Financial Terms Mathematical programming

# Definition of Mathematical programming

## Mathematical programming

An operations research technique that solves problems in which an optimal
value is sought subject to specified constraints. mathematical programming models include linear
programming, quadratic programming, and dynamic programming.

## mathematical programming

a variety of techniques used
to allocate limited resources among activities to achieve a
specific objective

# Related Terms:

## integer programming

a mathematical programming technique in which all solutions for variables must be restricted to whole numbers

## linear programming

a method of mathematical programming used to solve a problem that involves an objective function and multiple limiting factors or constraints long-term variable cost a cost that was traditionally viewed as a fixed cost

## Integer programming

Variant of linear programming whereby the solution values must be integers.

## Linear programming

Technique for finding the maximum value of some equation subject to stated linear constraints.

## Zero-one integer programming

An analytical method that can be used to determine the solution to a capital
rationing problem.

## Planning, programming and budgeting system (PPBS)

A method of budgeting in which budgets are allocated to projects or programmes rather than to responsibility centres.

## objective function

the linear mathematical equation that
states the purpose of a linear programming problem

## Zero-one integer programming

An analytical method that can be used to determine the solution to a capital
rationing problem.

## 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, . . .

## Point and figure chart

A price-only chart that takes into account only whole integer changes in price, i.e., a
2-point change. Point and figure charting disregards the element of time and is solely used to record changes
in price.

## 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 today’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, . . .

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.

## All equity rate

The discount rate that reflects only the business risks of a project and abstracts from the
effects of financing.

## All or none

Requirement that none of an order be executed unless all of it can be executed at the specified price.

## All-in cost

Total costs, explicit and implicit.

## All-or-none underwriting

An arrangement whereby a security issue is canceled if the underwriter is unable
to re-sell the entire issue.

## Arbitrage-free option-pricing models

Yield curve option-pricing models.

## Asset allocation decision

The decision regarding how an institution's funds should be distributed among the
major classes of assets in which it may invest.

## Balloon maturity

Any large principal payment due at maturity for a bond or loan with or without a a sinking
fund requirement.

## 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).

## Borrower fallout

In the mortgage pipeline, the risk that prospective borrowers of loans committed to be
closed will elect to withdraw from the contract.

## Call

An option that gives the right to buy the underlying futures contract.

## Call an option

To exercise a call option.

## Call date

A date before maturity, specified at issuance, when the issuer of a bond may retire part of the bond
for a specified call price.

## Call money rate

Also called the broker loan rate , the interest rate that banks charge brokers to finance
margin loans to investors. The broker charges the investor the call money rate plus a service charge.

## Call option

An option contract that gives its holder the right (but not the obligation) to purchase a specified
number of shares of the underlying stock at the given strike price, on or before the expiration date of the
contract.
Premium in price above the par value of a bond or share of preferred stock that must be paid to
holders to redeem the bond or share of preferred stock before its scheduled maturity date.

## Call price

The price, specified at issuance, at which the issuer of a bond may retire part of the bond at a
specified call date.

## Call price

The price for which a bond can be repaid before maturity under a call provision.

## Call protection

A feature of some callable bonds that establishes an initial period when the bonds may not be
called.

## Call provision

An embedded option granting a bond issuer the right to buy back all or part of the issue prior
to maturity.

## Call risk

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

## Call swaption

A swaption in which the buyer has the right to enter into a swap as a fixed-rate payer. The
writer therefore becomes the fixed-rate receiver/floating rate payer.

## Callable

A financial security such as a bond with a call option attached to it, i.e., the issuer has the right to
call the security.

## Capital allocation

decision allocation of invested funds between risk-free assets versus the risky portfolio.

Book value.

## Cash flow from operations

A firm's net cash inflow resulting directly from its regular operations
(disregarding extraordinary items such as the sale of fixed assets or transaction costs associated with issuing
securities), calculated as the sum of net income plus non-cash expenses that were deducted in calculating net
income.

## Cash-surrender value

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

## Chinese wall

Communication barrier between financiers (investment bankers) and traders. This barrier is
erected to prevent the sharing of inside information that bankers are likely to have.

## Company-specific risk

Related: Unsystematic risk

## Conversion value

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

## Cost of limited partner capital

The discount rate that equates the after-tax inflows with outflows for capital
raised from limited partners.

## Covered call

A short call option position in which the writer owns the number of shares of the underlying
stock represented by the option contracts. Covered calls generally limit the risk the writer takes because the
stock does not have to be bought at the market price, if the holder of that option decides to exercise it.

## Covered call writing strategy

A strategy that involves writing a call option on securities that the investor
owns in his or her portfolio. See covered or hedge option strategies.

