{"id":7483,"date":"2022-03-20T20:02:50","date_gmt":"2022-03-20T19:02:50","guid":{"rendered":"https:\/\/www.simtrade.fr\/blog_simtrade\/?p=7483"},"modified":"2022-03-20T20:02:50","modified_gmt":"2022-03-20T19:02:50","slug":"implementing-markowitz-asset-allocation-model","status":"publish","type":"post","link":"https:\/\/www.simtrade.fr\/blog_simtrade\/implementing-markowitz-asset-allocation-model\/","title":{"rendered":"Implementing Markowitz asset allocation model"},"content":{"rendered":"

\"Youssef_Louraoui\"<\/a><\/p>\n

In this article, Youssef LOURAOUI<\/a> (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022) explains how to implement the Markowitz asset allocation model. This model is used to determine optimal asset portfolios based on the risk-return trade-off.<\/p>\n

This article follows the following structure: first, we introduce the Markowitz model. We then present the mathematical foundations of this model. We conclude with an explanation of the methodology to build the spreadsheet with the results obtained. You will find in this post an Excel spreadsheet which implements the Markowitz asset allocation model.<\/p>\n

Introduction<\/h2>\n

Markowitz’s work is widely regarded as a pioneer work in financial economics and corporate finance due to its theoretical foundations and applicability in the financial sector. Harry Markowitz received the Nobel Prize in 1990 for his contributions to these disciplines, which he outlined in his 1952 article “Portfolio Selection” published in The Journal of Finance<\/i>. His major work established the foundation for what is now commonly referred to as “Modern Portfolio Theory” (MPT).<\/p>\n

To find the portfolio’s minimal variance, the Markowitz model uses a constrained optimization strategy. The goal of the Markowitz model is to take into account the expected return and volatility of the assets in the investable universe to provide an optimal weight vector that indicates the best allocation for a given level of expected return or the best allocation for a given level of volatility. The expected return, volatility (standard deviation of expected return), and the variance-covariance matrix to reflect the co-movement of each asset in the overall portfolio design are the major inputs for this portfolio allocation model for an n-asset portfolio. We’ll go over how to use this complex method to find the best portfolio weights in the next sections.<\/p>\n

Mathematical foundations<\/h2>\n

The investment universe is composed of N assets characterized by their expected returns \u03bc and variance-covariance matrix V. For a given level of expected return \u03bcP<\/sub>, the Markowitz model gives the composition of the optimal portfolio. The vector of weights of the optimal portfolio is given by the following formula:<\/p>\n

\"img_SimTrade_implementing_Markowitz_1\"<\/a><\/p>\n

With the following notations:<\/p>\n