Markowitz now divides his time between teaching (he is an adjunct professor at the Rady School of Management at the University of California at San Diego, UCSD); video casting lectures; and consulting (out of his Harry Markowitz Company offices). He currently serves on the Advisory Board of BPV Capital Management (formerly SkyView Investment Advisors), an alternative investment advisory firm and fund of hedge funds. Markowitz also serves on the Investment Committee of LWI Financial Inc. ("Loring Ward"), a San Jose, California-based investment advisor; on the advisory panel of Robert D. Arnott's Newport Beach, California based investment management firm, Research Affiliates; on the Advisory Board of Mark Hebner's Irvine, California and internet based investment advisory firm, Index Fund Advisors; and as an advisor to the Investment Committee of 1st Global, a Dallas, Texas-based wealth management and investment advisory firm. Markowitz advises and serves on the board of ProbabilityManagement.org, a 501(c)(3) non-profit founded by Dr. Sam L. Savage to reshape the communication and calculation of uncertainty.

Harry Markowitz put forward this model in 1952. It assists in the selection of the most efficient by analyzing various possible portfolios of the given securities. By choosing securities that do not 'move' exactly 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 it is based on expected returns (mean) and the standard deviation (variance) of the various portfolios. Harry Markowitz made the following assumptions while developing the HM model:

The company that would become CACI International was founded by Herb Karr and Harry Markowitz on July 17, 1962 as California Analysis Center, Inc. They helped develop SIMSCRIPT, the first simulation programming language, at RAND and after it was released to the public domain, CACI was founded to provide support and training for SIMSCRIPT.

In 1968, Markowitz joined Arbitrage Management company founded by Michael Goodkin. Working with Paul Samuelson and Robert Merton he created a hedge fund that represents the first known attempt at computerized arbitrage trading. He took over as chief executive in 1970. After a successful run as a private hedge fund, AMC was sold to Stuart & Co. in 1971. A year later, Markowitz left the company.

Markowitz won the Nobel Memorial Prize in Economic Sciences in 1990 while a professor of Finance at Baruch College of the City University of New York. In the preceding year, he received the John von Neumann Theory Prize from the Operations Research Society of America (now Institute for Operations Research and the Management Sciences, INFORMS) for his contributions in the theory of three fields: portfolio theory; sparse matrix methods; and simulation language programming (SIMSCRIPT). Sparse matrix methods are now widely used to solve very large systems of simultaneous equations whose coefficients are mostly zero. SIMSCRIPT has been widely used to program computer simulations of Manufacturing, transportation, and computer systems as well as war games. SIMSCRIPT (I) included the Buddy memory allocation method, which was also developed by Markowitz.

2. Practically more vexing, small changes in inputs can give rise to large changes in the portfolio. Mean-variance optimization has been dubbed an 'error maximization' device (Scherer 2002): 'an algorithm that takes point estimates (of returns and covariances) as inputs and treats them as if they were known with certainty will react to tiny return differences that are well 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.

1. Unless positivity constraints are assigned, the Markowitz solution 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 given their leveraged nature the returns from such a portfolio are extremely sensitive to small changes in the returns of the constituent assets and can therefore be extremely 'dangerous'. Positivity constraints are easy to enforce and fix this Problem, but if 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 manner when the set of investment assets is close to the available investment opportunities (the market portfolio) – but this is often not the case.

For selection of the optimal portfolio or the best portfolio, the risk-return preferences are analyzed. An investor who is highly risk averse will hold a portfolio on the lower left hand of the frontier, and an investor who isn’t too risk averse will choose a portfolio on the upper portion of the frontier.