Reading 46 LOS's

Question 1

Los 46a: Describe a security market index

Answer 1

_A security market index _consists of indiviual securities that represent a given security market, market segment, or asset class. Each security market index may have two versions depending on how returns are claculated

• A price return index only reflects the prices of the constituent securities
• A total return index not only reflects prices, but also assumes reinvestment of all income received since inception

The values of both versions of an index are the same at inception. However, as time passes, the total return index will be greater in value than the price return index by an increasing amount

Question 2

LOS 46b: Calculate and interpret the value, price return, and total return of an index

Answer 2

The value of a price return index is calculated as follows:

• V_PRI = (Σn_iP_i)/ d
• n_i = number of units of constituent security i heldo in the index portfolio
• P_i = Unit price of constiteunt security i
• D= value of the divisor

The divisor is initially chosen as a value that gives the index a concenient inital value. However, over time the divisor must be adjusted to ensure that changes in the index only reflect changes in prices of securities

Calculations of Single Period Returns

Price return of an index can be calculated as:

• PR_I= (V_PRI1 - V_PRI0) / V_PRI0 = ending price minus beginning price / beg price

The price return of the index equals the weighted average price return of the constituent securities and is calculated as:

• PR_I = w₁PR₁ + w₂PR₂ + …. + w_NPR_N

Total return of an index can be calculated as:

• TR_I = (V_PRI1 -V_PRI0 + Inc_I) / V_PRI0 = end value - beg value + total income from all securities in the index held over the period / beg value

The total return of the index equals the weighted average total return of the constituent securities and is calculated as:

• TR_I = w₁TR₁ + w₂TR₂+ …… w_NTR_N

Calculations of Index returns over Multiple Time Periods

The value of a price index would be:

• V_PRIT = V_PRI0 (1 + PR_I1) (1+ PR_I2)…. (1+PR_IT) = value of index at inception times the price returns of the index at each period

The value of the total return would be calculated similarly

• V_TRIT = V_TRI0(1 + TR_I1)(1+TR_I2)…… (1+TR_IT)

Question 3

LOS 46c: Describe the choices and issues in index contruction and management

Answer 3

Constructing and managing a security market index involves:

• target market selection
• security selection
• index weighting
• rebalancing
• reconstitution

Target Market and Security Selection

When constructing a security market index, the first decision that must be made relates to which market, market segment, or asset class the index should represent. The target market may be based on:

• Asset Class
• Geographic region
• The exchange on which the securities trade
• Other characteristics

An index may consist of all the securities in the target market or just a representative sample of the target market. Some fix the number of securities in the index, while others allow the number of securities to vary to reflect changes

Question 4

LOS 46d: Compare the different weighting methods used in index construction

LOS 46e: Calculate and analyze the value and return of an index given its weighting method

Answer 4

Price weighting

In a price-weighted index the weight of each constituent security is determined by dividing its price by the sume of the prices of all constituent securities:

w_i^p= P_i / ΣP_i

The value of the price-weighted index is computed by dividing the sum of the security prices by the divisor.

The advantage of a price-weighted index is simplicity. One of the issues is that a stock split or stock dividend by one of the constituent securities chnages the weights of all securities in the index. To prevent stock splits and stock dividends from changing the value of the index, the divisor of a price-weighted index must be adjusted

Equal Weighting

In this index, each security is given an indentical weight in the index at inception.

The number of shares of each security included in the index is calculated as the value allotted to each constituent security divided by the price of the security. Unlike a price-weighted index, where the weighted are arbitrarily determined by market prices, the weights in an equal-weighted index are effectively determined by the index provider.

Equal weighted indicies are also preferred because of their simplicity. However, they have a few disadvantages:

• Assigning an equal weight to all securities under-represents those securities that consitute a relatively large fraction of the target market
• The index does not remain equally weighted once the prices of the constituent securities change. Frequent adjustments must be made to maintain equal weighting

Market-Capitalization Weighting

A market cap weighted (value weighted) index is based on the total market value of all stocks in the index. The proportion of each security is determined by dividing its market cap by the total market cap of all securities in the index:

• w_i^M = Q_iP_i / Σ Q_jP_j

The initial market value is assigned a base number and a new market value is computed periodically. The change in the index is measured by comparing the new market value to the base market value.

Value weighted indicies automatically adjust for stock splits and stock dividends

Float-Adjusted Market- Cap Weighting

In a float-adjusted index, the proportion of each security is determined by adjusting its market cap for its market float. Market float generally refers to the number of shares of the security that are available to the investing public. Shares held by controlling shareholders, other corporations, and governments are subtracted from the total number of outstanding shares to determine the market float

The weight of each security is calculated as:

• w_i^M= f_iQ_iP_i / Σf_jQ_jP_j

The primary advantage is that securities are held in proportion to their value in the target market. A disadvantage is that stocks with larger market values have a larger impact on the index. Stocks that have seen their prices rise will see their relative weight in the index increase.

