Security Market Indexes

Equity

Index Definition and Calculations of Value and Returns

Learning Outcome Statement:

describe a security market index, calculate and interpret the value, price return, and total return of an index

Summary:

A security market index is a representation of a specific market, market segment, or asset class, typically constructed as a portfolio of marketable securities. The value of an index is calculated using the market prices of its constituent securities. Indexes can be categorized into price return indexes, which reflect only the prices of the securities, and total return indexes, which also account for reinvested income. The calculation of index values and returns can be done for single periods or multiple periods, using specific formulas to determine price and total returns.

Key Concepts:

Security Market Index

A tool that represents a specific market or segment, usually constructed as a portfolio of securities.

Price Return Index

An index that reflects only the price changes of its constituent securities.

Total Return Index

An index that reflects both price changes and reinvested dividends or interest of its constituent securities.

Single-Period Returns

Calculations that measure the change in index value from one period to the next, either as price return or total return.

Multiple Time Periods Calculation

Method to calculate index values over several periods, linking returns geometrically to reflect compounded growth.

Formulas:

Price Return Index Value

V_{PRI} = \sum_{i=1}^{N} n_i P_i / D

Calculates the value of a price return index using the prices of the constituent securities and a divisor.

Variables:

$V_{PRI}$ :: value of the price return index
$n_i$ :: number of units of constituent security i held in the index portfolio
$P_i$ :: unit price of constituent security i
$D$ :: value of the divisor
$N$ :: number of constituent securities in the index

Units: index points

Price Return of Index

PRI = (V_{PRI1} - V_{PRI0}) / V_{PRI0}

Calculates the price return of an index over a single period.

Variables:

$PRI$ :: price return of the index portfolio
$V_{PRI1}$ :: value of the price return index at the end of the period
$V_{PRI0}$ :: value of the price return index at the beginning of the period

Units: decimal

Total Return of Index

TRI = (V_{PRI1} - V_{PRI0} + IncI) / V_{PRI0}

Calculates the total return of an index over a single period, including price changes and income.

Variables:

$TRI$ :: total return of the index portfolio
$V_{PRI1}$ :: value of the price return index at the end of the period
$V_{PRI0}$ :: value of the price return index at the beginning of the period
$IncI$ :: total income from all securities in the index held over the period

Units: decimal

Value of Price Return Index Over Multiple Periods

VPRIT = VPRI_0(1 + PRI_1)(1 + PRI_2)...(1 + PRIT)

Calculates the value of a price return index over multiple periods, accounting for compounded returns.

Variables:

$VPRIT$ :: value of the price return index at time t
$VPRI_0$ :: value of the price return index at inception
$PRIT$ :: price return on the index over period t

Units: index points

Value of Total Return Index Over Multiple Periods

VTRIT = VTRI_0(1 + TRI_1)(1 + TRI_2)...(1 + TRIT)

Calculates the value of a total return index over multiple periods, including both price changes and reinvested income.

Variables:

$VTRIT$ :: value of the total return index at time t
$VTRI_0$ :: value of the index at inception
$TRIT$ :: total return on the index over period t

Units: index points

Index Construction

Learning Outcome Statement:

describe the choices and issues in index construction and management, compare the different weighting methods used in index construction, calculate and analyze the value and return of an index given its weighting method

Summary:

Index construction involves selecting a target market and specific securities to represent that market, and deciding how to weight these securities within the index. The process is akin to managing a portfolio of securities. Various weighting methods, such as price weighting, equal weighting, market-capitalization weighting, and fundamental weighting, each have unique impacts on the index's performance and management.

Key Concepts:

Target Market and Security Selection

The target market defines the investment universe for the index, which can be based on factors like asset class, geographic region, or economic sector. Securities are then selected to represent this market, either by including all or a representative sample.

Index Weighting

Weighting determines the influence each security has on the index's overall performance. Common methods include price weighting, where securities are weighted based on their price; equal weighting, where each security is given equal weight; market-capitalization weighting, based on the market value of each security; and fundamental weighting, which uses financial metrics other than market price.

Rebalancing and Reconstitution

Rebalancing involves adjusting the weights of securities in the index to maintain its original or desired profile. Reconstitution involves reviewing and possibly changing the securities included in the index. These processes are crucial for maintaining the relevance and accuracy of the index.

