Explain the Modern portfolio theory

Question

Explain the Modern portfolio theory.

Answer 1

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

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

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