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Rachev Ratio
The Rachev Ratio (or R-Ratio) is a risk-return performance measure of an investment asset, portfolio, or strategy. It was devised by Dr. Svetlozar Rachev and has been extensively studied in quantitative finance. Unlike the ''reward-to-variability'' ratios, such as Sharpe ratio and Sortino ratio, the Rachev ratio is a ''reward-to-risk'' ratio, which is designed to measure the right tail reward potential relative to the left tail risk in a non-Gaussian setting. Intuitively, it represents the potential for extreme positive returns compared to the risk of extreme losses (negative returns), at a rarity frequency q (quantile level) defined by the user. The ratio is defined as the Expected Tail Return (ETR) in the best q% cases divided by the Expected tail loss (ETL) in the worst q% cases. The ETL is the average loss incurred when losses exceed the Value at Risk at a predefined quantile level. The ETR, defined by symmetry to the ETL, is the average profit gained when profits exceed the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Svetlozar Rachev
Svetlozar (Zari) Todorov Rachev is a professor at Texas Tech University who works in the field of mathematical finance, probability theory, and statistics. He is known for his work in probability metrics, derivative pricing, financial risk modeling, and econometrics. In the practice of risk management, he is the originator of the methodology behind the flagship product of FinAnalytica. Life and work Rachev earned a MSc degree from the Faculty of Mathematics at Sofia University in 1974, a PhD degree from Lomonosov Moscow State University under the supervision of Vladimir Zolotarev in 1979, and a Dr Sci degree from Steklov Mathematical Institute in 1986 under the supervision of Leonid Kantorovich, a Nobel Prize winner in economic sciences, Andrey Kolmogorov and Yuri Prokhorov. Currently, he is Professor of Financial Mathematics at Texas Tech University. In mathematical finance, Rachev is known for his work on application of non- Gaussian models for risk assessment, option pricing, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sharpe Ratio
In finance, the Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) measures the performance of an investment such as a security or portfolio compared to a risk-free asset, after adjusting for its risk. It is defined as the difference between the returns of the investment and the risk-free return, divided by the standard deviation of the investment returns. It represents the additional amount of return that an investor receives per unit of increase in risk. It was named after William F. Sharpe, who developed it in 1966. Definition Since its revision by the original author, William Sharpe, in 1994, the ''ex-ante'' Sharpe ratio is defined as: : S_a = \frac = \frac, where R_a is the asset return, R_b is the risk-free return (such as a U.S. Treasury security). E_a-R_b/math> is the expected value of the excess of the asset return over the benchmark return, and is the standard deviation of the asset excess return. The ''ex-p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sortino Ratio
The Sortino ratio measures the risk-adjusted return of an investment asset, portfolio, or strategy. It is a modification of the Sharpe ratio but penalizes only those returns falling below a user-specified target or required rate of return, while the Sharpe ratio penalizes both upside and downside volatility equally. Though both ratios measure an investment's risk-adjusted return, they do so in significantly different ways that will frequently lead to differing conclusions as to the true nature of the investment's return-generating efficiency. The Sortino ratio is used as a way to compare the risk-adjusted performance of programs with differing risk and return profiles. In general, risk-adjusted returns seek to normalize the risk across programs and then see which has the higher return unit per risk. Definition The ratio S is calculated as : S = \frac , where R is the asset or portfolio average realized return, T is the target or required rate of return for the investment strate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tail Risk
Tail risk, sometimes called "fat tail risk," is the financial risk of an asset or portfolio of assets moving more than three standard deviations from its current price, above the risk of a normal distribution. Tail risks include low-probability events arising at both ends of a normal distribution curve, also known as tail events. However, as investors are generally more concerned with unexpected losses rather than gains, a debate about tail risk is focused on the left tail. Prudent asset managers are typically cautious with the tail involving losses which could damage or ruin portfolios, and not the beneficial tail of outsized gains. The common technique of theorizing a normal distribution of price changes underestimates tail risk when market data exhibit fat tails, thus understating asset prices, stock returns and subsequent risk management strategies. Tail risk is sometimes defined less strictly: as merely the risk (or probability) of rare events. The arbitrary definition o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expected Shortfall
Expected shortfall (ES) is a risk measure—a concept used in the field of financial risk measurement to evaluate the market risk or credit risk of a portfolio. The "expected shortfall at q% level" is the expected return on the portfolio in the worst q\% of cases. ES is an alternative to value at risk that is more sensitive to the shape of the tail of the loss distribution. Expected shortfall is also called conditional value at risk (CVaR), average value at risk (AVaR), expected tail loss (ETL), and superquantile. ES estimates the risk of an investment in a conservative way, focusing on the less profitable outcomes. For high values of q it ignores the most profitable but unlikely possibilities, while for small values of q it focuses on the worst losses. On the other hand, unlike the discounted maximum loss, even for lower values of q the expected shortfall does not consider only the single most catastrophic outcome. A value of q often used in practice is 5%. Expected shortfall is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Value At Risk
