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Single-index Model
The single-index model (SIM) is a simple asset pricing model to measure both the risk and the return of a stock. The model has been developed by William Sharpe in 1963 and is commonly used in the finance industry. Mathematically the SIM is expressed as: : r_ - r_f = \alpha_i + \beta_i(r_ - r_f) + \epsilon_ \, : \epsilon_ \sim N(0,\sigma_i^2) \, where: : ''rit'' is return to stock ''i'' in period ''t'' : ''rf'' is the risk free rate (i.e. the interest rate on treasury bills) : ''rmt'' is the return to the market portfolio in period ''t'' : \alpha_i is the stock's alpha, or abnormal return : \beta_i is the stock's beta, or responsiveness to the market return : Note that r_ - r_f is called the excess return on the stock, r_ - r_f the excess return on the market : \epsilon_ are the residual (random) returns, which are assumed independent normally distributed with mean zero and standard deviation \sigma_i These equations show that the stock return is influenced by the market (b ...
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Asset Pricing
In financial economics, asset pricing refers to a formal treatment and development of two interrelated Price, pricing principles, outlined below, together with the resultant models. There have been many models developed for different situations, but correspondingly, these stem from either General equilibrium theory, general equilibrium asset pricing or Rational pricing, rational asset pricing, the latter corresponding to risk neutral pricing. Investment theory, which is near synonymous, encompasses the body of knowledge used to support the decision-making process of choosing investments, and the asset pricing models are then applied in determining the Required rate of return, asset-specific required rate of return on the investment in question, and for hedging. General equilibrium asset pricing Under general equilibrium theory prices are determined through Market price, market pricing by supply and demand. See, e.g., Tim Bollerslev (2019)"Risk and Return in Equilibrium: The C ...
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Capital Stock
In economics, capital goods or capital are "those durable produced goods that are in turn used as productive inputs for further production" of goods and services. A typical example is the machinery used in a factory. At the macroeconomic level, "the nation's capital stock includes buildings, equipment, software, and inventories during a given year." The means of production is as a "... series of heterogeneous commodities, each having specific technical characteristics ..." "capital goods", are one of the three types of intermediate goods used in the production process, the other two being land and labour. The three are also known collectively as "primary factors of production". This classification originated during the classical economics period and has remained the dominant method for classification. Capital can be increased by the use of a production process (see production function and factors of production). Outputs of the production process are normally classifi ...
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William F
William is a masculine given name of Germanic languages, Germanic origin. It became popular in England after the Norman Conquest, Norman conquest in 1066,All Things William"Meaning & Origin of the Name"/ref> and remained so throughout the Middle Ages and into the modern era. It is sometimes abbreviated "Wm." Shortened familiar versions in English include Will (given name), Will or Wil, Wills, Willy, Willie, Bill (given name), Bill, Billie (given name), Billie, and Billy (name), Billy. A common Irish people, Irish form is Liam. Scottish people, Scottish diminutives include Wull, Willie or Wullie (as in Oor Wullie). Female forms include Willa, Willemina, Wilma (given name), Wilma and Wilhelmina (given name), Wilhelmina. Etymology William is related to the German language, German given name ''Wilhelm''. Both ultimately descend from Proto-Germanic ''*Wiljahelmaz'', with a direct cognate also in the Old Norse name ''Vilhjalmr'' and a West Germanic borrowing into Medieval Latin ''Wil ...
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Finance
Finance refers to monetary resources and to the study and Academic discipline, discipline of money, currency, assets and Liability (financial accounting), liabilities. As a subject of study, is a field of Business administration, Business Administration wich study the planning, organizing, leading, and controlling of an organization's resources to achieve its goals. Based on the scope of financial activities in financial systems, the discipline can be divided into Personal finance, personal, Corporate finance, corporate, and public finance. In these financial systems, assets are bought, sold, or traded as financial instruments, such as Currency, currencies, loans, Bond (finance), bonds, Share (finance), shares, stocks, Option (finance), options, Futures contract, futures, etc. Assets can also be banked, Investment, invested, and Insurance, insured to maximize value and minimize loss. In practice, Financial risk, risks are always present in any financial action and entities. Due ...
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Alpha (investment)
Alpha is a measure of the active return on an investment, the performance of that investment compared with a suitable stock market index, market index. An alpha of 1% means the investment's return on investment over a selected period of time was 1% better than the market during that same period; a negative alpha means the investment underperformed the market. Alpha, along with Beta (finance), beta, is one of two key coefficients in the capital asset pricing model used in modern portfolio theory and is closely related to other important quantities such as Standard deviation#Finance, standard deviation, R-squared and the Sharpe ratio#Use in finance, Sharpe ratio. In modern financial markets, where index funds are widely available for purchase, alpha is commonly used to judge the performance of mutual funds and similar investments. As these funds include various fees normally expressed in percent terms, the fund has to maintain an alpha greater than its fees in order to provide posi ...