Formulas:

Price Weighting Formula

w_{iP} = \frac{P_i}{\sum_{i=1}^N P_i}

This formula calculates the weight of each security in a price-weighted index, where the weight is proportional to the price of the security.

Variables:

$w_{iP}$ :: weight of security i in a price-weighted index
$P_i$ :: price of security i
$N$ :: total number of securities in the index

Units: dimensionless

Equal Weighting Formula

w_{iE} = \frac{1}{N}

In an equal-weighted index, each security is assigned the same weight, calculated as the reciprocal of the total number of securities.

Variables:

$w_{iE}$ :: weight of security i in an equal-weighted index
$N$ :: total number of securities in the index

Units: dimensionless

Market-Capitalization Weighting Formula

w_{iM} = \frac{Q_i P_i}{\sum_{j=1}^N Q_j P_j}

This formula calculates the weight of each security based on its market capitalization, which is the product of its price per share and the number of shares outstanding.

Variables:

$w_{iM}$ :: weight of security i in a market-capitalization-weighted index
$Q_i$ :: number of shares outstanding of security i
$P_i$ :: price per share of security i
$N$ :: total number of securities in the index

Units: dimensionless

Fundamental Weighting Formula

w_{iF} = \frac{F_i}{\sum_{j=1}^N F_j}

This formula assigns weights based on a fundamental measure of company size, such as earnings or dividends, rather than market price.

Variables:

$w_{iF}$ :: weight of security i in a fundamentally-weighted index
$F_i$ :: fundamental size measure of company i (e.g., earnings, dividends)
$N$ :: total number of securities in the index

Units: dimensionless

Index Management: Rebalancing and Reconstitution

Learning Outcome Statement:

describe rebalancing and reconstitution of an index

Summary:

Rebalancing involves adjusting the weights of the constituent securities in an index to maintain alignment with the index's weighting method, typically done on a scheduled basis. Reconstitution involves changing the constituent securities of an index to reflect changes in the target market or to re-apply the initial criteria for inclusion, often leading to turnover in the index.

Key Concepts:

Fundamental Weighting

Fundamental weighting uses company size measures independent of security price, such as earnings or dividends, to determine weights of securities in an index. This method often results in a 'value' tilt, favoring stocks that are undervalued relative to their fundamentals.

Rebalancing

Rebalancing is the process of adjusting the weights of securities within an index to ensure they align with the prescribed weighting method of the index, such as equal-weight or market-capitalization-weight. This is necessary due to changes in market prices affecting the original weights.

Reconstitution

Reconstitution involves reviewing and altering the constituent securities of an index based on set criteria. This process can lead to significant turnover within the index, especially in response to market events like mergers or bankruptcies.

Formulas:

Fundamental Weight of a Security

w_i^F = \frac{F_i}{\sum_{j=1}^N F_j}

This formula calculates the weight of a security within an index based on a fundamental measure (like earnings or dividends) relative to the sum of that measure across all securities in the index.

Variables:

$w_i^F$ :: weight of security i based on fundamental measure
$F_i$ :: fundamental measure of company i
$N$ :: total number of securities in the index
$F_j$ :: fundamental measure of company j

Units: dimensionless (ratio)

Uses of Market Indexes

Learning Outcome Statement:

describe uses of security market indexes

Summary:

Market indexes serve multiple roles in investment management and financial analysis. Initially designed to reflect the performance of securities on a given day, their applications have broadened to include gauging market sentiment, acting as proxies for various financial metrics, serving as benchmarks for actively managed portfolios, and forming the basis for investment products like index funds and ETFs.

Key Concepts:

Gauges of Market Sentiment

Market indexes provide insights into investor confidence and collective market opinions. Although frequently quoted, indexes like the Dow Jones Industrial Average may not fully represent the broader market sentiment as they cover a limited number of stocks.

Proxies for Measuring and Modeling Returns, Systematic Risk, and Risk-Adjusted Performance

Indexes are used to represent the market portfolio in models like the CAPM, helping in measuring and modeling systematic risk and market returns. They also facilitate the calculation of risk-adjusted performance metrics such as alpha, which indicates the performance of a portfolio relative to a benchmark.

Proxies for Asset Classes in Asset Allocation Models

Indexes represent the risk and return profiles of specific asset classes, providing essential historical data for modeling asset allocation in investment portfolios.

