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Multiple Factor Models
In mathematical finance, multiple factor models are asset pricing models that can be used to estimate the discount rate for the valuation of financial assets. They are generally extensions of the single-factor capital asset pricing model (CAPM). Model of Rosenberg and Marathe The multifactor equity risk model was first developed by Barr Rosenberg and Vinay Marathe. Initially they proposed a linear model of beta r(i,t)-r(0,t)=b(i,t) (t)-r(0,t)g(i,t) b(i,t)=\sum_j X(i,j,t) f(j,t) + e(i,t) where r(i,t) is the return to equity asset I in the period ,t+1 r(0,t) is the risk free return, m(t) is the market index return, e(i,t) is a market residual return and b(i,t) is a parameter fit by a time series regression over history prior to time t. Then X(i,j,t) are risk exposure values calculated from fundamental and technical data, f(j,t) are factor returns determined by a cross-sectional regression for each time period and g(i, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Finance
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio management on the other. Mathematical finance overlaps heavily with the fields of computational finance and financial engineering. The latter focuses on applications and modeling, often by help of stochastic asset models, while the former focuses, in addition to analysis, on building tools of implementation for the models. Also related is quantitative investing, which relies on statistical and numerical models (and lately machine learning) as opposed to traditional fundamental analysis when managing portfolios. French mathematician Louis Bachelier's doctoral thesis, defended in 1900, is considered the first scholarly work on mathematical fina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Valuation (finance)
In finance, valuation is the process of determining the present value (PV) of an asset. In a business context, it is often the hypothetical price that a third party would pay for a given asset. Valuations can be done on assets (for example, investments in marketable securities such as companies' shares and related rights, business enterprises, or intangible assets such as patents, data and trademarks) or on liabilities (e.g., bonds issued by a company). Valuations are needed for many reasons such as investment analysis, capital budgeting, merger and acquisition transactions, financial reporting, taxable events to determine the proper tax liability. Valuation overview Common terms for the value of an asset or liability are market value, fair value, and Intrinsic value (finance), intrinsic value. The meanings of these terms differ. For instance, when an analyst believes a stock's intrinsic value is greater (or less) than its market price, an analyst makes a "buy" (or "sell") reco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discounted Cash Flow
The discounted cash flow (DCF) analysis is a method in finance of valuing a security, project, company, or asset using the concepts of the time value of money. Discounted cash flow analysis is widely used in investment finance, real estate development, corporate financial management and patent valuation. It was used in industry as early as the 1700s or 1800s, widely discussed in financial economics in the 1960s, and became widely used in U.S. courts in the 1980s and 1990s. Application To apply the method, all future cash flows are estimated and discounted by using cost of capital to give their present values (PVs). The sum of all future cash flows, both incoming and outgoing, is the net present value (NPV), which is taken as the value of the cash flows in question; see aside. For further context see valuation overview; and for the mechanics see valuation using discounted cash flows, which includes modifications typical for startups, private equity and venture capital, co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 well-diversified 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 (β) in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset. CAPM assumes a particular form of utility functions (in which only first and second 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 diversification to get rid of all idiosyncratic risk). Under these conditions, CAPM shows that the cost of eq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fama–French Three-factor Model
In asset pricing and portfolio management the Fama–French three-factor model is a statistical model designed in 1992 by Eugene Fama and Kenneth French to describe stock returns. Fama and French were colleagues at the University of Chicago Booth School of Business, where Fama still works. In 2013, Fama shared the Nobel Memorial Prize in Economic Sciences for his empirical analysis of asset prices. The three factors are (1) market excess return, (2) the outperformance of small versus big companies, and (3) the outperformance of high book/market versus low book/market companies. There is academic debate about the last two factors. Background and development Factor models are statistical models that attempt to explain complex phenomena using a small number of underlying causes or factors. The traditional asset pricing model, known formally as the capital asset pricing model (CAPM) uses only one variable to describe the returns of a portfolio or stock with the returns of the market ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carhart Four-factor Model
