 Financial Terms Single index model

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# Definition of Single index model ## Single index model

A model of stock returns that decomposes influences on returns into a systematic factor,
as measured by the return on the broad market index, and firm specific factors.

## Single-index model

Related: market model

# Related Terms:

## Arbitrage-free option-pricing models

Yield curve option-pricing models.

## Arms index

Also known as a trading index (TRIN)= (number of advancing issues)/ (number of declining
issues) (Total up volume )/ (total down volume). An advance/decline market indicator. Less than 1.0 indicates
bullish demand, while above 1.0 is bearish. The index often is smoothed with a simple moving average.

## Asset pricing model

A model for determining the required rate of return on an asset.

## Asset pricing model

A model, such as the Capital Asset Pricing model (CAPM), that determines the required
rate of return on a particular asset.

## Binomial model

A method of pricing options or other equity derivatives in
which the probability over time of each possible price follows a binomial
distribution. The basic assumption is that prices can move to only two values
(one higher and one lower) over any short time period.

## Binomial option pricing model

An option pricing model in which the underlying asset can take on only two
possible, discrete values in the next time period for each value that it can take on in the preceding time period. ## Black-Scholes model

The first complete mathematical model for pricing
options, developed by Fischer Black and Myron Scholes. It examines market
price, strike price, volatility, time to expiration, and interest rates. It is limited
to only certain kinds of options.

## Black-Scholes option-pricing model

A model for pricing call options based on arbitrage arguments that uses
the stock price, the exercise price, the risk-free interest rate, the time to expiration, and the standard deviation
of the stock return.

## Bond indexing

Designing a portfolio so that its performance will match the performance of some bond index.

## Buying the index

Purchasing the stocks in the S&P 500 in the same proportion as the index to achieve the
same return.

## Capital asset pricing model (CAPM)

An economic theory that describes the relationship between risk and
expected return, and serves as a model for the pricing of risky securities. The CAPM asserts that the only risk
that is priced by rational investors is systematic risk, because that risk cannot be eliminated by diversification.
The CAPM says that the expected return of a security or a portfolio is equal to the rate on a risk-free security
plus a risk premium.

## Capital Asset Pricing Model (CAPM)

A model for estimating equilibrium rates of return and values of
assets in financial markets; uses beta as a measure of asset risk
relative to market risk

## capital asset pricing model (CAPM)

Theory of the relationship between risk and return which states that the expected risk
premium on any security equals its beta times the market risk premium.

## constant-growth dividend discount model

Version of the dividend discount model in which dividends grow at a constant rate.

## Constant-growth model

Also called the Gordon-Shapiro model, an application of the dividend discount
model which assumes (1) a fixed growth rate for future dividends and (2) a single discount rate.

## Consumer Price Index (CPI)

The CPI, as it is called, measures the prices of consumer goods and services and is a
measure of the pace of U.S. inflation. The U.S.Department of Labor publishes the CPI very month.

## Consumer Price Index (CPI)

An index calculated by tracking the cost of a typical bundle of consumer goods and services over time. It is commonly used to measure inflation.

## Deterministic models

Liability-matching models that assume that the liability payments and the asset cash
flows are known with certainty. Related: Compare stochastic models

## Discounted dividend model (DDM)

A formula to estimate the intrinsic value of a firm by figuring the
present value of all expected future dividends.

## dividend discount model

Computation of today’s stock price which states that share value equals the present value of all expected future dividends.

## Dividend discount model (DDM)

A model for valuing the common stock of a company, based on the
present value of the expected cash flows.

## Dividend growth model

A model wherein dividends are assumed to be at a constant rate in perpetuity.

## EAFE index

The European, Australian, and Far East stock index, computed by Morgan Stanley.

## economic components model

Abrams’ model for calculating DLOM based on the interaction of discounts from four economic components.
This model consists of four components: the measure of the economic impact of the delay-to-sale, monopsony power to buyers, and incremental transactions costs to both buyers and sellers.

## Enhanced indexing

Also called indexing plus, an indexing strategy whose objective is to exceed or replicate
the total return performance of some predetermined index.

## Extrapolative statistical models

models that apply a formula to historical data and project results for a
future period. Such models include the simple linear trend model, the simple exponential model, and the
simple autoregressive model.

## Factor model

A way of decomposing the factors that influence a security's rate of return into common and
firm-specific influences.

## Garmen-Kohlhagen option pricing model

A widely used model for pricing foreign currency options.

## Gordon model

present value of a perpetuity with growth.
The end-ofyear Gordon model formula is: 1/(r - g)
and the midyear formula is: SQRT(1 + r)/(r - g).

## Index

A series of numbers measuring percentage changes over time from a base period. The index number for the base period is by convention set equal to 100.
indexing
Linking money payments to a price index to hold the real value of those money payments constant.

## index

An index is a statistical measure of a market based on the performance of a sample of securities in that market. For example, the S&P/TSX Composite index reflects the performance of the most actively traded stocks on The Toronto Stock Exchange.

## Index and Option Market (IOM)

A division of the CME established in 1982 for trading stock index
products and options. Related: Chicago Mercantile Exchange (CME).

## Index arbitrage

An investment/trading strategy that exploits divergences between actual and theoretical
futures prices.

## Index fund

Investment fund designed to match the returns on a stockmarket index.

## index funds

Mutual funds that aim to track the performance of a specific stock or bond index. This process is also referred to as indexing and passive management.

## Index model

A model of stock returns using a market index such as the S&P 500 to represent common or
systematic risk factors.

## Index option

A call or put option based on a stock market index.

