Statistics, Modeling and Finance

Three tools the Fed can utilize to control monetary policy

-Open market operations -discount rate -revise requirements

Paramater

1. A constant or value used to index a function, such as use of degrees of freedom to derive an appropriate t-statistic or F-statistic function. 2. A number that describes a characteristic of a population.

how many observations in a large sample?

30 or more

In the compound interest tables, which columns provide present values as outputs?

4,5,6

Descriptive statistics

A branch of statistics concerned only with characterizing, or describing, a set of numbers. The measures used to characterize a set of data (e.g., average, maximum, coefficient of dispersion) or charts and tables depicting the data.

ordinal variable

A categorical variable indicating rank order, such as small, medium, and large; contrasts with nominal categorical variables, which do not indicate rank order.

annuity

A contract providing for regular payments of predictable amounts. Regular payments are those that occur at a constant periodic rate, such as monthly, quarterly, or annually.

Adjustable rate mortgages (ARMs)

A debt secured by real estate with an interest rate that may move up or down following a specified schedule or in accordance with the movements of a standard or index to which the interest rate is tied.

Graduated payment mortgage

A debt secured by real property in which mortgage payments are usually projected to match increases in the borrower's income. The periodic payments start out low and gradually increase.

mortgage note

A document or a clause in a document in which the borrower accepts responsibility for the repayment of a debt.

Junior lien

A lien placed on a property after a previous lien has been made and recorded; a lien made subordinate to another by agreement, e.g., second or third mortgages; also called second lien or third lien.

mode

A measure of central tendency consisting of the numerical value or categorical characteristic that occurs most frequently in a sample or population. For example, the mode of the data set (2,4,5,6,6,7,7,8,8,8,8,10,12) is 8, and the mode of (poor, poor, below average, average, average, average, average, good, good, excellent) is average.

median

A measure of central tendency identified as the middle value in an ordered array of numerical values, e.g., 7 is the median of (1,4,6,6,7,9,11,22,41). If the ordered array contains an even number of values, then the median is the mean of the two values on either side of the middle

Guaranteed Mortgages

A mortgage in which a party other than the borrower assures payment in the event of default, e.g., a VA-guaranteed mortgage or a SBA-guaranteed mortgage.

Insured mortgages

A mortgage in which a party other than the borrower assures payment on default by the mortgagor in return for the payment of a premium, e.g., FHA-insured mortgages, private mortgage insurance (PMI).

First mortgage

A mortgage that has priority over all other mortgage liens on a property.

balloon mortgage

A mortgage that is not fully amortized at maturity and requires a lump sum, or balloon, payment of the outstanding balance.

mortgage

A pledge of a described property interest as collateral or security for the repayment of a loan under certain terms and conditions.

Stepwise regression analysis

A programmed algorithm for systematically building a multiple linear regression model by adding significant variables, deleting insignificant variables, or both, and then assessing the model resulting from the addition or deletion.

nonprobability sample

A sample produced by an unscientific, non-random selection process; for example, a nonprobability sample may be a sample based upon an appraiser's judgment about which cases to select or based on a convenience sample.

Trend

A series of related changes brought about by a chain of causes and effects

Nominal interest rate

A stated or contract rate; an interest rate, usually annual, that does not necessarily correspond to the effective or compound interest rate.

Regression analysis

A statistical method that examines the relationship between one or more independent variables and a dependent variable

Regression analysis

A statistical method that examines the relationship between one or more independent variables and a dependent variable. Regression models can be used to examine the structure of a relationship or to forecast dependent variable values. Simple linear regression has one independent variable, whereas multiple linear regression includes more than one independent variable.

stratified random sample

A statistical sample in which the population is divided into one or more essential subgroups or strata, with random samples drawn from each subgroup.

normal distribution

A theoretical distribution often approximated in real-world situations. It is symmetrical and bell-shaped.

Linear regression

A type of statistical analysis used to investigate a linear relationship between a dependent variable and one or more independent variables; used to predict the value of the dependent variable on the basis of the values of the independent variables and to develop an understanding of how a unit change in an independent variable relates to change in the dependent variable. Linear regression models employing a single independent variable are called simple linear regression models. Those employing more than one independent variable are called multiple linear regression models.

A debt secured by real estate with an interest rate that may move up or down following a specified schedule or in accordance with the movements of a standard or index to which the interest rate is tied" is the definition of a(n) ___________ rate mortgage.

