# Mean-variance analysis

## Mean-variance analysis

Evaluation of risky prospects based on the expected value and variance of possible outcomes.

## Mean-Variance Analysis

The process of portfolio selection that assumes that every rational investor, at a given level of risk, will accept only the largest expected return. More specifically, mean-variance analysis attempts to account for risk and expected return mathematically to help the investor find a portfolio with the maximum return for the minimum about of risk. A Markowitz efficient porfolio represents just that: the most expected return at a given amount of risk (sometimes excluding zero risk). Harry Markowitz first began developing this form of analysis in an article published in 1952 and received the Nobel prize for economics for his work in 1990. See also: Homogenous expectations assumption, Markowitz efficient set of portfolios.
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With the insight that traditional mean-variance analysis measures of risk are not sufficient for diversification during, for example, market crashes, the Ziembas demonstrate how investors fail to diversify enough, describe the incentives in both directions, unpack rewards and dangers, and analyze results of a range of potential outcomes.
Thus, we use mean-variance analysis to determine the optimal mix of stocks and bonds in a portfolio for a given holding period and compare the percentage of equities to that actually held in five popular target retirement funds: Fidelity, Principal, T.
According to EDHEC, this is a formidable challenge that severely exacerbates the dimensionality problem already present with mean-variance analysis.
Ritchken, 1985, "Enhancing Mean-Variance Analysis with Options", Journal of Portfolio Management, 11:67-71
In addition, mean-variance analysis treats financial wealth in isolation from income.
Mean-Variance Analysis in Portfolio Choice and Capital Markets, New York: Basil Blackwell.
The results of mean-variance analysis are often presented in the context of the efficient frontier, which shows expected portfolio return as a strict function of risk (Figure 1).
We find that, contrary to recent Government policy and the results from a simple mean-variance analysis, the welfare-maximising policy requires that all public debt be denominated in foreign currency.
However, the usefulness of mean-variance analysis as a computable approximation to full EU analysis was defended vigorously, especially by Tobin (1969) (see Borch (1969), Feldstein (1969) and Tobin (1969)).
Furlong, 1990, "A Reexamination of Mean-Variance Analysis of Bank Capital Regulation", Journal of Banking and Finance, 14:69-84
Thanks to the property that a linear transformation of ellipticals of the same family is still elliptical of the same family, the mean-variance analysis can be generalized to non-normal, fat-tailed portfolios.

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