## Deferred call

A provision that prohibits the company from calling the bond before a certain date. During this
period the bond is said to be call protected.

## Deterministic models

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

## Dynamic asset allocation

An asset allocation strategy in which the asset mix is mechanistically shifted in
response to -changing market conditions, as in a portfolio insurance strategy, for example.

## Dynamic hedging

A strategy that involves rebalancing hedge positions as market conditions change; a
strategy that seeks to insure the value of a portfolio using a synthetic put option.

## Effective call price

The strike price in an optional redemption provision plus the accrued interest to the
redemption date.

## Exercise value

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

## 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.

## 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.

## Federally related institutions

Arms of the federal government that are exempt from SEC registration and
whose securities are backed by the full faith and credit of the U.S. government (with the exception of the
Tennessee Valley Authority).

## Financial objectives

objectives of a financial nature that the firm will strive to accomplish during the period
covered by its financial plan.

## Firm's net value of debt

Total firm value minus total firm debt.

## Firm-specific risk

See:diversifiable risk or unsystematic risk.

## First-call

With CMOs, the start of the cash flow cycle for the cash flow window.

## Funds From Operations (FFO)

used by real estate and other investment trusts to define the cash flow from
trust operations. It is earnings with depreciation and amortization added back. A similar term increasingly
used is Funds Available for Distribution (FAD), which is FFO less capital investments in trust property and
the amortization of mortgages.

## Future value

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

## Generally Accepted Accounting Principals (GAAP)

A technical accounting term that encompasses the
conventions, rules, and procedures necessary to define accepted accounting practice at a particular time.

## Glass-Steagall Act

A 1933 act in which Congress forbade commercial banks to own, underwrite, or deal in
corporate stock and corporate bonds.

## Implied call

The right of the homeowner to prepay, or call, the mortgage at any time.

## Income statement (statement of operations)

A statement showing the revenues, expenses, and income (the
difference between revenues and expenses) of a corporation over some period of time.

## Installment sale

The sale of an asset in exchange for a specified series of payments (the installments).

## Internally efficient market

Operationally efficient market.

## 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.

## Investor fallout

In the mortgage pipeline, risk that occurs when the originator commits loan terms to the
borrowers and gets commitments from investors at the time of application, or if both sets of terms are made at closing.

## Irrational call option

The implied call imbedded in the MBS. Identified as irrational because the call is
sometimes not exercised when it is in the money (interest rates are below the threshold to refinance).
Sometimes exercised when not in the money (home sold without regard to the relative level of interest rates).

## Law of large numbers

The mean of a random sample approaches the mean (expected value) of the
population as the sample grows.

## Limited liability

Limitation of possible loss to what has already been invested.

## Limited partner

A partner who has limited legal liability for the obligations of the partnership.

## Limited partnership

A partnership that includes one or more partners who have limited liability.

## Limited-liability instrument

A security, such as a call option, in which the owner can only lose his initial
investment.

## Limited-tax general obligation bond

A general obligation bond that is limited as to revenue sources.

## Linear programming

technique for finding the maximum value of some equation subject to stated linear constraints.

## Linear regression

A statistical technique for fitting a straight line to a set of data points.

## Liquidation value

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

## Loan value

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

## Log-linear least-squares method

A statistical technique for fitting a curve to a set of data points. One of the
variables is transformed by taking its logarithm, and then a straight line is fitted to the transformed set of data
points.

## Limited partnership

A partnership that includes one or more partners who have limited liability.

## Limited-liability instrument

A security, such as a call option, in which the owner can only lose his initial investment.

## Margin call

A demand for additional funds because of adverse price movement. Maintenance margin
requirement, security deposit maintenance
Margin of safety With respect to working capital management, the difference between 1) the amount of longterm
financing, and 2) the sum of fixed assets and the permanent component of current assets.

## 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.

## Mutually exclusive investment decisions

Investment decisions in which the acceptance of a project
precludes the acceptance of one or more alternative projects.

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.

## Net present value of future investments

The present value of the total sum of NPVs expected to result from
all of the firm's future investments.

## Net present value rule

An investment is worth making if it has a positive NPV. Projects with negative NPVs
should be rejected.

## Net salvage value

The after-tax net cash flow for terminating the project.

## Non-parallel shift in the yield curve

A shift in the yield curve in which yields do not change by the same
number of basis points for every maturity. Related: Parallel shift in the yield curve.

## Objective (mutual fund)

The fund's investment strategy category as stated in the prospectus. There are
more than 20 standardized categories.

## Operationally efficient market

Also called an internally efficient market, one in which investors can obtain
transactions services that reflect the true costs associated with furnishing those services.

## Optimal contract

The contract that balances the three types of agency costs (contracting, monitoring, and
misbehavior) against one another to minimize the total cost.