Adjustable

The six functions of a dollar are:

Amount of $1 (The amount to which $1 will grow) Amount of $1 Per Period (The amount to which $1 per period will grow) Sinking Fund Factor (The amount per period which will grow to $1) Present Value of $1 (What $1 due in the future is worth today) Present Value of $1 per period (What $1 payable periodically is worth today) Partial Payment (Amount to amortize $1)

An appraiser may be asked to review an appraisal report that includes an opinion of value based on the output of an AVM. This is __________ under USPAP.

An appraisal review assignment

Effective interest rate

An interest rate, usually expressed in an annual rate, that includes the effect of compounding; also, the lender's yield to maturity, which in many instances is equivalent to the lender's internal rate of return; also called effective rate.

AVM's may be used in the development of

Appraisals, appraisal reviews and appraisal consulting assignments

Computer-assisted mass appraisals (CAMAs) were first adopted by _________________ in the ____________.

Assessors, 1970s

When are payments made for a sinking fund?

At the beginning of the period

As it is used in statistics, the symbol delta (?) means:

Change

Money is a:

Commodity

automated valuation model (AVM)

Computer software that queries property and market data, analyzes comparable property and market information to assign a value or range of value to a particular property; or generates metrics applicable to assessing the credibility of valuation-related statements or conclusions.

An example of an insured loan

FHA Loan

In 1968, FNMA was split into two organizations:

Fannie Mae and Ginnie Mae

An appraiser must be able to reasonably conclude that the AVM's output is _________ before using the AVM.

Credible

Credibility of the AVM output depends on the quality of its _________.

Database

Central tendency is part of ________________ statistics.

Descriptive

Which federal agency was created for the purpose of providing funds to savings and loan (thrift) institutions to make mortgages more affordable?

Federal Home Loan Bank Board

Interest rate ceiling

For an adjustable-rate mortgage (ARM), the maximum interest rate, as specified in the mortgage note.

variable

In statistics, a characteristic or attribute of an item, service, or individual that can change from observation to observation. For example, improved living area is a characteristic of a house that can change with each observation.

Universe

In statistics, a population or entire body of data; used to distinguish between a population and a sample obtained from the population. Population is a more generally used term.

Sample

In statistics, a subset of a population selected for analysis.

Bias

In statistics, a systematic error. A statistic is biased if it systematically differs from the population parameter being estimated, such as the average sale price. An example in appraisal valuation modeling would be if the model results in consistently overvalued or undervalued properties.

Degrees of freedom

In statistics, the number of values in a calculation of a statistic that are free to vary. For example, if a sample of size four adds up to a sum of 50, only three of the sample values can vary. Once the three varying sample items values are ascertained, the fourth sample item value will be known with certainty and must be equal to the unique number required to equate to a sum of 50. Therefore, the degrees of freedom in this example is n - 1 = 3.

confidence interval

In statistics, the specification of a zone within a population, based on a sample mean and its standard error, within which the true mean most probably lies.

A _____________ is one in which the independent variable's marginal contribution to the value of the dependent variable is constant over the entire range of the data.

Linear Model

one stepwise regression analysis could be performed through the use of standard spreadsheet application such as all of the following EXCEPT

Microsoft Word

Conventional mortgages

Mortgages that are neither insured nor guaranteed by an agency of the government, although they may be privately insured.

Is an AVM an appraisal?

No

Standard deviation formula

OR, enter all data in (number -> sigma+) then g x-bar, then g s

Graphic analysis

Quantitative techniques used to identify and measure adjustments to the sale prices of comparable properties; a variant of statistical analysis in which an appraiser interprets graphically displayed data visually or through curve fit analysis. Graphs can also be used to support and exhibit value trends for comparison elements in qualitative analysis.

Band of Investment analysis

RO = M x RM + [(1 - M) x RE]

What can be used in the analysis of dispersion?

Range

____________ are known as thrift institutions.

Saving and Loans

A market created by government and private agencies for the purchase and sale of existing mortgages, which provides greater liquidity for mortgages. Fannie Mae, Freddie Mac, and Ginnie Mae are the principal operators..." is the definition of the ___________ mortgage market.

Secondary

Unbundled mortgage models are found in

Secondary mortgage market

Which USPAP STANDARD(s) address mass appraisals?

Standards 5 and 6

Statistics

The body of principles and methods concerned with extracting useful information from numerical data.

mortgage capitalization rate

The capitalization rate for debt; the ratio of the annual debt service to the principal amount of the mortgage loan. The mortgage capitalization rate (Rm) is equivalent to the periodic (monthly, quarterly, annually) mortgage constant times the number of payments per year on a given loan on the day the loan is initiated.

