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Roll's Critique
Roll's critique is a famous analysis of the validity of empirical tests of the capital asset pricing model (CAPM) by Richard Roll. It concerns methods to formally test the statement of the CAPM, the equation :E(R_i) = R_f + \beta_ (R_m) - R_f\, This equation relates an asset's expected return E(R_i) to the asset's sensitivity \beta_ to the market portfolio return R_m. The market return is defined as the wealth-weighted sum of all investment returns in the economy. Roll's critique makes two statements regarding the market portfolio: 1. Mean-variance tautology: Any mean-variance efficient portfolio R_p satisfies the CAPM equation ''exactly'': :E(R_i) = R_f + \beta_ (R_p) - R_f,. (A portfolio is mean-variance efficient if there is no portfolio that has a higher return and lower risk than those for the efficient portfolio.) Mean-variance efficiency of the market portfolio is equivalent to the CAPM equation holding. This statement is a mathematical fact, requiring ''no'' model assu ... [...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] |
Richard Roll
Richard Roll (born October 31, 1939) is an American economist and professor of finance at UCLA, best known for his work on portfolio theory and asset pricing, both theoretical and empirical. He earned his bachelor's degree in aerospace engineering from Auburn University in 1961, and his M.B.A. in 1963 at the University of Washington while working for Boeing in Seattle, Washington. In 1968, he received his Ph.D. from the Graduate School of Business at the University of Chicago in economics, finance, and statistics. His Ph.D. thesis, "The Behavior of Interest Rates: An Application of the Efficient Market Model to U.S. Treasury Bills," won the Irving Fisher Prize as the best American dissertation in economics in 1968. Roll co-authored the first event study that sought to analyze how stock prices respond to an event in 1969, using price data from the newly available CRSP database. Roll has co-authored major papers with Stephen Ross, Eugene Fama, Michael Jensen and Kenneth French ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mean Variance Efficiency
In portfolio theory, a mutual fund separation theorem, mutual fund theorem, or separation theorem is a theorem stating that, under certain conditions, any investor's optimal portfolio can be constructed by holding each of certain mutual funds in appropriate ratios, where the number of mutual funds is smaller than the number of individual assets in the portfolio. Here a mutual fund refers to any specified benchmark portfolio of the available assets. There are two advantages of having a mutual fund theorem. First, if the relevant conditions are met, it may be easier (or lower in transactions costs) for an investor to purchase a smaller number of mutual funds than to purchase a larger number of assets individually. Second, from a theoretical and empirical standpoint, if it can be assumed that the relevant conditions are indeed satisfied, then implications for the functioning of asset markets can be derived and tested. Portfolio separation in mean-variance analysis Portfolios can be ... [...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] |
Data Dredging
Data dredging (also known as data snooping or ''p''-hacking) is the misuse of data analysis to find patterns in data that can be presented as statistically significant, thus dramatically increasing and understating the risk of false positives. This is done by performing many statistical tests on the data and only reporting those that come back with significant results. The process of data dredging involves testing multiple hypotheses using a single data set by exhaustively searching—perhaps for combinations of variables that might show a correlation, and perhaps for groups of cases or observations that show differences in their mean or in their breakdown by some other variable. Conventional tests of statistical significance are based on the probability that a particular result would arise if chance alone were at work, and necessarily accept some risk of mistaken conclusions of a certain type (mistaken rejections of the null hypothesis). This level of risk is called the ''s ... [...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] |
