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Explain the Modern portfolio theory

Explain the Modern portfolio theory.

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In the Modern Portfolio Theory world of N assets there are 2N + N(N − 1)/2 parameters: standard deviation, one per stock; expected return, one per stock; correlations, among any two stocks (select two from N without replacement, order unimportant). To Markowitz all investments and all portfolios should be compared and contrasted through a plot of expected return versus risk that measured by standard deviation. When we write µA to shows the expected return from investment or portfolio A (and the same for B and C, etc.) and σB for its standard deviation after that investment/portfolio A is at least as fine as B if µA ≥ µB and σA ≤ σB.

The mathematics of risk and return is extremely simple. See a portfolio, Π, of N assets, along with Wi being the fraction of wealth invested into the ith asset. The expected return is subsequently

721_expected return.png

and the standard deviation of the return, therefore the risk is

1788_standard deviation.png

Here ρij is the correlation among the ith and jth investments, along with ρii = 1.

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