In portfolio management, the Carhart four-factor model is an extra factor addition in the Fama–French three-factor model, proposed by Mark Carhart. The Fama-French model, developed in the 1990, argued most stock market returns are explained by three factors: risk, price (value stocks tending to outperform) and company size (smaller company stocks tending to outperform). Carhart added a momentum factor for asset pricing of stocks. The Four Factor Model is also known in the industry as the Monthly Momentum Factor (MOM). Momentum is the speed or velocity of price changes in a stock, security, or tradable instrument. Development The Monthly Momentum Factor(MOM) can be calculated by subtracting the equal weighted average of the lowest performing firms from the equal weighed average of the highest performing firms, lagged one month (Carhart, 1997). A stock would be considered to show momentum if its prior 12-month average of returns is positive, or greater. Similar to the thr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 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 arbitrage. The linear fac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MSCI
MSCI Inc. is an American finance company headquartered in New York City. MSCI is a global provider of equity, fixed income, real estate indexes, multi-asset portfolio analysis tools, ESG and climate products. It operates the MSCI World, MSCI All Country World Index (ACWI), MSCI Emerging Markets Indexes. The company is headquartered at 7 World Trade Center in Manhattan, New York City, U.S. History In 1968, Capital International published indexes covering the global stock market for non-U.S. markets. In 1986, Morgan Stanley licensed the rights to the indexes from Capital International and branded the indexes as the Morgan Stanley Capital International (MSCI) indexes. By the 1980s, the MSCI indexes were the primary benchmark indexes outside of the U.S. before being joined by FTSE, Citibank, and Standard & Poor's. After Dow Jones started float weighting its index funds, MSCI followed. In 2004, MSCI acquired Barra, Inc., to form MSCI Barra. In mid-2007, parent company Morgan Stanl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Goldman Sachs Asset Management Factor Model
Goldman Sachs asset management (GSAM) factor model is one of the quantitative/ factor models used by financial analysts to assess the performance and financial condition of a company. Typically quantitative models are based on inputs obtained from financial statements(FS). There are various types of factor models – statistical models, macroeconomic models and fundamental models. A fundamental factor model uses company and industry attributes and market data known as "factors" to explain a company's historical returns. Since the input factors from FS may be questionable or the data may not be comparable over time this model includes a factor that is based on an assessment by equity analysts performing traditional equity analysis. Goldman Sachs Asset Management factor model uses the following three measures. * (A). Value ** i. Book/price ** ii. Retained EPS/price ** iii EBITD/enterprise value * (B). Growth and momentum ** i. Estimate revisions ** ii. Price momentum ** iii. Sust ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Financial Risk Modeling
Financial risk modeling is the use of formal mathematical and econometric techniques to measure, monitor and control the market risk, credit risk, and operational risk on a firm's balance sheet, on a bank's trading book, or re a fund manager's portfolio value; see Financial risk management. Risk modeling is one of many subtasks within the broader area of financial modeling. Application Risk modeling uses a variety of techniques including market risk, value at risk (VaR), historical simulation (HS), or extreme value theory (EVT) in order to analyze a portfolio and make forecasts of the likely losses that would be incurred for a variety of risks. As above, such risks are typically grouped into credit risk, market risk, model risk, liquidity risk, and operational risk categories. Many large financial intermediary firms use risk modeling to help portfolio managers assess the amount of capital reserves to maintain, and to help guide their purchases and sales of various classes of f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Financial Markets
A financial market is a market in which people trade financial securities and derivatives at low transaction costs. Some of the securities include stocks and bonds, raw materials and precious metals, which are known in the financial markets as commodities. The term "market" is sometimes used for what are more strictly ''exchanges'', organizations that facilitate the trade in financial securities, e.g., a stock exchange or commodity exchange. This may be a physical location (such as the New York Stock Exchange (NYSE), London Stock Exchange (LSE), JSE Limited (JSE), Bombay Stock Exchange (BSE) or an electronic system such as NASDAQ. Much trading of stocks takes place on an exchange; still, corporate actions (merger, spinoff) are outside an exchange, while any two companies or people, for whatever reason, may agree to sell the stock from the one to the other without using an exchange. Trading of currencies and bonds is largely on a bilateral basis, although some bonds trade o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
