Extrapolative statistical models

Extrapolative statistical models are models that attempts to use past trends in data in order to predict future trends. This may be used in any number of business or non-business situations. They are the 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.

The technical analysts commonly use extrapolative statistical models in order to predict future prices of securities. This can be quite important in the futures and option markets.

Variable-rate mortgage

A variable-rate mortgage or adjustable-rate mortgage (ARM) is a mortgage loan with the interest rate on the note periodically adjusted based on an index which reflects the cost to the lender of borrowing on the credit markets. The loan may be offered at the lender's standard variable rate/base rate. There may be a direct and legally defined link to the underlying index, but where the lender offers no specific link to the underlying market of index they can choose to increase or decrease at their discretion. The term "variable-rate mortgage" is most common outside the United States, whilst in the United States, "adjustable-rate mortgage" is most common, and implies a mortgage regulated by the Federal government,  with limitations on charges ("caps"). In many countries, adjustable rate mortgages are the norm, and in such places, may simply be referred to as mortgages.

Adjustable rate mortgage is a mortgage that features predetermined adjustments of the loan interest rate at regular intervals based on an established index. The interest rate is adjusted at each interval to a rate equivalent to the index value plus a predetermined spread, or margin, over the index, usually subject to per-interval and to life-of-loan interest rate and/or payment rate caps.

Holding period return

Holding period return (HPR) is the total return on an asset or portfolio over the period during which it was held. It is one of the simplest measures of investment performance.

HPR is the percentage by which the value of a portfolio (or asset) has grown for a particular period. It is the sum of income and capital gains divided by the initial period value (asset value at the beginning of the period).

HPR = ((Present Value, or face Value, End-Of-Period Value) + (Any Intermediate Gains eg. Dividends) - (Initial Value)) /(Initial Value)

HPR_n = Income + (P_n+1 – P_n)/ P_n

Annualized holding period return is the annual rate of return that when compounded t times, would have given the same t-period holding return as actually occurred from period 1 to period t.

Quality spread

Quality spread is, the spread between Treasury securities and non-Treasury securities that are identical in all respects except for quality rating. For instance, the difference between yields on Treasuries and those on single A-rated industrial bonds. It is also called credit spread. 

In an interest rate swap quality spread differential is the difference between the interest rates of debt obligations offered by two parties of different creditworthiness that engage in the swap. A swap transaction is considered beneficial to both parties only when the QSD is positive.

J-curve

The term J-curve is used in several different fields to refer to a variety of unrelated J-shaped diagrams where a curve initially falls, but then rises to higher than the starting point.

In private equity, the J curve is used to illustrate the historical tendency of private equity funds to deliver negative returns in early years and investment gains in the outlying years as the portfolios of companies mature.

In economics, the 'J curve' refers to the trend of a country’s trade balance following a devaluation or depreciation under a certain set of assumptions. A devalued currency means imports are more expensive, and on the assumption that the volume of imports and exports change little immediately, this causes a depreciation of the current account (a bigger deficit or smaller surplus). After some time, though, the volume of exports may start to rise because of their lower more competitive prices to foreign buyers, and domestic consumers may buy fewer of the costlier imports. Eventually, if this happens, the trade balance may improve on what it was before the devaluation. If there is a currency revaluation or appreciation the same reasoning leads to an inverted J-curve.

Decile rank

Decile rank is a rating of performance over time. It is rated on a scale of 1-10, where 1 is best and 10 is worst. For performance of mutual funds, 1 indicates that a mutual fund's return was in the top 10% of funds being compared, while 3 means the return was in the top 30%.

General ledger

The general ledger is where financial information from all aspects of your business is consolidated.  Each General Ledger is divided into debits and credits sections. The general ledger is a collection of the group of accounts that supports the value items shown in the major financial statements. It is built up by posting transactions recorded in the sales daybook, purchases daybook, cash book and general journals daybook. The general ledger can be supported by one or more subsidiary ledgers that provide details for accounts in the general ledger. For instance, an accounts receivable subsidiary ledger would contain a separate account for each credit customer, tracking that customer's balance separately. This subsidiary ledger would then be totaled and compared with its controlling account (in this case, Accounts Receivable) to ensure accuracy as part of the process of preparing a trial balance.

There basic categories in which all accounts are grouped are:

1. Assets
2. Liability
3. Owner's equity
4. Revenue
5. Expense
6. (Gains)
7. (Loss)

The balance sheet and the income statement are both derived from the general ledger.

Earnings per share

Earnings per share (EPS) is calculated by dividing company’s profit by its number of outstanding shares. If a company earned $2 million in one year had 2 million shares of stock outstanding, its EPS would be $1 per share.

