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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).
The amount of information (the covariance matrix, specifically, or a complete joint probability distribution among assets in the market portfolio) needed to compute a mean-variance optimal portfolio is often intractable and certainly has no room for subjective measurements ('views' about the returns of portfolios of subsets of investable assets ...
(A portfolio is mean-variance efficient if there is no portfolio that has a higher return and lower risk than those for the efficient portfolio. [1]) Mean-variance efficiency of the market portfolio is equivalent to the CAPM equation holding. This statement is a mathematical fact, requiring no model assumptions. Given a proxy for the market ...
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 ...
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.
Merton's portfolio problem is a problem in continuous-time finance and in particular intertemporal portfolio choice. An investor must choose how much to consume and must allocate their wealth between stocks and a risk-free asset so as to maximize expected utility .
Traditional portfolio rebalancing simply means returning your asset allocation to its original model. Imagine, for example, that you design a portfolio in line with your investment objectives that ...
In the case of adding investments, the portfolio's return is + + + instead of (/) + (/) +... + (/), and the variance of the portfolio return if the assets are uncorrelated is [+ + +] = + + + =, which is increasing in n rather than decreasing. Thus, for example, when an insurance company adds more and more uncorrelated policies to its portfolio ...