Markowitz_bullet - Modern Portfolio Theory
Plotting Markowitz bullets and an efficient frontier for a given Portfolio of Equity and devising the Weights for the portfolio with maximum Sharpe ratio.
Modern portfolio theory (MPT), or mean-variance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk. It is a formalization and extension of diversification in investing, the idea that owning different kinds of financial assets is less risky than owning only one type.
Graph shows expected return (vertical) versus standard deviation called the 'risk-expected return space.' Every possible combination of risky assets, can be plotted in this risk-expected return space, and the collection of all such possible portfolios defines a region in this space.
The upper part of the parabolic boundary is the efficient frontier in the absence of a risk-free asset (sometimes called "the Markowitz bullet"). Combinations along this upper edge represent portfolios (including no holdings of the risk-free asset) for which there is lowest risk for a given level of expected return.
Equivalently, a portfolio lying on the efficient frontier represents the combination offering the best possible expected return for given risk level.