Financial Terms Value-at-Risk model (VAR)

# Definition of Value-at-Risk model (VAR)

## 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.

# Related Terms:

## economic components model

Abramsâ€™ 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.

## 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).

## log size model

Abramsâ€™ model to calculate discount rates as a function of the logarithm of the value of the firm.

## NPV (net present value of cash flows)

Same as PV, but usually includes a subtraction for an initial cash outlay.

## PV (present value of cash flows)

the value in todayâ€™s dollars of cash flows that occur in different time periods.
present value factor equal to the formula 1/(1 - r)n, where n is the number of years from the valuation date to the cash flow and r is the discount rate.
For business valuation, n should usually be midyear, i.e., n = 0.5, 1.5, . . .

## QMDM (quantitative marketability discount model)

model for calculating DLOM for minority interests r the discount rate

The net present value analysis of an asset if financed solely by equity
(present value of un-levered cash flows), plus the present value of any financing decisions (levered cash
flows). In other words, the various tax shields provided by the deductibility of interest and the benefits of
other investment tax credits are calculated separately. This analysis is often used for highly leveraged
transactions such as a leverage buy-out.

## Arbitrage-free option-pricing models

Yield curve option-pricing models.

## 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.

## Bankruptcy risk

The risk that a firm will be unable to meet its debt obligations. Also referred to as default or insolvency risk.

## Basis risk

The uncertainty about the basis at the time a hedge may be lifted. Hedging substitutes basis risk for
price risk.

## 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 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 value

With respect to convertible bonds, the value the security would have if it were not convertible
apart from the conversion option.

## Book value

A company's book value is its total assets minus intangible assets and liabilities, such as debt. A
company's book value might be more or less than its market value.

## Book value per share

The ratio of stockholder equity to the average number of common shares. Book value
per share should not be thought of as an indicator of economic worth, since it reflects accounting valuation
(and not necessarily market valuation).

The risk that the cash flow of an issuer will be impaired because of adverse economic
conditions, making it difficult for the issuer to meet its operating expenses.

## Call risk

The combination of cash flow uncertainty and reinvestment risk introduced by a call provision.

## 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

Book value.

## Cash-surrender value

An amount the insurance company will pay if the policyholder ends a whole life
insurance policy.

## Commercial risk

The risk that a foreign debtor will be unable to pay its debts because of business events,
such as bankruptcy.

## Company-specific risk

Related: Unsystematic risk

## Completion risk

The risk that a project will not be brought into operation successfully.

## 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.

## Continuous random variable

A random value that can take any fractional value within specified ranges, as
contrasted with a discrete variable.

## Conversion value

Also called parity value, the value of a convertible security if it is converted immediately.

## Counterparty risk

The risk that the other party to an agreement will default. In an options contract, the risk
to the option buyer that the option writer will not buy or sell the underlying as agreed.
Country economic risk Developments in a national economy that can affect the outcome of an international
financial transaction.

## Country financial risk

The ability of the national economy to generate enough foreign exchange to meet
payments of interest and principal on its foreign debt.

## Country risk General

Level of political and economic uncertainty in a country affecting the value of loans or
investments in that country.

## Covariance

A statistical measure of the degree to which random variables move together.

## Credit risk

The risk that an issuer of debt securities or a borrower may default on his obligations, or that the
payment may not be made on a negotiable instrument. Related: Default risk

## Cross-border risk

Refers to the volatility of returns on international investments caused by events associated
with a particular country as opposed to events associated solely with a particular economic or financial agent.

## Currency risk

Related: Exchange rate risk

## Currency risk sharing

An agreement by the parties to a transaction to share the currency risk associated with
the transaction. The arrangement involves a customized hedge contract embedded in the underlying
transaction.

## Default risk

Also referred to as credit risk (as gauged by commercial rating companies), the risk that an
issuer of a bond may be unable to make timely principal and interest payments.

## 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.

## Discrete random variable

A random variable that can take only a certain specified set of discrete possible
values - for example, the positive integers 1, 2, 3, . . .

## Diversifiable risk

Related: unsystematic risk.

## 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.

## Economic risk

In project financing, the risk that the project's output will not be salable at a price that will
cover the project's operating and maintenance costs and its debt service requirements.

## Endogenous variable

A value determined within the context of a model.

## Equilibrium market price of risk

The slope of the capital market line (CML). Since the CML represents the
return offered to compensate for a perceived level of risk, each point on the line is a balanced market
condition, or equilibrium. The slope of the line determines the additional return needed to compensate for a
unit change in risk.

## Event risk

The risk that the ability of an issuer to make interest and principal payments will change because
of rare, discontinuous, and very large, unanticipated changes in the market environment such as (1) a natural
or industrial accident or some regulatory change or (2) a takeover or corporate restructuring.

## Exchange rate risk

Also called currency risk, the risk of an investment's value changing because of currency
exchange rates.

## Exchange risk

The variability of a firm's value that results from unexpected exchange rate changes or the
extent to which the present value of a firm is expected to change as a result of a given currency's appreciation
or depreciation.

