牧龙在野!

Prospect theory is a theory that describes decisions between alternatives that involve risk, i.e. alternatives with uncertain outcomes, where the probabilities are known. The model is descriptive: it tries to model real-life choices, rather than optimal decisions.

这个理论很有趣的一点是：人们对金钱上的收入和损失的心里感受是完全不平均的。当你得到一点点的时候，你满足感会上升的很快，以至于你持续得到很多钱以后，你的满足感反而上升的变慢了；当你失去一点钱的时候，你很痛苦，但是随着你失去的越来越多，你反而不会像以前那么痛苦了。

                                      

In probability theory, Bayes' theorem (often called Bayes' Law) relates the conditional and marginal probabilities of two random events. It is often used to compute posterior probabilities given observations. For example, a patient may be observed to have certain symptoms. Bayes' theorem can be used to compute the probability that a proposed diagnosis is correct, given that observation. (See example 2)

As a formal theorem, Bayes' theorem is valid in all interpretations of probability. However, it plays a central role in the debate around the foundations of statistics: frequentist and Bayesian interpretations disagree about the ways in which probabilities should be assigned in applications. Frequentists assign probabilities to random events according to their frequencies of occurrence or to subsets of populations as proportions of the whole, while Bayesians describe probabilities in terms of beliefs and degrees of uncertainty. The articles on Bayesian probability and frequentist probability discuss these debates at greater length.

Variance = Standard deviation Squared


In finance, standard deviation is a representation of the risk associated with a given security (stocks, bonds, property, etc.), or the risk of a portfolio of securities. Risk is an important factor in determining how to efficiently manage a portfolio of investments because it determines the variation in returns on the asset and/or portfolio and gives investors a mathematical basis for investment decisions. The overall concept of risk is that as it increases, the expected return on the asset will increase as a result of the risk premium earned – in other words, investors should expect a higher return on an investment when said investment carries a higher level of risk.

For example, you have a choice between two stocks: Stock A historically returns 5% with a standard deviation of 10%, while Stock B returns 6% and carries a standard deviation of 20%. On the basis of risk and return, an investor may decide that Stock A is the better choice, because Stock B's additional percentage point of return generated (an additional 20% in dollar terms) is not worth double the degree of risk associated with Stock A. Stock B is likely to fall short of the initial investment more often than Stock A under the same circumstances, and will return only one percentage point more on average. In this example, Stock A has the potential to earn 10% more than the expected return, but is equally likely to earn 10% less than the expected return.

Calculating the average return (or arithmetic mean) of a security over a given number of periods will generate an expected return on the asset. For each period, subtracting the expected return from the actual return results in the variance. Square the variance in each period to find the effect of the result on the overall risk of the asset. The larger the variance in a period, the greater risk the security carries. Taking the average of the squared variances results in the measurement of overall units of risk associated with the asset. Finding the square root of this variance will result in the standard deviation of the investment tool in question. Use this measurement, combined with the average return on the security, as a basis for comparing securities.

From: http://en.wikipedia.org/wiki/Standard_deviation

Topic Related:

Variance

Beta

Variance, Beta and Risk 对我来说，是比较容易混淆的概念，需要熟读的~


In probability theory and statistics, the variance of a random variable, probability distribution, or sample is one measure of statistical dispersion, averaging the squared distance of its possible values from the expected value(mean). Whereas the mean is a way to describe the location of adistribution, the variance is a way to capture its scale or degree ofbeing spread out. The unit of variance is the square of the unit of the original variable. The positive square root of the variance, called the standard deviation, has the same units as the original variable and can be easier to interpret for this reason.The variance of a real-valued random variable is its second central moment, and it also happens to be its second cumulant.Just as some distributions do not have a mean, some do not have avariance as well. The mean exists whenever the variance exists, but notvice versa.