Central tendency

The central point, or representative value, around which items cluster in a frequency distribution. The measures of central tendency (called averages) are the mean, the median, and the mode.

Regression coefficient

The coefficient calculated by the regression algorithm for the data supplied that, when multiplied by the value of the variable with which it is associated, will predict (for simple regression) or help to predict (for multiple regression) the value of the dependent variable. For example, in the equation, Value = $10,000 + $5,000 x number of rooms, $5,000 is a regression coefficient for number of rooms.

Absolute deviation

The difference between an observation and the measure of central tendency (such as the arithmetic mean or median) for that array, without regard as to the sign (positive or negative) of the difference. For example, if the observed value is 6 and the mean of these observations is 10, then the difference (or deviation) would be 6 - 10 or -4; dropping the negative sign would yield the absolute deviation, which in this case would be 4.

Annual percentage rate (APR)

The effective annual interest rate. Truth-in-lending legislation requires that loan instruments and advertising show the interest cost to the borrower in the form of an annual rate, as distinguished from the nominal rate.

Monetary policy

The efforts by a central bank, such as the Federal Reserve in the United States, to influence the level of economic activity in the country by regulating the availability of money and the rate of interest.

Money market

The interaction of buyers and sellers who trade short-term money instruments.

Regression line

The line on a graph that represents the relationship defined by the regression coefficients. For example, the line from the relationship given in the definition of regression coefficient would cross the y-axis at the value $10,000 and would go up $5,000 for each movement of one to the right. This example illustrates one of the subtleties required in understanding regressions analysis: in fact, there is no line, because the independent variable is not a continuous variable, but it is easier to talk about the relationship by pretending that the variable is continuous and represent the relationship by a line rather than the more nearly correct series of vertical bars on a bar chart.

array

The listing of a set of observations, such as sales ratios, in a specific order, e.g., alphabetical, alpha-numeric, chronological, order of magnitude.

Initial interest rate

The original interest rate of the mortgage at the time of closing. This rate changes for an adjustable-rate mortgage (ARM). Sometimes known as start rate or teaser rate.

Inferential statistics

The process of drawing conclusions about population characteristics through analysis of sample data.

inferential statistics

The process of drawing conclusions about population characteristics through analysis of sample data.

Amortization

The process of retiring a debt or recovering a capital investment, typically through scheduled, systematic repayment of the principal; a program of periodic contributions to a sinking fund or debt retirement fund.

Mass Appraisal

The process of valuing a universe of properties as of a given date using standard methodology, employing common data, and allowing for statistical testing

Interest rate

The rate of return or yield rate on debt capital

Aggregate

The sum of all the observations within a population; e.g., the aggregate sale price of all the houses sold in a given community.

dependent variable

The variable being estimated (outcome or response variable) in a predictive model such as a multiple linear regression equation.

some of the weaknesses of AVMs:

There are no existing standards They cannot ascertain property condition They ignore marketability issues - supply and demand They do not work well in heterogeneous areas There is no data verification They are not very accurate

some of the strengths of AVMs:

They are fast They are free of appraiser bias They have a low cost They can be a source of property data They help understand value trends They help assess probabilities of value They can be utilized in reviewing and quality control

The deviation of any variable (X) from the mean, measured in terms of standard deviations is

Z?

Income Model

a formula developed to project a pattern of periodic income. Income models can be applied to level income with no change in value, level income with changing value, income and value that change fixed amounts per period (straight-line), income and value that change at a constant ratio 9exponential-curve), and variable or irregular income with changing value

Confidence Interval

a numerical range around a sample mean accompanied with a statement of how confident one is that the true population mean lies within the interval

How many households participate in the Nielsen ratings?

about 1400

decile

divides the data set into 10 equal parts

Fractiles

intervals that total 100% of the distribution.

how many observations in a small sample?

less than 30

The most common competitors for mortgage funds are

long-term government bonds

The interaction of buyers and sellers who trade short-term money instruments" is the definition of the _____________ market.

money

"Currency plus demand and time deposits plus the liabilities of nonbank financial intermediaries" is the definition of

money supply

quartile is equal to:

one-fourth of the data set

Mass appraisal is most often associated with ______________ valuation purposes.

real estate tax assessment

capital market

the interaction of buyers and sellers who trade long-term or intermediate-term money instruments.

Advisory Opinion 18 specifically addresses

use of an automated valuation model