# 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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Conceptually, the mean-variance analysis links diversification with the notion of efficiency because optimal diversification is achieved along the EF (Markowitz 1987).
practical implementation of mean-variance analysis has proven problematic.
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.
Hakansson, "Multi-period mean-variance analysis: toward a general theory of portfolio choice," Journal of Finance, vol.
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. The paper presents an application of the improved estimators for higher order co-moment parameters, recently introduced by Martellini and Ziemann (2010), in the context of hedge fund portfolio optimisation.
Ritchken, 1985, "Enhancing Mean-Variance Analysis with Options", Journal of Portfolio Management, 11:67-71
Mean-variance analysis, developed almost 50 years ago by Harry Markowitz,  has provided a basic paradigm for portfolio choice.
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.
It emerged that mean-variance analysis is a special case of NM expected utility that will generate preference orderings consistent with EU (and NM axioms of rational behavior) under certain conditions: (1) when the utility function is quadratic; (2) when probabilities are compact (smaller and smaller risk) (Samuelson 1970); (3) when the payoffs of all lotteries or gambles are jointly normal such that any combination (portfolio) of lotteries will also generate payoffs that are normally distributed; and (4) when the location and scale (LS) condition is satisfied (Meyer 1987).
 The comments by Borch (1969) on uncertainty and indifference curves, the re-examination by Feldstein (1969) of mean-variance analysis in the theory of liquidity preference and portfolio selection, and the responses by Tobin to both Borch and Feldstein clarify the issues and take portfolio theory to a higher notch.

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