Once the expected return, E(ri), is calculated using CAPM, the future cash flows of the asset can be discounted to their present value using this rate to establish the correct price for the asset. In theory, therefore, an asset is correctly priced when its observed price is the same as its value calculated using the CAPM derived discount rate. If the observed price is higher than the valuation, then t ...

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Capital asset pricing model, Capital asset pricing model - The formula, Capital asset pricing model - Asset pricing, Capital asset pricing model - Asset-specific required return, Capital asset pricing model - Risk and diversification, Capital asset pricing model - The efficient Markowitz frontier, Capital asset pricing model - The market portfolio, Capital asset pricing model - Assumptions of CAPM, Capital asset pricing model - Shortcomings of CAPM, Capital asset pricing model - Finding related topics

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Using matrix algebra, the true variance can be measured by computing all possible differences between elements of a population. Consider that a major difference of a vector results in a skew-symmetric matrix with elements describing all possible differences between its values. For instance, the major difference of the vector x [0, 1, 2, 3] with true variance equal to 1.25 and unbiased variance equal to 1.67, The above matrix contains the information necessary to compute either the true variance, or the unbised variance. ...

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True variance, True variance - Computation of the true and unbiased variance, True variance - Changing true variance to unbiased variance and vice versa, True variance - Degrees of freedom, True variance - Degrees of freedom: Monte Carlo simulation, True variance - True variance and all possible differences between values of a variable, True variance - Matrices of differences, True variance - Differences between data elements and their mean, True variance - Variance and Information, True variance - Retrospect, True variance - Conventional language of computation

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The cumulative distribution function is where Bx(α,β) is the incomplete beta function and Ix(α,β) is the regularized incomplete beta function. ...

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Beta distribution, Beta distribution - Parameter estimation, Beta distribution - Cumulative distribution function, Beta distribution - Shapes, Beta distribution - Related distributions, Beta distribution - Applications

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Organisms that reproduce through asexual reproduction tend to grow in number exponentially. However, because they rely on mutation for variations in their DNA, all members of the species have similar vulnerabilities. Organisms that reproduce sexually yield a smaller amount of offspring, but the large amount of variation in their genes makes them less susceptible to disease. Many organisms can reproduce sexually as well as asexually. Aphids, slime molds, sea anemones and many plants are examples. When environmental factors are favorabl ...

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Biological reproduction, Biological reproduction - Asexual reproduction, Biological reproduction - Sexual reproduction, Biological reproduction - Mitosis and Meiosis, Biological reproduction - Reproductive strategies, Biological reproduction - Asexual vs. sexual reproduction, Biological reproduction - The Red Queen hypothesis, Biological reproduction - Life without reproduction

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The risk of a portfolio is comprised of systematic risk and specific risk. Systematic risk refers to the risk common to all securities - i.e. market risk. Specific risk is the risk associated with individual assets. Specific risk can be diversified away (specific risks "average out"); systematic risk (within one market) cannot. Depending on the market, a portfolio of approximately 15 (or more) well selected shares might be sufficie ...

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Capital asset pricing model, Capital asset pricing model - The formula, Capital asset pricing model - Asset pricing, Capital asset pricing model - Asset-specific required return, Capital asset pricing model - Risk and diversification, Capital asset pricing model - The efficient Markowitz frontier, Capital asset pricing model - The market portfolio, Capital asset pricing model - Assumptions of CAPM, Capital asset pricing model - Shortcomings of CAPM, Capital asset pricing model - Finding related topics

Read more here: » Capital asset pricing model: Encyclopedia II - Capital asset pricing model - Risk and diversification

South Slavs were christianized in 9th century. Until the Ottoman conqueror of Bosnia, we have evidence of three Christian denominations in Bosnia: Eastern Orthodox, Roman Catholic and an indigenous church known as the Bosnian Church. Both Orthodox and Catholic officials declared this church to be a heresy. Apart from testimonies of inquisitors and a few excerpts from allegedly apocryphal texts, we have very little knowledge of the Bosnian Church. Its connection with Bogomils is spurious, however. Discussion about how numerous each of these d ...

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Nations of Bosnia and Herzegovina, Nations of Bosnia and Herzegovina - Ethnic background of Bosnia and Herzegovina, Nations of Bosnia and Herzegovina - Brief history of religions in Bosnia and Herzegovina, Nations of Bosnia and Herzegovina - Transformation of ethnicity to religion its cause and course

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The expected values of the powers of X are called the moments of X; the moments about the mean of X are expected values of powers of X − E(X). The moments of some random variables can be used to specify their distributions, via their moment generating functions. To empirically estimate the expected value of a random variable, one repeatedly measures observations of the variable and co ...

