nine categories (3 cap × 3 value/growth)

中文翻譯

多數全球指數採市值加權並做流通調整，成分檔數常為變動。常見指數比較：

DJIA：30 檔美股，價格加權，由《華爾街日報》編輯選股
Nikkei：225 檔日股，修正價格加權（對高價股調整）
TOPIX：東證一部全部股票，市值（流通調整）；含 93% 日股市值，因小型股流動性差難複製
MSCI ACWI：23 已開發 + 24 新興市場，市值（流通調整），美元或當地貨幣
S&P Developed Ex-U.S. BMI Energy：全球能源股（不含美），ETF 模板
Barclays Capital Global Aggregate Bond：全球投資級債券，市值加權，前身為 Lehman
Markit iBoxx Euro 高收益：投資級以下，月再平衡
FTSE EPRA/NAREIT：全球公開交易 REIT
HFRX Global Hedge Fund：依各基金資產加權；HFRX Equal Weighted：相同基金等權重
Morningstar Style：美股，市值（流通調整），3×3=9 種風格分類

LOS 40.j

Describe types of fixed-income indexes.

Fixed-income securities vary widely with respect to their coupon rates, ratings, maturities, and embedded options. Consequently, a wide variety of fixed-income indexes is available. Like equity indexes, fixed-income indexes are created for various sectors, geographic regions, and levels of country economic development. They can also be constructed based on type of issuer or collateral, coupon, maturity, default risk, or inflation protection. Broad market, sector, style, and other specialized indexes are available.

Investors should be aware of several issues with the construction of fixed-income indexes:

Large universe of securities. The fixed-income security universe is much broader than the universe of stocks. Fixed-income securities are issued not just by firms, but also by governments and government agencies. Each entity may issue various types of fixed-income securities. Also, unlike stocks, bonds mature and must be replaced in fixed-income indexes — so turnover is high.
Dealer markets and infrequent trading. Fixed-income securities are primarily traded by dealers, so index providers must depend on dealers for recent prices. Because securities are typically illiquid, a lack of recent trades may require providers to estimate values from recent prices of similar securities.

The large number of fixed-income securities results in large differences in the number of constituent securities among fixed-income indexes. Illiquidity, transactions costs, and high turnover make it both difficult and expensive for fixed-income portfolio managers to replicate a fixed-income index.

中文翻譯

固定收益證券的票息、評等、期限、嵌入選擇權差異大，故固定收益指數種類繁多——涵蓋產業、地區、經濟階段，並可依發行人／擔保品／票息／到期／違約風險／通膨保護分類。

編製問題：

債券宇宙廣大：發行人含企業、政府、政府機構；債券會到期需替換，週轉率高。
交易商市場、低流動性：價格須仰賴交易商；缺乏成交時須以類似債券價格估價。

結果：成分檔數差異大；交易成本與週轉率高，複製困難且昂貴。

LOS 40.k

Describe indexes representing alternative investments.

Alternative assets are of interest to investors because of their potential diversification benefits. Three of the most widely held alternative assets are commodities, real estate, and hedge funds.

Commodity Indexes

Commodity indexes represent futures contracts on commodities such as grains, livestock, metals, and energy. Examples include the Thomson Reuters/Core Commodity CRB Index (previously the Commodity Research Bureau Index) and the S&P GSCI (previously the Goldman Sachs Commodity Index). Issues:

Weighting method. Providers use a variety of schemes — equal weighting, weighting by global production values, or fixed weights set by the provider. As a result, different indexes have significantly different commodity exposures and risk-return characteristics (one index may be heavy in energy, another in agriculture).
Futures vs. actual. Commodity indexes are based on the prices of commodity futures contracts, not the spot prices. Futures contracts reflect the risk-free rate of return, changes in futures prices, and the roll yield. Contracts mature and must be replaced over time. For these reasons, the return on commodity futures differs from the returns on a long position in the commodity itself.

Real Estate Indexes

Real estate indexes can be constructed using returns based on:

Appraisals of properties
Repeat property sales
Performance of Real Estate Investment Trusts (REITs)

REITs are similar to closed-end mutual funds in that they invest in properties or mortgages and then issue ownership interests in the pool of assets to investors. While real properties are quite illiquid, REIT shares trade like any common shares and many offer good liquidity. FTSE International produces a family of REIT indexes.

Hedge Fund Indexes

Hedge funds pool investor money and invest in nontraditional assets, using leverage (borrowed money or derivative contracts) and both long and short positions. Most hedge fund indexes equally weight the returns of the hedge funds included in the index.

Hedge funds are largely unregulated and not required to report performance to index providers. Consequently, some funds will report to one index but not another, and the performance of different indexes can vary substantially.

Furthermore, it is often the case that those funds that report are the funds that have been successful, as poorly performing funds do not want to publicize their performance. Funds that have reported in the past but have recently had poor returns may stop reporting. The result is an upward bias in index returns, with hedge funds appearing to be better investments than they actually are.

