|
Black–Litterman Model
In finance, the Black–Litterman model is a mathematical model for portfolio allocation developed in 1990 at Goldman Sachs by Fischer Black and Robert Litterman. It seeks to overcome problems that institutional investors have encountered in applying modern portfolio theory in practice. The model starts with an asset allocation based on the equilibrium assumption (assets will perform in the future as they have in the past) and then modifies that allocation by taking into account the opinion of the investor regarding future asset performance. Attilio Meucci (2010). https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1117574 he Black-Litterman Approach: Original Model and Extensions/ref> Background Asset allocation is the decision faced by an investor who must choose how to allocate their portfolio across a number of asset classes. For example, a globally invested pension fund must choose how much to allocate to each major country or region. In principle modern portfolio theory ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Model
A mathematical model is an abstract and concrete, abstract description of a concrete system using mathematics, mathematical concepts and language of mathematics, language. The process of developing a mathematical model is termed ''mathematical modeling''. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science). It can also be taught as a subject in its own right. The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, linguistics, and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different components, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Portfolio Allocation
Portfolio optimization is the process of selecting an optimal portfolio (asset distribution), out of a set of considered portfolios, according to some objective. The objective typically maximizes factors such as expected return, and minimizes costs like financial risk, resulting in a multi-objective optimization problem. Factors being considered may range from tangible (such as assets, liabilities, earnings or other fundamentals) to intangible (such as selective divestment). Modern portfolio theory Modern portfolio theory was introduced in a 1952 doctoral thesis by Harry Markowitz, where the Markowitz model was first defined. The model assumes that an investor aims to maximize a portfolio's expected return contingent on a prescribed amount of risk. Portfolios that meet this criterion, i.e., maximize the expected return given a prescribed amount of risk, are known as efficient portfolios. By definition, any other portfolio yielding a higher amount of expected return must also hav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Goldman Sachs
The Goldman Sachs Group, Inc. ( ) is an American multinational investment bank and financial services company. Founded in 1869, Goldman Sachs is headquartered in Lower Manhattan in New York City, with regional headquarters in many international financial centers. Goldman Sachs is the second-largest investment bank in the world by revenue and is ranked 55th on the ''Fortune'' 500 list of the largest United States corporations by total revenue. In the Forbes Global 2000 of 2024, Goldman Sachs ranked 23rd. It is considered a systemically important financial institution by the Financial Stability Board. Goldman Sachs offers services in investment banking (advisory for mergers and acquisitions and restructuring), securities underwriting, prime brokerage, asset management, and wealth management. It is a market maker for many types of financial products and provides clearing and custodian bank services. It operates private-equity funds and hedge funds. It structures complex and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fischer Black
Fischer Sheffey Black (January 11, 1938 – August 30, 1995) was an American economist, best known as one of the authors of the Black–Scholes equation. Working variously at the University of Chicago, the Massachusetts Institute of Technology, and at Goldman Sachs, Black died two years before the Nobel Memorial Prize in Economic Sciences (which is not given posthumously) was awarded to his collaborator Myron Scholes and former colleague Robert C. Merton for the Black-Scholes model and Merton's application of the model to a continuous-time framework. Black also made significant contributions to the capital asset pricing model and the theory of accounting, as well as more controversial contributions in monetary economics and the theory of business cycles. Background Fischer Sheffey Black was born on January 11, 1938. He graduated from Harvard College with a major in physics in 1959 and received a PhD in applied mathematics from Harvard University in 1964. He was initially ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Litterman
Robert Bruce Litterman (born 1951) is chairman of the Risk Committee and a founding partner of Kepos Capital in New York. Prior to Kepos Capital, Litterman spent 23 years at Goldman Sachs, where he was head of the Quantitative Resources Group in Goldman Sachs Asset Management for 11 years, starting in 1998. Prior to that position, Litterman headed the firm-wide risk department from 1994 to 1998, and prior to that he was the co-head of the model development group in the research department of Goldman Sachs' Fixed Income Division. Litterman received a Ph.D. in economics from the University of Minnesota in 1980. Black–Litterman model At Goldman Sachs, Litterman developed the Black–Litterman model together with Fischer Black in 1990. The model solves a seemingly simple yet perplexing problem: it is difficult to consistently estimate expected returns from various assets. The Black–Litterman model solves this problem by making expected returns an output, rather than an inpu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modern Portfolio Theory