Fundamental Weighting

Instead of using prices of securities, a fundamental weighted index uses other measures of a company’s size such as book value, cash flow, revenues, and earnings to determine weights of securities in the index. Some fundamental indicies use a single measure to weight the constituent securities, while others combine weights from several measures to form a composite value that is used to weighting

The weight on each security can be calculated as

• w_i^F = F_i / ΣF_j

Question 5

Los 46f; Describe rebalancing and reconstitution of an index

Answer 5

Rebalancing

In order to keep the weights of constituent securities consistent with the index’s weighting method, security weights must be adjusted or rebalanced:

• In equal-weighted indicies, the weights of the securities have witnessed price appreciation increase over time, while those that underperformed decrease in weight. So rebalancing would involve doing the opposite to these securities
• Price weighted index indicies do not need to be rebalanced, as the weight of each security is determined by its price
• Market cap indices rebalance themselves to changes in market cap of securities. They only need to be rebalanced to reflect mergers, acquisitions, liquidations and so on

Reconstitution

This refers to the process of changing the constituent securities in an index. Constituent securites need to be examined on a regular basis to evaluate whether they still meet the cirteria for inclusion in the index. If they don’t they must be replaced with ones that do. This is done in order to:

• Reflect changes in the target market as a result of bankruptcies, de-listing, mergers, and so on
• Reflect the judgement of the selection committee

Reconstitution creates turnover within the index as once the revised list of constituent securities is determined, the weights of all constituent securities must be recalculated

Question 6

LOS 46g: Describe uses of security market indices

Answer 6

• Indicies are good indicatorsof the collective opinion of market participants and are used to gauge market sentiment. However, indicies typically only include a sample of stocks and therefore do not reflect the behavior of investors who trade their own stocks
• They are used as proxies for measuring and modeling returns, systematic risk, and risk-adjusted performance.
• By exhibiting the risk and return profiles of select groups of securities, indicies act as proxies for asset classes in asset allocation models. They provide historical data used to model the risks and returns of different asset classes
• In the field of performance evaluation, indicies are used as benchmarks for actively managed portfolios
• Securty market indicies serve as the basis for the creation of numerous investment products.

Question 7

LOS 46h: Describe types of equity indices

Answer 7

Broad market indicies A broad equity market index contains securities representing more than 90% of the selected market. Ex. Russell 3000

Multi-Market indicies consist of security market indices from different countries and may represent multiple national markets, geographic regions, economic development groups, or even the entire world

Sector Indicies only include securities representing a particular economic sector where the economic sector may be classified on a national, regional, or global basis. These play an important role in evaluating a portfolio manager’s performance and determing whether she is better as stock selection or section allocation

Style Indices financial firms like Dow Jones and S&P have developed different indices based on specific investment strategies used by portfolio managers. These indicies include those based on size and others based on style

Question 8

LOS 46i; Describe Types of fixed-income indices

Answer 8

Creating bond-market indices presents the following challenges:

• there is a broader universe of bonds than of stocks
• The universe of bonds is constantly changing as a result of new issues, calls, and maturities
• The price volatility of a bond is constantly changing. Duration changes with a bond’s maturity and market yields
• Current and contunious transaction prices are not available for bonds

Types of Fixed-Income Indices

Fixed income securities can be classified along the following dimensions:

• Type of issuer
• Type of financing
• Currency Payments
• Maturity
• Credit Quality
• Absence or prescense of inflation protection

Fixed Income indices can be categorized as follows:

• Aggregate or broad market indices
• Market sector indices
• Style indices
• Economic sector indices
• Specialized indices such as high-yield, inflation-linked, and emerging market indices

Question 9

LOS 46j: Decribe the indices representing alternative investments

Answer 9

Commodity Indices consist of futures contracts on one or more commodities and have the following characteristics:

• They do not have an obvious weighting method so index providers create their own weighting methods. They may either be equally weighted or on the basis of price, or may have fixed-weights
• Different weighting methods lead to different exposures to specific commodities, which result in very different risk and return profiles of commodity indices.
• The performance of commodity indices may differ from that of the underlying commodities because indices consist of future contracts on commodities rather than on the actual commodities

Real estate investment trust indicies represent the market for real estate and real estate securities. They can be categorized as:

• Appraisal indices
• Repeat sales indices
• Real estate investment trust (REIT) indices

REIT indices consist of shares of publicily traded REITs and shares issued by REITs trade on various exchanges around the world and are priced continuously

Hedge fund indices are designed to represent the performance of hedge funds on a very broad, global level or the strategy level. Hedge fund indices have the following characteristics:

• They rely on voluntary disclosures from funds, as it is not mandatory for hedge funds to disclose performance to any party other than investors
• If they do decide to disclose performance, hedge funds have a choice regardgin which index or indices they report their performance to . Therefore, rather than index providers determining the constituents, the constituents determine the index.
• Poorly performing hedge funds may stop reporting their performance to hedge fund indices or may cease to exist altogether. This leads to survivorship bias and an upward bias in hedge fund performance as represented by these indices

Question 10

LOS 46k: Compare types of security market indices