Minimum-variance frontier

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Minimum-variance frontier

Graph of the lowest possible portfolio variance that is attainable for a given portfolio expected return.

Minimum-Variance Frontier

In Markowitz portfolio theory, the frontier on a chart representing a portfolio with the least amount of volatility. That is, a minimum-variance frontier consists of data points representing stocks with a certain level of volatility and therefore risk, while the frontier represents a portfolio in which the volatilities of each individual stock offset each other. A minimum-variance frontier is also a Markowitz efficient frontier if it also represents the maximum level of return for its level of risk.
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Markowitz's minimum variance frontier and TEV frontier appear in Fig.
This section sets out various propositions, including one that shows that the curvature of the TEV frontier generated from a subset of n stocks matches the curvature of the minimum variance frontier generated from the same n stocks.
Nevertheless, the following proposition shows how the computation is equivalent to the curvature of the minimum variance frontier generated using the same subset of stocks.
The curvature of the TEV frontier generated from a subset of n stocks has the same curvature as the minimum variance frontier generated from the same subset of stocks (3).
The TEV frontier generated from a subset of n stocks (n < N) is a shift of the minimum variance frontier obtained from the same subset of stocks.
In other words, the partial tracking minimum variance frontier and the full tracking frontier are not parallel.
For nearly the entire spectrum of G values considered in the graph, the minimum variance frontier dominates the two frontiers generated with the monoobjective models: the TEV frontier and the frontier curvature.
The greater curvature of the minimum variance frontier implies that the distance between it and the multiobjective frontier grows rapidly when [absolute value of G] ncreases.
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