Modern portfolio theory (MPT), or mean-variance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk. It is a formalization and extension of Diversification (finance), diversification in investing, the idea that owning different kinds of financial assets is less risky than owning only one type. Its key insight is that an asset's risk and return should not be assessed by itself, but by how it contributes to a portfolio's overall risk and return. The variance of return (or its transformation, the standard deviation) is used as a measure of risk, because it is tractable when assets are combined into portfolios. Often, the historical variance and covariance of returns is used as a proxy for the forward-looking versions of these quantities, but other, more sophisticated methods are available. Economist Harry Markowitz introduced MPT in a 1952 paper, for which he was later awarded a Nobel Memorial ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harry Markowitz
Harry Max Markowitz (August 24, 1927 – June 22, 2023) was an American economist who received the 1989 John von Neumann Theory Prize and the 1990 Nobel Memorial Prize in Economic Sciences. Markowitz was a professor of finance at the Rady School of Management at the University of California, San Diego (UCSD). He is best known for his pioneering work in modern portfolio theory, studying the effects of asset risk, return, correlation and diversification on probable investment portfolio returns. Biography Harry Markowitz was born to a Jewish family, the son of Morris and Mildred Markowitz.Harry M. Markowitz �Autobiography The Nobel Prizes 1990, Editor Tore Frängsmyr, obel Foundation Stockholm, 1991 During high school, Markowitz developed an interest in physics and philosophy, in particular the ideas of David Hume, an interest he continued to follow during his undergraduate years at the University of Chicago. After receiving his Ph.B. in Liberal Arts, Markowitz decided t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expected Return
The expected return (or expected gain) on a financial investment is the expected value of its return (of the profit on the investment). It is a measure of the center of the distribution of the random variable that is the return. It is calculated by using the following formula: :E \sum_^R_P_ where :: R_ is the return in scenario i; ::P_ is the probability for the return R_ in scenario i; and ::n is the number of scenarios. The expected rate of return is the expected return per currency unit (e.g., dollar) invested. It is computed as the expected return divided by the amount invested. The required rate of return is what an investor would require to be compensated for the risk borne by holding the asset; "expected return" is often used in this sense, as opposed to the more formal, mathematical, sense above. Application Although the above represents what one expects the return to be, it only refers to the long-term average. In the short term, any of the various scenarios could occu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Short (finance)
In finance, being short in an asset means investing in such a way that the investor will profit if the market value of the asset falls. This is the opposite of the more common Long (finance), long Position (finance), position, where the investor will profit if the market value of the asset rises. An investor that sells an asset short is, as to that asset, a short seller. There are a number of ways of achieving a short position. The most basic is physical selling short or short-selling, by which the short seller Securities lending, borrows an asset (often a security (finance), security such as a share (finance), share of stock or a bond (finance), bond) and sells it. The short seller must later buy the same amount of the asset to return it to the lender. If the market price of the asset has fallen in the meantime, the short seller will have made a profit equal to the difference in price. Conversely, if the price has risen then the short seller will bear a loss. The short seller ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modern Portfolio Theory
Modern portfolio theory (MPT), or mean-variance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk. It is a formalization and extension of Diversification (finance), diversification in investing, the idea that owning different kinds of financial assets is less risky than owning only one type. Its key insight is that an asset's risk and return should not be assessed by itself, but by how it contributes to a portfolio's overall risk and return. The variance of return (or its transformation, the standard deviation) is used as a measure of risk, because it is tractable when assets are combined into portfolios. Often, the historical variance and covariance of returns is used as a proxy for the forward-looking versions of these quantities, but other, more sophisticated methods are available. Economist Harry Markowitz introduced MPT in a 1952 paper, for which he was later awarded a Nobel Memorial ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constrained Optimization
In mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function with respect to some variables in the presence of constraints on those variables. The objective function is either a cost function or energy function, which is to be minimized, or a reward function or utility function, which is to be maximized. Constraints can be either hard constraints, which set conditions for the variables that are required to be satisfied, or soft constraints, which have some variable values that are penalized in the objective function if, and based on the extent that, the conditions on the variables are not satisfied. Relation to constraint-satisfaction problems The constrained-optimization problem (COP) is a significant generalization of the classic constraint-satisfaction problem (CSP) model. COP is a CSP that includes an ''objective function'' to be optimized. Many algorithms are used to hand ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