Benchmarks for Actively Managed Portfolios

Indexes are crucial for evaluating the performance of active portfolio managers against appropriate benchmarks that reflect the manager's investment strategy.

Model Portfolios for Investment Products

Market indexes underpin the development of index funds and ETFs, offering investors standardized, passive investment options that aim to replicate the performance of the indexes.

Formulas:

Alpha

\alpha = R_p - R_b

Alpha measures the excess return of an investment relative to the return of a benchmark index.

Variables:

$R_p$ :: return of the actively managed portfolio
$R_b$ :: return of the benchmark or passive portfolio

Units: percentage or basis points

Equity indexes

Learning Outcome Statement:

describe types of equity indexes, compare types of security market indexes

Summary:

Equity indexes are tools used to measure and report the performance of specific market segments. They serve as benchmarks for investment performance, help in the development of investment products like ETFs, and assist in investment decision-making. The main types of equity indexes include broad market indexes, multi-market indexes, sector indexes, and style indexes.

Key Concepts:

Broad Market Indexes

Broad market indexes represent a wide section of an equity market, typically including securities that cover more than 90% of the market by capitalization. Examples include the Shanghai Stock Exchange Composite Index and the Wilshire 5000 Total Market Index in the US.

Multi-Market Indexes

Multi-market indexes comprise indexes from different countries or regions, designed to represent multiple security markets. They can be based on geographic regions, economic development, or both. MSCI, for example, offers a variety of multi-market indexes categorized by economic development and geographic region.

Sector Indexes

Sector indexes track the performance of specific economic sectors such as consumer goods, energy, or technology. These indexes can be national, regional, or global and are crucial for analyzing performance across different economic sectors.

Style Indexes

Style indexes categorize securities based on investment style factors like market capitalization, value, and growth. They help in reflecting the performance of different investment styles and can be subdivided into categories such as large-cap value, mid-cap growth, etc.

Fixed-income indexes

Learning Outcome Statement:

describe types of fixed-income indexes, compare types of security market indexes

Summary:

Fixed-income indexes are essential tools for representing various segments of the bond market, but their construction faces challenges such as the vast number of securities, pricing data availability, and liquidity. These indexes can be categorized based on issuer type, financing type, currency, maturity, credit quality, and inflation protection. They are further divided into aggregate, market sector, style, economic sector, and specialized indexes like high-yield and inflation-linked.

Key Concepts:

Challenges in Fixed-Income Index Construction

The construction of fixed-income indexes is complicated by the large number of securities, the predominantly dealer-based market structure, and the illiquidity of many securities. This complexity makes it costly and difficult to replicate these indexes accurately.

Types of Fixed-Income Indexes

Fixed-income indexes vary widely and can be categorized by issuer type (government, corporate), type of financing (collateralized, general obligation), currency, maturity, credit quality, and inflation protection. They include broad market indexes, sector-specific indexes, and specialized indexes such as high-yield and inflation-linked.

Index Categorization

Fixed-income indexes are categorized into aggregate or broad market indexes, market sector indexes, style indexes, economic sector indexes, and specialized indexes. This categorization helps in targeting specific investment objectives and market segments.

Indexes for Alternative Investments

Learning Outcome Statement:

describe indexes representing alternative investments, compare types of security market indexes

Summary:

This content discusses the construction and use of indexes for alternative investments such as commodities, real estate, and hedge funds. It explains how these indexes are constructed, their weighting methods, and how they differ from traditional equity and bond indexes. The content also highlights the unique characteristics of each type of alternative investment index and the challenges associated with accurately representing their respective markets.

Key Concepts:

Commodity Indexes

Commodity indexes track futures contracts on commodities like agricultural products, livestock, metals, and energy commodities. They use various weighting methods, such as equal weighting or based on liquidity and world production values. The performance of these indexes can differ significantly from the actual commodities due to factors like roll yield and changes in future prices.

Real Estate Investment Trust Indexes

REIT indexes consist of shares of publicly traded REITs and represent the market for real estate securities. They are continuously priced due to their public market presence. These indexes can be based on different methodologies like appraisal, repeat sales, or direct representation through REITs.

Hedge Fund Indexes

Hedge fund indexes reflect the returns of hedge funds and are often compiled from databases of hedge fund returns. These indexes can vary greatly due to different reporting practices by hedge funds, leading to issues like survivorship bias. They typically use equal weighting and represent a broad or strategy-specific performance of hedge funds.

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