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Expected value, Expected value - Mathematical definition, Expected value - Properties, Expected value - Linearity, Expected value - Iterated expectation, Expected value - Inequality, Expected value - Representation, Expected value - Non-multiplicativity, Expected value - Functional non-invariance, Expected value - Uses and applications of the expected value, Expected value - Expectation of matrices

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Expected value - Linearity. The expected value operator (or expectation operator) E is linear in the sense that for any two random variables X and Y (which need to be defined on the same probability space) and any real numbers a and b. Expected value - Iterated expectation. For any two random variables X,Y one may define the ...

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Expected value, Expected value - Mathematical definition, Expected value - Properties, Expected value - Linearity, Expected value - Iterated expectation, Expected value - Inequality, Expected value - Representation, Expected value - Non-multiplicativity, Expected value - Functional non-invariance, Expected value - Uses and applications of the expected value, Expected value - Expectation of matrices

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In Bayesian statistical inference, a prior probability distribution, often called simply the prior, of an uncertain quantity p (for example, suppose p is the proportion of voters who will vote for a politician in a future election, let's call him Smith) is the probability distribution that would express one's uncertainty about p before the "data" (for example, an opinion poll) are taken into account. It is meant to att ...

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Prior probability, Prior probability - Prior probability distribution, Prior probability - Informative priors, Prior probability - Uninformative priors, Prior probability - Improper priors

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If X is an matrix, then the expected value of the matrix is a matrix of expected values: This property is utilized in covariance matrices. ...

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Expected value, Expected value - Mathematical definition, Expected value - Properties, Expected value - Linearity, Expected value - Iterated expectation, Expected value - Inequality, Expected value - Representation, Expected value - Non-multiplicativity, Expected value - Functional non-invariance, Expected value - Uses and applications of the expected value, Expected value - Expectation of matrices

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In Austria, a 5-point grading scale is used, where: 1 (very good) is the best possible grade. 2 (good) is the next-highest. 3 (satisfactory) indicates "average" performance. 4 (sufficient) is the lowest passing grade. 5 (insufficient) is the lowest possible grade and the only failing grade. The textual form of the grades is: 1 sehr gut 2 gut 3 befriedigend 4 ...

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Grade education, Grade education - Argentina, Grade education - Austria, Grade education - Belgium, Grade education - Central and Eastern Europe, Grade education - Chile, Grade education - Croatia, Grade education - Denmark, Grade education - Finland, Grade education - France, Grade education - Germany, Grade education - India, Grade education - International Baccalaureate, Grade education - Italy, Grade education - Iran, Grade education - The Netherlands, Grade education - Norway, Grade education - Peru, Grade education - Philippines, Grade education - Poland, Grade education - Portugal, Grade education - Russia, Grade education - United Kingdom, Grade education - Scotland, Grade education - England Wales and Northern Ireland, Grade education - Singapore, Grade education - Lower Primary Primary 1 to 3, Grade education - Upper Primary Primary 4 to 6, Grade education - Secondary Level for GCE O levels, Grade education - Junior College Level GCE A and AO levels, Grade education - Slovenia, Grade education - Sweden, Grade education - Switzerland, Grade education - Ukraine, Grade education - United States Canada Hong Kong Australia New Zealand, Grade education - Yugoslavia former, Grade education - Related Links

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In Argentina, grades from 1 (sometimes 0) up to 10 are used, with some schools allowing decimals (up to 2) and some others only allowing whole numbers where: 10 (excellent) is the best possible grade 8-9.99 (very good) 6-7.99 (good) 4-5.99 (sufficient) up to 3.99 (insufficient) Most universities evaluate classes with two mid exams and a final. The final exam encompasses the whole course syllabus wheres the mid exams usually take just half. In some schools, if the average grade of ...

