Markowitz model

In finance, a Markowitz framework ─ put forward by Harry Markowitz in 1952 ─ is a portfolio optimization model; it assists in the choice of the near efficient portfolio by analyzing various possible portfolios of the condition securities. Here, by choosing securities that earn not 'move' precisely together, the HM model shows investors how to reduce their risk. The HM model is also called mean-variance model due to the fact that this is the based on expected returns mean in addition to the standard deviation variance of the various portfolios. It is foundational to Modern portfolio theory.

Demerits of the HM model

1. Unless positivity constraints are assigned, the Markowitz total can easily find highly leveraged portfolios large long positions in a subset of investable assets financed by large short positions in another subset of assets[], but assumption their leveraged set the returns from such(a) a portfolio are extremely sensitive to small revise in the returns of the segment assets and can therefore be extremely 'dangerous'. Positivity constraints are easy to enforce and ready this problem, but whether the user wants to 'believe' in the robustness of the Markowitz approach, it would be nice if better-behaved solutions at the very least, positive weights were obtained in an unconstrained species when the set of investment assets isto the available investment opportunities the market portfolio – but this is often non the case.

2. virtually more vexing, small reorientate in inputs can administer rise to large changes in the portfolio. Mean-variance optimization suffers from 'error maximization': 'an algorithm that takes bit estimates of returns and covariances as inputs and treats them as if they were required with certainty will react to tiny return differences that are alive within measurement error'. In the real world, this degree of instability will lead, to begin with, to large transaction costs, but it is also likely to shake the confidence of the portfolio manager in the model.

3. The amount of information the covariance matrix, specifically, or a fix ].