## Index Portfolio Rebalancing Service (IPRS)

index Portfolio Rebalancing Service (IPRS) is a comprehensive investment service that can help increase potential returns while reducing volatility. Several portfolios are available, each with its own strategic balance of index Funds. IPRS maintains your personal asset allocation by monitoring and rebalancing your portfolio semi-annually.

## Index warrant

A stock index option issued by either a corporate or sovereign entity as part of a security
offering, and guaranteed by an option clearing corporation.

## Indexation

The adjustment of benefits to compensate for the effects of inflation.

## Indexed bond

Bond whose payments are linked to an index, e.g. the consumer price index.

## Indexing

A passive instrument strategy consisting of the construction of a portfolio of stocks designed to
track the total return performance of an index of stocks.

## Internet business model

a model that involves
(1) few physical assets,
(2) little management hierarchy, and
(3) a direct pipeline to customers

## Jensen index

An index that uses the capital asset pricing model to determine whether a money manager
outperformed a market index. The "alpha" of an investment or investment manager.

## log size model

Abrams’ model to calculate discount rates as a function of the logarithm of the value of the firm.

## market index

Measure of the investment performance of the overall market.

## Market model

This relationship is sometimes called the single-index model. The market model says that the
return on a security depends on the return on the market portfolio and the extent of the security's
responsiveness as measured, by beta. In addition, the return will also depend on conditions that are unique to
the firm. Graphically, the market model can be depicted as a line fitted to a plot of asset returns against
returns on the market portfolio.

## Market value-weighted index

An index of a group of securities computed by calculating a weighted average
of the returns on each security in the index, with the weights proportional to outstanding market value.

## Markowitz model

A model for selecting an optimum investment portfolio,
devised by H. M. Markowitz. It uses a discrete-time, continuous-outcome
approach for modeling investment problems, often called the mean-variance
paradigm. See Efficient frontier.

## Modeling

The process of creating a depiction of reality, such as a graph, picture, or mathematical
representation.

## Optimization approach to indexing

An approach to indexing which seeks to Optimize some objective, such
as to maximize the portfolio yield, to maximize convexity, or to maximize expected total returns.

## percentage of sales models

Planning model in which sales forecasts are the driving variables and most other variables are
proportional to sales.

## Pie model of capital structure

A model of the debt/equity ratio of the firms, graphically depicted in slices of
a pie that represent the value of the firm in the capital markets.

## present value index

see profitability index

## Price Index

A measure of the price level calculated by comparing the cost of a bundle of goods and services in a given year with its cost in a base year. See also index.

## Profitability index

The present value of the future cash flows divided by the initial investment. Also called
the benefit-cost ratio.

## Profitability index

See cash value added.

## Profitability Index

A method for determining the profitability of an investment. It is
calculated by dividing the present value of the future net cash flows
by the initial cash investment.

## profitability index

Ratio of net present value to initial investment.

## profitability index (Pl)

a ratio that compares the present value of net cash flows to the present value of the net investment

## Pure index fund

A portfolio that is managed so as to perfectly replicate the performance of the market portfolio.

## QMDM (quantitative marketability discount model)

model for calculating DLOM for minority interests r the discount rate

## Risk indexes

Categories of risk used to calculate fundamental beta, including (1) market variability, (2)
earnings variability, (3) low valuation, (4) immaturity and smallness, (5) growth orientation, and (6) financial risk.

## Simple linear trend model

An extrapolative statistical model that asserts that earnings have a base level and
grow at a constant amount each period.

## Single country fund

A mutual fund that invests in individual countries outside the United States.

## Single factor model

A model of security returns that acknowledges only one common factor.
See: factor model.

## Single-level bill of material

A list of all components used in a parent item.

## Single-payment bond

A bond that will make only one payment of principal and interest.

## Single-premium deferred annuity

An insurance policy bought by the sponsor of a pension plan for a single
premium. In return, the insurance company agrees to make lifelong payments to the employee (the
policyholder) when that employee retires.

## Single sourcing

Using a single supplier as the only source of a part.

## Standard & Poor’s Composite Index

index of the investment performance of a portfolio of 500 large stocks. Also called the
S&P 500.

## Stochastic models

Liability-matching models that assume that the liability payments and the asset cash flows
are uncertain. Related: Deterministic models.

## Stock index option

An option in which the underlying is a common stock index.

## Stratified equity indexing

A method of constructing a replicating portfolio in which the stocks in the index
are classified into stratum, and each stratum is represented in the portfolio.

## Stratified sampling approach to indexing

An approach in which the index is divided into cells, each
representing a different characteristic of the index, such as duration or maturity.

## Stratified sampling bond indexing

A method of bond indexing that divides the index into cells, each cell
representing a different characteristic, and that buys bonds to match those characteristics.

## Strike index

For a stock index option, the index value at which the buyer of the option can buy or sell the
underlying stock index. The strike index is converted to a dollar value by multiplying by the option's contract multiple.
Related: strike price

## Treynor Index

A measure of the excess return per unit of risk, where excess return is defined as the
difference between the portfolio's return and the risk-free rate of return over the same evaluation period and
where the unit of risk is the portfolio's beta.

## Two-factor model

Black's zero-beta version of the capital asset pricing model.

## Two-state option pricing model

An option pricing model in which the underlying asset can take on only two
possible (discrete) values in the next time period for each value it can take on in the preceding time period.
Also called the binomial option pricing model.

## Value-at-Risk model (VAR)

Procedure for estimating the probability of portfolio losses exceeding some
specified proportion based on a statistical analysis of historical market price trends, correlations, and volatilities.

## Yield curve option-pricing models

models that can incorporate different volatility assumptions along the
yield curve, such as the Black-Derman-Toy model. Also called arbitrage-free option-pricing models.

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