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Grade education, Grade education - Argentina, Grade education - Austria, Grade education - Belgium, Grade education - Central and Eastern Europe, Grade education - Chile, Grade education - Croatia, Grade education - Denmark, Grade education - Finland, Grade education - France, Grade education - Germany, Grade education - India, Grade education - International Baccalaureate, Grade education - Italy, Grade education - Iran, Grade education - The Netherlands, Grade education - Norway, Grade education - Peru, Grade education - Philippines, Grade education - Poland, Grade education - Portugal, Grade education - Russia, Grade education - United Kingdom, Grade education - Scotland, Grade education - England Wales and Northern Ireland, Grade education - Singapore, Grade education - Lower Primary Primary 1 to 3, Grade education - Upper Primary Primary 4 to 6, Grade education - Secondary Level for GCE O levels, Grade education - Junior College Level GCE A and AO levels, Grade education - Slovenia, Grade education - Sweden, Grade education - Switzerland, Grade education - Ukraine, Grade education - United States Canada Hong Kong Australia New Zealand, Grade education - Yugoslavia former, Grade education - Related Links

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An informative prior expresses specific, definite information about a variable. An example is a prior distribution for the temperature at noon tomorrow. A reasonable approach is to make the prior a normal distribution with expected value equal to today's noontime temperature, with variance equal to the day-to-day variance of atmospheric temperature. This example has a property in common with many priors, namely, that the posterior from one problem (today's temperature) becomes the prior for another problem (tomorrow's temperatu ...

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Prior probability, Prior probability - Prior probability distribution, Prior probability - Informative priors, Prior probability - Uninformative priors, Prior probability - Improper priors

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If an estimator of a parameter, , attains e(T) = 1 for all values of the parameter, then the estimator is called efficient. Equivalently, the estimator attains the equality on the Cramér-Rao inequality . Furthermore, an efficient estimator that is unbiased is also a minimum variance unbiased estimator. This is because an efficient estimator maintains equality on the Cramér-Rao inequality for all parameter values, which means it attains the minimum variance for all parameters (the def ...

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Efficiency statistics, Efficiency statistics - Efficient estimator, Efficiency statistics - Asymptotic efficiency, Efficiency statistics - Examples, Efficiency statistics - Relative efficiency

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  Ecological effects of biodiversity - Human Mediated Loss of Species.   It has become clear in recent years that we live on a human dominated earth. Ever growing human populations have caused ever increasing land and resource use. Human enterprises such as agriculture, industry, recreation, and international commerce have greatly affected land transformations, biotic additions and losses in the form of hunting, fishing, and invasions, and global biochemistry. These have in turn affected both clim ...

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Ecological effects of biodiversity, Ecological effects of biodiversity - CONTEXT AND MOTIVATION, Ecological effects of biodiversity - Human Mediated Loss of Species, Ecological effects of biodiversity - Definitions of Diversity Productivity and Stability, Ecological effects of biodiversity - Productivity and Stability as Indicators of Ecosystem Health, Ecological effects of biodiversity - Does Biodiversity Have Value?, Ecological effects of biodiversity - EFFECTS OF DIVERSITY ON COMMUNITY PRODUCTIVITY, Ecological effects of biodiversity - How Species Diversity May Influence Productivity, Ecological effects of biodiversity - Review of Data, Ecological effects of biodiversity - Implications for Ecology/Future Research, Ecological effects of biodiversity - EFFECTS OF DIVERSITY ON COMMUNITY STABILITY, Ecological effects of biodiversity - How Species Diversity may Influence Community Stability, Ecological effects of biodiversity - Review of Temporal Stability Data, Ecological effects of biodiversity - Review of Resistance/Resilience Stability Data, Ecological effects of biodiversity - Implications for Ecology/Future Research, Ecological effects of biodiversity - THEORY AND PRELIMINARY RESULTS FROM EXAMINING FOOD WEBS, Ecological effects of biodiversity - CONCLUSIONS

Read more here: » Ecological effects of biodiversity: Encyclopedia II - Ecological effects of biodiversity - CONTEXT AND MOTIVATION

Among many applications, we consider here one of broad theoretical and practical importance. Given a parametrized family of probability density functions where θ is the parameter (in the case of discrete distributions, the probability density functions are probability "mass" functions) the likelihood function is where x is the observed outcome of an experiment. In other words, when f(x | θ) is viewed as a function of x with θ fixed, it is a probability density function, an ...

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Likelihood function, Likelihood function - Concentrated likelihood, Likelihood function - Historical remarks, Likelihood function - Likelihood function of a parametrized model, Likelihood function - Example, Likelihood function - Notes

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For a likelihood function of more than one parameter, it is sometimes possible to write some parameters as functions of other parameters, thereby reducing the number of independent parameters. (The function is the parameter value which maximises the likelihood given the value of the other parameters.) This procedure is called concentration of the parameters and results in the concentrated likelihood function. For example, consider a regression analysis model with normally distributed errors. The most likely value of the error variance ...

