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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 may in turn be used to manage portfolio risk. 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/math>, 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 b ... [...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 in the financial field. 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 with the 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discounted Cash Flow
The discounted cash flow (DCF) analysis, in financial analysis, is a method used to value a security, project, company, or asset, that incorporates the time value of money. Discounted cash flow analysis is widely used in investment finance, real estate development, corporate financial management, and patent valuation. Used in industry as early as the 1700s or 1800s, it was widely discussed in financial economics in the 1960s, and U.S. courts began employing the concept in the 1980s and 1990s. Application In discount cash flow analysis, 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 ; and for the mechanics see valuation using discounted cash flows, which includes modifications typical for startups, private equity and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Financial Risk Management
Financial risk management is the practice of protecting Value (economics), economic value in a business, firm by managing exposure to financial risk - principally credit risk and market risk, with more specific variants as listed aside - as well as some aspects of operational risk. As for risk management more generally, financial risk management requires identifying the sources of risk, measuring these, and crafting plans to mitigation, mitigate them. See for an overview. Financial risk management as a "science" can be said to have been bornW. Kenton (2021)"Harry Markowitz" investopedia.com with modern portfolio theory, particularly as initiated by Professor Harry Markowitz in 1952 with his article, "Portfolio Selection"; see . The discipline can be qualitative and quantitative; as a specialization of risk management, however, financial risk management focuses more on when and how to Hedge (finance), hedge, often using financial instruments to manage costly exposures to risk. * ... [...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 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 ... [...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: # Market excess return, # Outperformance of small versus big companies, and # 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 compare the returns of a portfolio or stock with the returns of the market as a whol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carhart Four-factor Model
In Investment management, 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 investing, value stocks tending to outperform) and company size (smaller company stocks tending to outperform). Carhart added a Momentum (finance), 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 weighted 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 ... [...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 (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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MSCI
MSCI Inc. (formerly Morgan Stanley Capital International) is an American finance company headquartered in New York City. MSCI is a global provider of equity, fixed income, real estate indices, multi-asset portfolio analysis tools, ESG and climate finance products. It operates the MSCI World, MSCI Emerging Markets, and MSCI All Country World (ACWI) indices, among others. The company is headquartered at 7 World Trade Center in Manhattan. Its business primarily consists of licensing its indices to index funds, such as exchange-traded funds (ETFs), which pay a fee of around 0.02 to 0.04 percent of the invested volume for the use of the index. funds worth over 16.5 trillion US$ were based on MSCI indices. History In 1968, Capital International published indices covering the global stock market for non-U.S. markets. In 1986, Morgan Stanley licensed the rights to the indices from Capital International and branded the indices as the Morgan Stanley Capital International (MSCI) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Goldman Sachs Asset Management Factor Model
The Goldman Sachs asset management (GSAM) factor model is a quantitative investment model used by financial analysts to assess the potential performance and risk of company. There are various types of factor models – statistical models, macroeconomic models and fundamental models. While Goldman Sachs employs several, gsam.com that described below is of the latter type. The quantitative model here uses company and industry attributes, [...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 accounting ledger of tradeable financial assets, or of 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 purcha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