The portion of a company's profit allocated to each outstanding share of common stock. Earnings per share serve as an indicator of a company's profitability.

The company often uses a weighted average of shares outstanding over the reporting term. When calculating, it is more accurate to use a weighted average number of shares outstanding over the reporting term, because the number of shares outstanding can change over time. However, data sources sometimes simplify the calculation by using the number of shares outstanding at the end of the period.

Global Internet body to unleash domain names

The regulatory body that oversees Internet domain names voted on Monday to revamp the domain naming system for websites, allowing them to end with words like "apple" and "orange" instead of suffixes such as ".com" or ".gov."

"ICANN has opened the Internet's naming system to unleash the global human imagination. Today's decision respects the rights of groups to create new top level domains in any language or script," the regulatory body said after a board meeting in Singapore.

Complete news.

Statistical hypothesis test

A one-sided test is a statistical hypothesis test in which the values for which we can reject the null hypothesis, H0 are located entirely in one tail of the probability distribution. In other words, the critical region for a one-sided test is the set of values less than the critical value of the test, or the set of values greater than the critical value of the test.

A two-sided test is a statistical hypothesis test in which the values for which we can reject the null hypothesis, H0, are located in both tails of the probability distribution.

Law of diminishing returns

In economics, diminishing returns (also called diminishing marginal returns) refers to progressive decrease in the marginal (per-unit) output of a production process as the amount of a single factor of production is increased, while holding the amounts of all other factors of production constant.

The law of diminishing returns states that in all productive processes, adding more of one factor of production, while holding all others constant, will at some point yield lower per-unit returns. The law of diminishing returns does not imply that adding more of a factor will decrease the total production, a condition known as negative returns, though in fact this is common.

Naïve diversification

Naïve diversification is a strategy whereby an investor simply invests in a number of different assets and hopes that the variance of the expected return on the portfolio is lowered. It is a diversification of a portfolio without regard, for the mathematical formulas in the capital asset pricing model. Naive diversification rests on the assumption that simply investing in enough unrelated assets will reduce risk sufficiently to make a profit. Alternately, one may diversify naively by applying the capital asset pricing model incorrectly and finding the wrong efficient portfolio frontier. Such diversification does not necessarily decrease risk at a given expected return, and may in fact increase risk.

Hell or high water contract

A contract that obligates a purchaser of a project's output to make cash payments to the project in all events, even if no product is offered for sale. It is a non-cancellable contract whereby the purchaser must make the specified payments to the seller, regardless of any difficulties they may encounter. 

It is a contract including a clause stating that payments must be made regardless of what happens. Specifically, a hell or high water contract requires one party to continue to receive payments even if an act of God prevents the contract from being completed. For example, suppose two parties sign a contract renting an apartment. The contract may contain a hell or high water clause saying that the renter must pay rent every month even if the apartment floods or burns down. It is also called a promise to pay contract.

Growing equity mortgages

Growing equity mortgages are the mortgages in which annual increases in monthly payments are used to reduce outstanding principal and to shorten the term of the loan. 

It is a fixed rate mortgage on which the monthly payments increase over time according to a set schedule. The interest rate on the loan does not change, and there is never any negative amortization. In other words, the first payment is a fully amortizing payment. As the payments increase, the additional amount above and beyond what would be a fully amortizing payment is applied directly to the remaining balance of the mortgage, shortening the life of the mortgage and increasing interest savings.

Working Capital

Working capital is defined as those funds a business has available to meet its day-to-day financial obligations. A sustainable business must have sufficient funds available at all times to meet its financial obligations as they become due. Working capital can be expressed in a layman's formula: 

Working Capital = Available funds - day to day financial obligations 

In accounting terms,

Working Capital = Current Assets – Current Liabilities

Current assets are items of economic value that can be converted into cash quite quickly in the accounting period (usually 1-3 months). These items typically include cash, inventory, accounts receivable (i.e. what customers owe to the business).

Current liabilities are monies that a business owes to external parties (not owners) and are due for payment within the current accounting period (usually within the next 12 months). These items are typically accounts payable (i.e. what the business owes to suppliers) plus other payables like income tax or council rates.

Operating Cycle

The Operating Cycle of a business is the length of time between the cash outflow on purchased material and cash inflow from the sale of goods. The Operating Cycle determines the amount of working capital that a business requires to operate on a day-to-day basis. The shorter the Operating Cycle the lower the amount of working capital required for the business and the greater opportunity for investments in other value-adding activities.