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Likelihood function, Likelihood function - Concentrated likelihood, Likelihood function - Historical remarks, Likelihood function - Likelihood function of a parametrized model, Likelihood function - Example, Likelihood function - Notes

Read more here: » Likelihood function: Encyclopedia II - Likelihood function - Concentrated likelihood

  Ecological effects of biodiversity - How Species Diversity may Influence Community Stability.   Averaging Effect – If all species have differential responses to changes in the ecosystem over time, then the averaging of these responses will cause a more temporally stable ecosystem if more species are in the ecosystem (See also:

Ecological effects of biodiversity, Ecological effects of biodiversity - CONTEXT AND MOTIVATION, Ecological effects of biodiversity - Human Mediated Loss of Species, Ecological effects of biodiversity - Definitions of Diversity Productivity and Stability, Ecological effects of biodiversity - Productivity and Stability as Indicators of Ecosystem Health, Ecological effects of biodiversity - Does Biodiversity Have Value?, Ecological effects of biodiversity - EFFECTS OF DIVERSITY ON COMMUNITY PRODUCTIVITY, Ecological effects of biodiversity - How Species Diversity May Influence Productivity, Ecological effects of biodiversity - Review of Data, Ecological effects of biodiversity - Implications for Ecology/Future Research, Ecological effects of biodiversity - EFFECTS OF DIVERSITY ON COMMUNITY STABILITY, Ecological effects of biodiversity - How Species Diversity may Influence Community Stability, Ecological effects of biodiversity - Review of Temporal Stability Data, Ecological effects of biodiversity - Review of Resistance/Resilience Stability Data, Ecological effects of biodiversity - Implications for Ecology/Future Research, Ecological effects of biodiversity - THEORY AND PRELIMINARY RESULTS FROM EXAMINING FOOD WEBS, Ecological effects of biodiversity - CONCLUSIONS

Read more here: » Ecological effects of biodiversity: Encyclopedia II - Ecological effects of biodiversity - EFFECTS OF DIVERSITY ON COMMUNITY STABILITY

  One major problem with both the diversity-productivity and diversity-stability debates discussed up to this point is that both focus on interactions at just a single trophic level. That is, they are concerned with only one level of the food web, namely plants. Other research, unconcerned with the effects of diversity, has demonstrated strong top-down forcing of ecosystems (see keystone species). There is very little actual data available regarding the effects of different food webs, but theory helps us in this area. Firs ...

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Ecological effects of biodiversity, Ecological effects of biodiversity - CONTEXT AND MOTIVATION, Ecological effects of biodiversity - Human Mediated Loss of Species, Ecological effects of biodiversity - Definitions of Diversity Productivity and Stability, Ecological effects of biodiversity - Productivity and Stability as Indicators of Ecosystem Health, Ecological effects of biodiversity - Does Biodiversity Have Value?, Ecological effects of biodiversity - EFFECTS OF DIVERSITY ON COMMUNITY PRODUCTIVITY, Ecological effects of biodiversity - How Species Diversity May Influence Productivity, Ecological effects of biodiversity - Review of Data, Ecological effects of biodiversity - Implications for Ecology/Future Research, Ecological effects of biodiversity - EFFECTS OF DIVERSITY ON COMMUNITY STABILITY, Ecological effects of biodiversity - How Species Diversity may Influence Community Stability, Ecological effects of biodiversity - Review of Temporal Stability Data, Ecological effects of biodiversity - Review of Resistance/Resilience Stability Data, Ecological effects of biodiversity - Implications for Ecology/Future Research, Ecological effects of biodiversity - THEORY AND PRELIMINARY RESULTS FROM EXAMINING FOOD WEBS, Ecological effects of biodiversity - CONCLUSIONS

Read more here: » Ecological effects of biodiversity: Encyclopedia II - Ecological effects of biodiversity - THEORY AND PRELIMINARY RESULTS FROM EXAMINING FOOD WEBS

In Chile, grades from 1.0 up to 7.0 (with one decimal place) are used, where: 7.0 (excellent) is the best possible grade 6.0-6.9 (very good) 5.0-5.9 (good) 4.0-4.9 (sufficient); 4.0 is the lowest passing grade 1.0-3.9 (insufficient) are failing grades; 1.0 is the worst possible grade. Generally, it's a linear scale, with 1.0 meaning 0% achievement, 4.0 meaning 50% or 60% achievement (depending of the scale used), and 7.0 meaning 100% achievement. Rounding of averages is generally done to the second decimal; hence, a 3.95 is rounded up to a 4.0, ...

