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Downside Beta
In investing, downside beta is the beta that measures a stock's association with the overall stock market (risk) only on days when the market’s return is negative. Downside beta was first proposed by Roy 1952 and then popularized in an investment book bMarkowitz (1959) Formula It is common to measure r_i and r_m as the excess returns to security i and the market m, u_m as the average market excess return, and Cov and Var as the covariance and variance operators, Downside beta is :\beta^-=\frac, while upside beta is given by this expression with the direction of the inequalities reversed. Therefore, \beta^- can be estimated with a regression of the excess return of security i on the excess return of the market, conditional on (excess) market return being negative. Downside beta vs. beta Downside beta was once hypothesized to have greater explanatory power than standard beta in bearish markets. As such, it would have been a better measure of risk than ordinary beta. Use in Equi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beta (finance)
In finance, the beta (β or market beta or beta coefficient) is a measure of how an individual asset moves (on average) when the overall stock market increases or decreases. Thus, beta is a useful measure of the contribution of an individual asset to the risk of the market portfolio when it is added in small quantity. Thus, beta is referred to as an asset's non-diversifiable risk, its systematic risk, market risk, or hedge ratio. Beta is ''not'' a measure of idiosyncratic risk. Interpretation of values By definition, the value-weighted average of all market-betas of all investable assets with respect to the value-weighted market index is 1. If an asset has a beta above (below) 1, it indicates that its return moves more (less) than 1-to-1 with the return of the market-portfolio, on average. In practice, few stocks have negative betas (tending to go up when the market goes down). Most stocks have betas between 0 and 3. Treasury bills (like most fixed income instruments) a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Financial Risk
Financial risk is any of various types of risk associated with financing, including financial transactions that include company loans in risk of default. Often it is understood to include only downside risk, meaning the potential for financial loss and uncertainty about its extent. A science has evolved around managing market and financial risk under the general title of modern portfolio theory initiated by Dr. Harry Markowitz in 1952 with his article, "Portfolio Selection". In modern portfolio theory, the variance (or standard deviation) of a portfolio is used as the definition of risk. Types According to Bender and Panz (2021), financial risks can be sorted into five different categories. In their study, they apply an algorithm-based framework and identify 193 single financial risk types, which are sorted into the five categories market risk, liquidity risk, credit risk, business risk and investment risk. Market risk The four standard market risk factors are equity ri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roy's Safety-first Criterion
Roy's safety-first criterion is a risk management technique, devised by A. D. Roy, that allows an investor to select one portfolio rather than another based on the criterion that the probability of the portfolio's return falling below a minimum desired threshold is minimized. For example, suppose there are two available investment strategies—portfolio A and portfolio B, and suppose the investor's threshold return level (the minimum return that the investor is willing to tolerate) is −1%. Then, the investor would choose the portfolio that would provide the maximum probability of the portfolio return being at least as high as −1%. Thus, the problem of an investor using Roy's safety criterion can be summarized symbolically as: \underset\Pr(R_<\underline) where is the probability of (the actual return of asset i) being less than (the minimum acceptable return). Normally distributed return and SFRatio If the portfolios under consideratio ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Covariance Operator
In probability theory, for a probability measure P on a Hilbert space ''H'' with inner product \langle \cdot,\cdot\rangle , the covariance of P is the bilinear form Cov: ''H'' × ''H'' → R given by :\mathrm(x, y) = \int_ \langle x, z \rangle \langle y, z \rangle \, \mathrm \mathbf (z) for all ''x'' and ''y'' in ''H''. The covariance operator ''C'' is then defined by :\mathrm(x, y) = \langle Cx, y \rangle (from the Riesz representation theorem, such operator exists if Cov is bounded). Since Cov is symmetric in its arguments, the covariance operator is self-adjoint. When P is a centred Gaussian measure, ''C'' is also a nuclear operator. In particular, it is a compact operator of trace class, that is, it has finite trace. Even more generally, for a probability measure P on a Banach space ''B'', the covariance of P is the bilinear form on the algebraic dual ''B''#, defined by :\mathrm(x, y) = \int_ \langle x, z \rangle \langle y, z \rangle \, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variance
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. Variance has a central role in statistics, where some ideas that use it include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling. Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by \sigma^2, s^2, \operatorname(X), V(X), or \mathbb(X). An advantage of variance as a measure of dispersion is that it is more amenable to algebraic manipulation than other measures of dispersion such as the expected absolute deviation; for e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Upside Beta
In Investment#In finance, investing, upside beta is the element of traditional Beta (finance), beta that investors do not typically associate with the true meaning of Financial risk, risk. It is defined to be the scaled amount by which an asset tends to move compared to a benchmark, calculated only on days when the benchmark’s return is positive. Formula Upside beta measures this upside risk. Defining r_i and r_m as the excess returns to security i and market m, u_m as the average market excess return, and Cov and Var as the Covariance operator, covariance and variance operators, the CAPM can be modified to incorporate upside (or Downside beta, downside) beta as follows. :\beta^+=\frac, with downside beta \beta^- defined with the inequality directions reversed. Therefore, \beta^- and \beta^+ can be estimated with a regression of excess return of security i on excess return of the market, conditional on excess market return being below the mean (downside beta) and above the mean ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beta (finance)
In finance, the beta (β or market beta or beta coefficient) is a measure of how an individual asset moves (on average) when the overall stock market increases or decreases. Thus, beta is a useful measure of the contribution of an individual asset to the risk of the market portfolio when it is added in small quantity. Thus, beta is referred to as an asset's non-diversifiable risk, its systematic risk, market risk, or hedge ratio. Beta is ''not'' a measure of idiosyncratic risk. Interpretation of values By definition, the value-weighted average of all market-betas of all investable assets with respect to the value-weighted market index is 1. If an asset has a beta above (below) 1, it indicates that its return moves more (less) than 1-to-1 with the return of the market-portfolio, on average. In practice, few stocks have negative betas (tending to go up when the market goes down). Most stocks have betas between 0 and 3. Treasury bills (like most fixed income instruments) a ... [...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] |
Standard Deviation
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. Standard deviation may be abbreviated SD, and is most commonly represented in mathematical texts and equations by the lower case Greek letter σ (sigma), for the population standard deviation, or the Latin letter '' s'', for the sample standard deviation. The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler, though in practice less robust, than the average absolute deviation. A useful property of the standard deviation is that, unlike the variance, it is expressed in the same unit as the data. The standard deviation of a popu ... [...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] |
