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Low-volatility investors aim to achieve market-like returns, but with lower risk. This investment style is also referred to as minimum volatility, minimum variance, managed volatility, smart beta, defensive and conservative investing.
If all the asset pairs have correlations of 0 — they are perfectly uncorrelated — the portfolio's return variance is the sum over all assets of the square of the fraction held in the asset times the asset's return variance (and the portfolio standard deviation is the square root of this sum).
In statistics a minimum-variance unbiased estimator (MVUE) or uniformly minimum-variance unbiased estimator (UMVUE) is an unbiased estimator that has lower variance than any other unbiased estimator for all possible values of the parameter.
A portfolio that gives maximum return for a given risk, or minimum risk for given return is an efficient portfolio. Thus, portfolios are selected as follows: (a) From the portfolios that have the same return, the investor will prefer the portfolio with lower risk, and [ 1 ]
Comparison of asset and risk allocations. Risk parity is a conceptual approach to investing which attempts to provide a lower risk and lower fee alternative to the traditional portfolio allocation of 60% in shares and 40% bonds which carries 90% of its risk in the stock portion of the portfolio (see illustration).
Portfolio optimization is the process of selecting an optimal portfolio (asset distribution), out of a set of considered portfolios, according to some objective.The objective typically maximizes factors such as expected return, and minimizes costs like financial risk, resulting in a multi-objective optimization problem.
To see two-fund separation in a context in which no risk-free asset is available, using matrix algebra, let be the variance of the portfolio return, let be the level of expected return on the portfolio that portfolio return variance is to be minimized contingent upon, let be the vector of expected returns on the available assets, let be the vector of amounts to be placed in the available ...
Capital market line. Capital market line (CML) is the tangent line drawn from the point of the risk-free asset to the feasible region for risky assets. The tangency point M represents the market portfolio, so named since all rational investors (minimum variance criterion) should hold their risky assets in the same proportions as their weights in the market portfolio.