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Grade education, Grade education - Argentina, Grade education - Austria, Grade education - Belgium, Grade education - Central and Eastern Europe, Grade education - Chile, Grade education - Croatia, Grade education - Denmark, Grade education - Finland, Grade education - France, Grade education - Germany, Grade education - India, Grade education - International Baccalaureate, Grade education - Italy, Grade education - Iran, Grade education - The Netherlands, Grade education - Norway, Grade education - Peru, Grade education - Philippines, Grade education - Poland, Grade education - Portugal, Grade education - Russia, Grade education - United Kingdom, Grade education - Scotland, Grade education - England Wales and Northern Ireland, Grade education - Singapore, Grade education - Lower Primary Primary 1 to 3, Grade education - Upper Primary Primary 4 to 6, Grade education - Secondary Level for GCE O levels, Grade education - Junior College Level GCE A and AO levels, Grade education - Slovenia, Grade education - Sweden, Grade education - Switzerland, Grade education - Ukraine, Grade education - United States Canada Hong Kong Australia New Zealand, Grade education - Yugoslavia former, Grade education - Related Links

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The current Danish gradation scale is called the 13-scale consists of 10 grades ranging from 00 to 13, with 00 being the worst. The gaps between 00 & 03, 03 & 5 and 11 & 13 are there to signify a larger difference between those grades. The leading 0 in 00 and 03 are used to prevent fraud with grades. The highest grade 13 and the lowest grade ...

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Grade education, Grade education - Argentina, Grade education - Austria, Grade education - Belgium, Grade education - Central and Eastern Europe, Grade education - Chile, Grade education - Croatia, Grade education - Denmark, Grade education - Finland, Grade education - France, Grade education - Germany, Grade education - India, Grade education - International Baccalaureate, Grade education - Italy, Grade education - Iran, Grade education - The Netherlands, Grade education - Norway, Grade education - Peru, Grade education - Philippines, Grade education - Poland, Grade education - Portugal, Grade education - Russia, Grade education - United Kingdom, Grade education - Scotland, Grade education - England Wales and Northern Ireland, Grade education - Singapore, Grade education - Lower Primary Primary 1 to 3, Grade education - Upper Primary Primary 4 to 6, Grade education - Secondary Level for GCE O levels, Grade education - Junior College Level GCE A and AO levels, Grade education - Slovenia, Grade education - Sweden, Grade education - Switzerland, Grade education - Ukraine, Grade education - United States Canada Hong Kong Australia New Zealand, Grade education - Yugoslavia former, Grade education - Related Links

Read more here: » Grade education: Encyclopedia II - Grade education - Denmark

In Slovenia a five-point grading scale is used in elementary schools and high schools, where: 5 (excellent) is the best possible grade 4 (very good) 3 (good) 2 (sufficient) is the lowest passing grade 1 (insufficient) is the lowest possible grade, and the failing one. In universities a ten-point grading scale is used, where: 10 (excellent) is the best possible grade 9 (very good) 8 (very good) 7 (good) 6 (sufficient) is the lowest passing gradeSee also:

Grade education, Grade education - Argentina, Grade education - Austria, Grade education - Belgium, Grade education - Central and Eastern Europe, Grade education - Chile, Grade education - Croatia, Grade education - Denmark, Grade education - Finland, Grade education - France, Grade education - Germany, Grade education - India, Grade education - International Baccalaureate, Grade education - Italy, Grade education - Iran, Grade education - The Netherlands, Grade education - Norway, Grade education - Peru, Grade education - Philippines, Grade education - Poland, Grade education - Portugal, Grade education - Russia, Grade education - United Kingdom, Grade education - Scotland, Grade education - England Wales and Northern Ireland, Grade education - Singapore, Grade education - Lower Primary Primary 1 to 3, Grade education - Upper Primary Primary 4 to 6, Grade education - Secondary Level for GCE O levels, Grade education - Junior College Level GCE A and AO levels, Grade education - Slovenia, Grade education - Sweden, Grade education - Switzerland, Grade education - Ukraine, Grade education - United States Canada Hong Kong Australia New Zealand, Grade education - Yugoslavia former, Grade education - Related Links

Read more here: » Grade education: Encyclopedia II - Grade education - Slovenia