## Exercise value

The amount of advantage over a current market transaction provided by an in-the-money
option.

## Exogenous variable

A variable whose value is determined outside the model in which it is used. Also called
a parameter.

## Expected value

The weighted average of a probability distribution.

## Expected value of perfect information

The expected value if the future uncertain outcomes could be known
minus the expected value with no additional information.

## Extraordinary positive value

A positive net present value.

## 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.

See: Par value.

## Factor model

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

## Fallout risk

A type of mortgage pipeline risk that is generally created when the terms of the loan to be
originated are set at the same time as the sale terms are set. The risk is that either of the two parties, borrower
or investor, fails to close and the loan "falls out" of the pipeline.

## Financial risk

The risk that the cash flow of an issuer will not be adequate to meet its financial obligations.
Also referred to as the additional risk that a firm's stockholder bears when the firm utilizes debt and equity.

## Firm's net value of debt

Total firm value minus total firm debt.

## Firm-specific risk

See:diversifiable risk or unsystematic risk.

## Flat price risk

Taking a position either long or short that does not involve spreading.

## Force majeure risk

The risk that there will be an interruption of operations for a prolonged period after a
project finance project has been completed due to fire, flood, storm, or some other factor beyond the control

## Foreign exchange risk

The risk that a long or short position in a foreign currency might have to be closed out
at a loss due to an adverse movement in the currency rates.

## Funding risk

Related: interest rate risk

## Future value

The amount of cash at a specified date in the future that is equivalent in value to a specified
sum today.

## Garmen-Kohlhagen option pricing model

A widely used model for pricing foreign currency options.

## Geographic risk

risk that arises when an issuer has policies concentrated within certain geographic areas,
such as the risk of damage from a hurricane or an earthquake.

## Herstatt risk

The risk of loss in foreign exchange trading that one party will deliver foreign exchange but the counterparty financial institution will fail to deliver its end of the contract. It is also referred to as settlement risk.

## Idiosyncratic Risk

Unsystematic risk or risk that is uncorrelated to the overall market risk. In other words,
the risk that is firm specific and can be diversified through holding a portfolio of stocks.

## Index model

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

## Inflation risk

Also called purchasing-power risk, the risk that changes in the real return the investor will
realize after adjusting for inflation will be negative.

## Insolvency risk

The risk that a firm will be unable to satisfy its debts. Also known as bankruptcy risk.

## Interest rate risk

The risk that a security's value changes due to a change in interest rates. For example, a
bond's price drops as interest rates rise. For a depository institution, also called funding risk, the risk that
spread income will suffer because of a change in interest rates.

## Intrinsic value of an option

The amount by which an option is in-the-money. An option which is not in-themoney
has no intrinsic value. Related: in-the-money.

## Intrinsic value of a firm

The present value of a firm's expected future net cash flows discounted by the
required rate of return.

## Investment value

Related:straight value.

## Liquidation value

Net amount that could be realized by selling the assets of a firm after paying the debt.

## Liquidity risk

The risk that arises from the difficulty of selling an asset. It can be thought of as the difference
between the "true value" of the asset and the likely price, less commissions.

## Loan value

The amount a policyholder may borrow against a whole life insurance policy at the interest rate
specified in the policy.

## 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 price of risk

A measure of the extra return, or risk premium, that investors demand to bear risk. The
reward-to-risk ratio of the market portfolio.

## Market risk

risk that cannot be diversified away. Related: systematic risk

## Market value

1) The price at which a security is trading and could presumably be purchased or sold.
2) The value investors believe a firm is worth; calculated by multiplying the number of shares outstanding by the
current market price of a firm's shares.

## Market value ratios

Ratios that relate the market price of the firm's common stock to selected financial
statement items.

## 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.

## Maturity value

Related: par value.

## Mean-variance analysis

Evaluation of risky prospects based on the expected value and variance of possible outcomes.

## Mean-variance criterion

The selection of portfolios based on the means and variances of their returns. The
choice of the higher expected return portfolio for a given level of variance or the lower variance portfolio for
a given expected return.

## Mean-variance efficient portfolio

Related: Markowitz efficient portfolio

## Minimum-variance frontier

Graph of the lowest possible portfolio variance that is attainable for a given
portfolio expected return.

## Minimum-variance portfolio

The portfolio of risky assets with lowest variance.
Minority interest An outside ownership interest in a subsidiary that is consolidated with the parent for
financial reporting purposes.

## Modeling

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

## Mortgage-pipeline risk

The risk associated with taking applications from prospective mortgage borrowers
who may opt to decline to accept a quoted mortgage rate within a certain grace period.

The adjusted present value minus the initial cost of an investment.

## Net asset value (NAV)

The value of a fund's investments. For a mutual fund, the net asset value per share
usually represents the fund's market price, subject to a possible sales or redemption charge. For a closed end
fund, the market price may vary significantly from the net asset value.

## Net book value

The current book value of an asset or liability; that is, its original book value net of any

## Net present value (NPV)

The present value of the expected future cash flows minus the cost.

## Net present value of growth opportunities

A model valuing a firm in which net present value of new
investment opportunities is explicitly examined.