The Operating Cycle for a manufacturing based business can involve many stages, namely:

1. Purchase - the receipt of raw materials from suppliers on account.
2. Conversion - the conversion of these raw materials into finished goods
3. Inventory - the holding and storage of raw materials, Work-In-Progress (WIP) and Finished Goods.
4. Payment - the payment of the supplier's account for the raw materials received earlier.
5. Sale - the sale of finished goods to customers on account
6. Collection - the collection of money from these customers in payment of their account

Learning curve

A learning curve is a graphical representation of the changing rate of learning (in the average person) for a given activity or tool. Typically, the increase in retention of information is sharpest after the initial attempts, and then gradually evens out, meaning that less and less new information is retained after each repetition.

The learning curve can also represent at a glance the initial difficulty of learning something and, to an extent, how much there is to learn after initial familiarity.

In economics, learning curve is a curve showing how a firm's costs of producing at a given rate of output fall as the total amount produced increases over time as a result of accumulated learning of how to make the product efficiently using given equipment.

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.

 Mathematically it is expressed as:

where:

r_it is return to stock i in period t

r_f is the risk free rate (i.e. the interest rate on treasury bills)

r_mt is the return to the market portfolio in period t

α_i is the stock's alpha, or abnormal return

β_i is the stocks's beta, or responsiveness to the market return

Note that r_it − r_f is called the excess return on the stock, r_mt − r_f the excess return on the market

ε_it is the residual (random) return, which is assumed normally distributed with mean zero and standard deviation σ_i

These equations show that the stock return is influenced by the market (beta), has a firm specific expected value (alpha) and firm-specific unexpected component (residual). Each stock's performance is in relation to the performance of a market index.

Program (or Project) Evaluation and Review Technique

The Program (or Project) Evaluation and Review Technique (PERT), is a model for project management designed to analyze and represent the tasks involved in completing a given project. It is commonly used in conjunction with the critical path method or CPM.

PERT is a method to analyze the involved tasks in completing a given project, especially the time needed to complete each task, and identifying the minimum time needed to complete the total project.

PERT was developed primarily to simplify the planning and scheduling of large and complex projects. It was developed for the U.S. Navy Special Projects Office in 1957 to support the U.S. Navy's Polaris nuclear submarine project. It was able to incorporate uncertainty by making it possible to schedule a project while not knowing precisely the details and durations of all the activities. It is more of an event-oriented technique rather than start- and completion-oriented, and is used more in projects where time, rather than cost, is the major factor. It is applied to very large-scale, one-time, complex, non-routine infrastructure and Research and Development projects.

A PERT chart is a tool that facilitates decision making. The first draft of a PERT chart will number its events sequentially in 10s (10, 20, 30, etc.) to allow the later insertion of additional events. Two consecutive events in a PERT chart are linked by activities, which are conventionally represented as arrows. The events are presented in a logical sequence and no activity can commence until its immediately preceding event is completed. The planner decides which milestones should be PERT events and also decides their “proper” sequence. A PERT chart may have multiple pages with many sub-tasks.

PERT is valuable to manage where multiple tasks are occurring simultaneously to reduce redundancy.

Passive portfolio strategy

Passive portfolio strategy is a strategy that involves minimal expectational input, and instead relies on diversification to match the performance of some market index. A passive strategy assumes that the marketplace will reflect all available information in the price paid for securities, and therefore, does not attempt to find mispriced securities. 

It is a strategy in which an investor (or a fund manager) invests in accordance with a pre-determined strategy that doesn't entail any forecasting (e.g., any use of market timing or stock picking would not qualify as passive management). The idea is to minimize investing fees and to avoid the adverse consequences of failing to correctly anticipate the future. The most popular method is to mimic the performance of an externally specified index. Retail investors typically do this by buying one or more 'index funds'. By tracking an index, an investment portfolio typically gets good diversification, low turnover (good for keeping down internal transaction costs), and extremely low management fees. With low management fees, an investor in such a fund would have higher returns than a similar fund with similar investments but higher management fees and/or turnover/transaction costs.

Active portfolio strategy

Active portfolio strategy is a strategy that uses available information and forecasting techniques to seek a better performance than a portfolio that is simply diversified broadly.

It is a strategy where the manager makes specific investments with the goal of outperforming an investment benchmark index. Investors or mutual funds that do not aspire to create a return in excess of a benchmark index will often invest in an index fund that replicates as closely as possible the investment weighting and returns of that index; this is called passive management. Active management is the opposite of passive management, because in passive management the manager does not seek to outperform the benchmark index.

Cash flow matching

Cash flow matching is the practice of matching returns on a portfolio to future capital outlays. It involves investing in certain securities with a certain expected return so that the investor will be able to pay for future liabilities. Pension funds and annuities perform the most cash flow matching, as they have future liabilities that are both large and relatively easy to estimate. Portfolios that perform cash flow matching usually invest in low-risk, investment-grade securities. The practice is also called portfolio dedication, matching, or the structured portfolio strategy.