Definition of Probability

Probability

The relative likelihood of a particular outcome among all possible outcomes.

Base probability of loss

The probability of not achieving a portfolio expected return.

Cumulative probability distribution

A function that shows the probability that the random variable will
attain a value less than or equal to each value that the random variable can take on.

Normal probability distribution

A probability distribution for a continuous random variable that is forms a
symmetrical bell-shaped curve around the mean.

Probability density function

The probability function for a continuous random variable.

Probability distribution

Also called a probability function, a function that describes all the values that the random variable can
take and the probability associated with each.

Probability function

A function that assigns a probability to each and every possible outcome.

Probability Distribution

A list of all possible outcomes and the chance of each outcome
occurring

probability distribution

a range of possible values for which each value has an assigned likelihood of occurrence

Coinsurance effect

Refers to the fact that the merger of two firms decreases the probability of default on
either firm's debt.

Discriminant analysis

A statistical process that links the probability of default to a specified set of financial ratios.

Expected return

The return expected on a risky asset based on a probability distribution for the possible rates
of return. Expected return equals some risk free rate (generally the prevailing U.S. Treasury note or bond rate)
plus a risk premium (the difference between the historic market return, based upon a well diversified index
such as the S&P500 and historic U.S. Treasury bond) multiplied by the assets beta.

Expected value

The weighted average of a probability distribution.

Monte Carlo simulation

An analytical technique for solving a problem by performing a large number of trail
runs, called simulations, and inferring a solution from the collective results of the trial runs. Method for
calculating the probability distribution of possible outcomes.

Mortality tables

Tables of probability that individuals of various ages will die within one year.

Normal random variable

A random variable that has a normal probability distribution.

Payments pattern

escribes the lagged collection pattern of receivables, for instance the probability that a
72-day-old account will still be unpaid when it is 73-days-old.

Random walk

Theory that stock price changes from day to day are at random; the changes are independent
of each other and have the same probability distribution. Many believers of the random walk theory believe
that it is impossible to outperform the market consistently without taking additional risk.

Risk-adjusted profitability

A probability used to determine a "sure" expected value (sometimes called a
certainty equivalent) that would be equivalent to the actual risky expected value.

Skewed distribution

probability distribution in which an unequal number of observations lie below and
above the mean.

Tail

1) The difference between the average price in Treasury auctions and the stopout price.
2) A future
money market instrument (one available some period hence) created by buying an existing instrument and
financing the initial portion of its life with a term repo.
3) The extreme end under a probability curve.
4) The odd amount in a MBS pool.

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.

Volatility

The probability of change

total expected value (for a project)

the sum of the individual cash flows in a probability distribution multiplied by their related probabilities

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.

Stochastic

Involving or containing a random variable or variables; involving
chance or probability.

Valuation Allowance

A contra- or reduction account to deferred tax assets.
The valuation allowance represents that portion of total deferred tax assets that the firm judges is unlikely to be realized. The probability threshold applied in evaluating realization is 50%. That is, if it is more than 50% likely that some or all of a deferred tax asset will not be realized, then a valuation allowance must be set off against part or all of the deferred tax asset.

Lapse subsidized

This refers to the practice of some life insurance companies to offer policies which are lower in price because they have assumed a high probability that the policies will be cashed in by their owners for one reason or another before the death benefit becomes available. It is a bold and risky offer by the insurance company because sometimes the purchasers of these policies simply don't lapse them.

Mortality Tables

This is a statistical table used by life insurance companies showing the probability of death of male and females at all ages.

Morbidity Tables

These are statistical tables used by life insurance companies showing the probability of disease of male and females at all ages.

Risk

A state in which the number of possible future events exceeds the number of events that will actually occur, and some measure of probability can be attached to them.

Actuary

One who uses statistical information to evaluate the probability of future events and prices insurance products.

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