Value at risk (VaR) is a measure of the risk of loss for investments. It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day. VaR is typically used by firms and regulators in the financial industry to gauge the amount of assets needed to cover possible losses. For a given portfolio, time horizon, and probability ''p'', the ''p'' VaR can be defined informally as the maximum possible loss during that time after excluding all worse outcomes whose combined probability is at most ''p''. This assumes mark-to-market pricing, and no trading in the portfolio. For example, if a portfolio of stocks has a one-day 95% VaR of $1 million, that means that there is a 0.05 probability that the portfolio will fall in value by more than $1 million over a one-day period if there is no trading. Informally, a loss of $1 million or more on this portfolio is expected on 1 day out of 20 days (because of 5% pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Profit At Risk
Profit-at-Risk (PaR) is a risk management quantity most often used for electricity portfolios that contain some mixture of generation assets, trading contracts and end-user consumption. It is used to provide a measure of the downside risk to profitability of a portfolio of physical and financial assets, analysed by time periods in which the energy is delivered. For example, the expected profitability and associated downside risk (PaR) might be calculated and monitored for each of the forward looking 24 months. The measure considers both price risk and volume risk (e.g. due to uncertainty in electricity generation volumes or consumer demand). Mathematically, the PaR is the quantile of the profit distribution of a portfolio. Since weather related volume risk drivers can be represented in the form of historical weather records over many years, a Monte-Carlo simulation approach is often used. Example If the confidence interval for evaluating the PaR is 95%, there is a 5% probabilit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CVaR
Expected shortfall (ES) is a risk measure—a concept used in the field of financial risk measurement to evaluate the market risk or credit risk of a portfolio. The "expected shortfall at q% level" is the expected return on the portfolio in the worst q\% of cases. ES is an alternative to value at risk that is more sensitive to the shape of the tail of the loss distribution. Expected shortfall is also called conditional value at risk (CVaR), average value at risk (AVaR), expected tail loss (ETL), and superquantile. ES estimates the risk of an investment in a conservative way, focusing on the less profitable outcomes. For high values of q it ignores the most profitable but unlikely possibilities, while for small values of q it focuses on the worst losses. On the other hand, unlike the discounted maximum loss, even for lower values of q the expected shortfall does not consider only the single most catastrophic outcome. A value of q often used in practice is 5%. Expected shortfall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Value At Risk
Value at risk (VaR) is a measure of the risk of loss for investments. It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day. VaR is typically used by firms and regulators in the financial industry to gauge the amount of assets needed to cover possible losses. For a given portfolio, time horizon, and probability ''p'', the ''p'' VaR can be defined informally as the maximum possible loss during that time after excluding all worse outcomes whose combined probability is at most ''p''. This assumes mark-to-market pricing, and no trading in the portfolio. For example, if a portfolio of stocks has a one-day 95% VaR of $1 million, that means that there is a 0.05 probability that the portfolio will fall in value by more than $1 million over a one-day period if there is no trading. Informally, a loss of $1 million or more on this portfolio is expected on 1 day out of 20 days (because of 5% pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distribution For Rratio
Distribution may refer to: Mathematics *Distribution (mathematics), generalized functions used to formulate solutions of partial differential equations *Probability distribution, the probability of a particular value or value range of a variable **Cumulative distribution function, in which the probability of being no greater than a particular value is a function of that value * Frequency distribution, a list of the values recorded in a sample *Inner distribution, and outer distribution, in coding theory *Distribution (differential geometry), a subset of the tangent bundle of a manifold *Distributed parameter system, systems that have an infinite-dimensional state-space * Distribution of terms, a situation in which all members of a category are accounted for * Distributivity, a property of binary operations that generalises the distributive law from elementary algebra *Distribution (number theory) *Distribution problems, a common type of problems in combinatorics where the goal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Post-modern Portfolio Theory
Post-Modern Portfolio Theory (PMPT) is an extension of the traditional Modern Portfolio Theory (MPT), an application of mean-variance analysis (MVA). Both theories propose how rational investors can use diversification to optimize their portfolios. History Post-Modern Portfolio Theory was introduced in 1991 by software entrepreneurs Brian M. Rom and Kathleen Ferguson to differentiate the portfolio-construction software developed by their company, Investment Technologies, LLC, from those provided by the traditional modern portfolio theory. It first appeared in the literature in 1993 in an article by Rom and Ferguson in ''The Journal of Performance Measurement''. It combines the theoretical research of many authors and has expanded over several decades as academics at universities in many countries tested these theories to determine whether or not they had merit. The essential difference between PMPT and the modern portfolio theory of Markowitz and Sharpe (MPT) is that PMPT focuses on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Upside Potential Ratio
The upside-potential ratio is a measure of a return of an investment asset relative to the minimal acceptable return. The measurement allows a firm or individual to choose investments which have had relatively good upside performance, per unit of downside risk. : U = = \frac, where the returns R_r have been put into increasing order. Here P_r is the probability of the return R_r and R_\min which occurs at r=\min is the minimal acceptable return. In the secondary formula (X)_+ = \beginX &\textX \geq 0\\ 0 &\text\end and (X)_- = (-X)_+. The upside-potential ratio may also be expressed as a ratio of partial moments since \mathbb R_r - R_\min)_+/math> is the first upper moment and \mathbb R_r - R_\min)_-^2/math> is the second lower partial moment. The measure was developed by Frank A. Sortino. Discussion The upside-potential ratio is a measure of risk-adjusted returns. All such measures are dependent on some measure of risk. In practice, standard deviation is often used, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