中文翻譯

另類投資因具分散效益備受關注，三大常見類別：商品、不動產、避險基金。

商品指數：以商品期貨契約為基礎（穀物、畜產、金屬、能源），例如 CRB、S&P GSCI。

加權方式：等權、依全球產量、或提供者指定固定權重，導致各指數曝險差異大。
期貨 vs. 現貨：以期貨價編製，含無風險報酬、期貨價格變動、轉倉收益（roll yield）三要素；契約到期需轉倉，故商品期貨報酬不同於現貨多頭。

不動產指數：可採三類資料：物件估值、重複交易、REIT 績效。REIT 類似封閉式基金，雖實體不動產流動性差但 REIT 股票流動性佳。FTSE International 編製多檔 REIT 指數。

避險基金指數：多採等權。避險基金不受監管、自願申報，故各指數差異大；績效差者多不申報、過去報的若績效轉壞會停報，導致指數報酬向上偏誤，使避險基金看起來比實際好。

Module Quiz 40.2

1. The publisher of an index that includes 50 corporate bonds removes from the index three bonds that are nearing maturity and one whose issuer has defaulted and selects four actively traded bonds to replace them in the index. This bond index is said to have been:

A. redefined.
B. rebalanced.
C. reconstituted.

C — Changing the constituent securities of an index is referred to as reconstituting the index. Rebalancing refers to adjusting the index weights to their target levels. (LOS 40.f)

2. Which of the following would most likely represent an inappropriate use of an index?

A. As a reflection of market sentiment.
B. Comparing a small-cap manager against a broad market.
C. Using the CAPM to determine the expected return and beta.

B — Comparing a small-cap manager against a broad market would be an inappropriate use of an index. A benchmark should be consistent with the manager's investment approach and style. A manager's performance will depend to a large degree on its chosen style. (LOS 40.g)

3. An index of 200 mid-cap growth stocks is best described as a:

A. style index.
B. sector index.
C. broad market index.

A — An index for mid-cap growth stocks is best described as a style index. Sector indexes typically measure returns for a specific industry or sector of the economy (e.g., utilities or financial services firms). (LOS 40.h)

4. Which of the following is least accurate regarding fixed-income indexes?

A. Replicating the return on a fixed-income security index is difficult for investors.
B. There is a great deal of heterogeneity in the composition of fixed-income security indexes.
C. Due to the large universe of fixed-income security issues, data for fixed-income securities are relatively easy to obtain.

C — Fixed-income securities are largely traded by dealers and trade infrequently. Data are therefore difficult to obtain. (LOS 40.j)

5. Which of the following indexes of alternative investments is most likely to be calculated from derivatives prices?

A. Real estate index.
B. Commodity index.
C. Hedge fund index.

B — Commodity indexes are typically calculated from prices of commodity futures contracts. (LOS 40.k)

6. Most of the widely used global security indexes are:

A. price weighted.
B. equal weighted.
C. market capitalization weighted.

C — Most global security indexes are market capitalization-weighted with a float adjustment to reflect the amount of shares available to investors. (LOS 40.i)

Key Concepts

LOS 40.a — Security Market Index

A security market index represents the performance of an asset class, security market, or segment of a market. The performance of the market or segment over a period of time is represented by the percentage change in (i.e., the return on) the value of the index.

LOS 40.b — Price Return vs. Total Return

A price index uses only the prices of the constituent securities — the rate of return is called a price return. A total return index uses both the price of and the income from the index securities in the return calculation.

LOS 40.c — Construction Decisions

The target market the index will measure
Which securities from the target market to include
The appropriate weighting method
How frequently to rebalance the index to its target weights
How frequently to re-examine the selection and weighting of securities

LOS 40.d — Weighting Methods

Price-weighted: arithmetic mean of prices; divisor adjusted for splits and composition changes
Equal-weighted: same weight to each constituent
Market cap-weighted: weight = security's market value ÷ total market value (can be float- or free-float-adjusted)
Fundamental-weighted: weights independent of price — based on earnings, revenue, assets, or cash flow

LOS 40.e — Index Calculations

\[ \text{Price-weighted index} = \frac{\text{sum of stock prices}}{\text{number of stocks (adjusted for splits)}} \]

\[ \text{Market cap-weighted index} = \frac{\text{current total market value of index stocks}}{\text{base year total market value}} \times \text{base year index value} \]

\[ \text{Equal-weighted index} = (1 + \text{average \% change in index stocks}) \times \text{initial index value} \]

LOS 40.f — Rebalancing & Reconstitution

Rebalancing: periodically adjust constituent weights to targets — most important for equal-weighted indexes. Reconstitution: change the securities included; necessary when securities mature or no longer have the required characteristics.

LOS 40.g — Uses of Indexes

Reflection of market sentiment
Benchmark of manager performance
Measure of market return
Measure of beta and excess return
Model portfolio for index funds

LOS 40.h — Types of Equity Indexes

Broad market — majority of stocks in a market
Multi-market — combine indexes of several countries
Multi-market with fundamental weighting — country indexes weighted by fundamental factor (e.g., GDP)
Sector — useful because some sectors do better in certain business cycle phases
Style — market-cap and value/growth; higher constituent turnover due to migration

LOS 40.i — Comparing Security Market Indexes

Security market indexes can be classified by:

Geographic location (country, regional, global)
Sector or industry (e.g., energy producers)
Level of economic development (e.g., emerging markets)
Fundamental factors (value or growth indexes)

LOS 40.j — Fixed-Income Indexes

Classified by issuer, collateral, coupon, maturity, credit risk (investment grade vs. high-yield), and inflation protection. Can be broad market, sector, style, or specialized. The fixed-income universe is much broader than equity, and indexes have higher turnover. Index providers depend on dealers for prices, and securities are often illiquid — making indexes difficult and expensive to replicate.

LOS 40.k — Alternative Investment Indexes

Commodities — issues include weighting method (vastly different commodity exposures across indexes) and the fact that indexes are based on commodity futures rather than the actual commodities
Real estate — appraisal indexes, repeat property sales indexes, and REIT indexes
Hedge funds — voluntary reporting causes indexes to vary substantially and creates an upward bias in returns