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All Ordinaries
The All Ordinaries (XAO) (colloquially known as the All Ords; also known as the All Ordinaries Index, AOI) is the oldest index of shares in Australia. Established in January 1980, it is made up of the share prices for 500 of the largest companies listed on the Australian Securities Exchange (ASX). The market capitalisation of the companies included in the All Ords index amounts to over 95% of the value of all shares listed on the ASX. The 3-letter exchange ticker in Australia for the All Ordinaries is "XAO". ASX indices are managed by S&P Dow Jones Indices. History When established, the All Ords had a base index of 500; this means that if the index is currently at 5000 points, the nominal value of stocks in the All Ords in Australian dollars has increased tenfold since January 1980. On 3 April 2000, the All Ords was restructured to consist of the 500 largest companies by market capitalisation. This coincided with the introduction of new benchmark indices such as the S&P/ASX ...
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Arbitrage Pricing Theory
In finance, arbitrage pricing theory (APT) is a multi-factor model for asset pricing which relates various macro-economic (systematic) risk variables to the pricing of financial assets. Proposed by economist Stephen Ross (economist), Stephen Ross in 1976, it is widely believed to be an improved alternative to its predecessor, the capital asset pricing model (CAPM). APT is founded upon the law of one price, which suggests that within an equilibrium market, rational investors will implement arbitrage such that the equilibrium price is eventually realised. As such, APT argues that when opportunities for arbitrage are exhausted in a given period, then the expected return of an asset is a linear function of various factors or theoretical market indices, where sensitivities of each factor is represented by a factor-specific beta coefficient or factor loading. Consequently, it provides traders with an indication of ‘true’ asset value and enables exploitation of market discrepancies via ...
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Systematic Risk
In finance and economics, systematic risk (in economics often called aggregate risk or undiversifiable risk) is vulnerability to events which affect aggregate outcomes such as broad market returns, total economy-wide resource holdings, or aggregate income. In many contexts, events like earthquakes, epidemics and major weather catastrophes pose aggregate risks that affect not only the distribution but also the total amount of resources. That is why it is also known as contingent risk, unplanned risk or risk events. If every possible outcome of a stochastic economic process is characterized by the same aggregate result (but potentially different distributional outcomes), the process then has no aggregate risk. Properties Systematic or aggregate risk arises from market structure or dynamics which produce shocks or uncertainty faced by all agents in the market; such shocks could arise from government policy, international economic forces, or acts of nature. In contrast, specific ris ...
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Stock Market Index
In finance, a stock index, or stock market index, is an Index (economics), index that measures the performance of a stock market, or of a subset of a stock market. It helps investors compare current stock price levels with past prices to calculate market performance. Two of the primary criteria of an index are that it is ''investable'' and ''transparent'': The methods of its construction are specified. Investors may be able to invest in a stock market index by buying an index fund, which is structured as either a mutual fund or an exchange-traded fund, and "track" an index. The difference between an index fund's performance and the index, if any, is called ''tracking error''. Types of indices by coverage Stock market indices may be classified and segmented by the set of underlying stocks included in the index, sometimes referred to as the "coverage". The underlying stocks are typically grouped together based on their underlying economics or underlying investor demand that the ...
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S&P 500
The Standard and Poor's 500, or simply the S&P 500, is a stock market index tracking the stock performance of 500 leading companies listed on stock exchanges in the United States. It is one of the most commonly followed equity indices and includes approximately 80% of the total market capitalization of U.S. public companies, with an aggregate market cap of more than $49.8 trillion as of March 31, 2025. The S&P 500 index is a Free-float weighted/ capitalization-weighted index. As of April 2025, the ten largest companies on the list of S&P 500 companies accounted for approximately 35% of the market capitalization of the index and were, in order of highest to lowest weighting: Apple (6.4%), Microsoft (6.2%), Nvidia (6.0%), Amazon.com (3.8%), Alphabet (3.6%, including both class A & C shares), Meta Platforms (2.7%), Berkshire Hathaway (2.0%), Broadcom (1.8%), Tesla (1.6%), and JPMorgan Chase (1.4%). The components that have increased their dividends in 25 consecutive ye ...
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Risk Factor (finance)
In finance, risk factors are the building blocks of investing, that help explain the systematic returns in equity market, and the possibility of losing money in investments or business adventures. A risk factor is a concept in finance theory such as the capital asset pricing model, arbitrage pricing theory and other theories that use pricing kernels. In these models, the rate of return of an asset (''hence the converse its price'') is a random variable whose realization in any time period is a linear combination of other random variables plus a disturbance term or white noise. In practice, a linear combination of observed factors included in a linear asset pricing model (for example, the Fama–French three-factor model) proxy for a linear combination of unobserved risk factors if financial market efficiency is assumed. In the Intertemporal CAPM, non-market factors proxy for changes in the investment opportunity set. Risk factors occur whenever any sort of asset is involved, an ...
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Capital Asset Pricing Model
In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a Diversification (finance), well-diversified Portfolio (finance), portfolio. The model takes into account the asset's sensitivity to non-diversifiable risk (also known as systematic risk or market risk), often represented by the quantity Beta (finance), beta (β) in the financial industry, as well as the expected return of the market and the expected return of a theoretical Risk-free bond, risk-free asset. CAPM assumes a particular form of utility functions (in which only first and second Moment (mathematics), moments matter, that is risk is measured by variance, for example a quadratic utility) or alternatively asset returns whose probability distributions are completely described by the first two moments (for example, the normal distribution) and zero transaction costs (necessary for diversifi ...
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