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Markowitz Portfolio Example

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In the March, 1952, issue of Journal of Finance, Harry M. Markowitz published an article titled Portfolio Selection. In the article, he demonstartes how to reduce the risk of asset portfolios by selecting assets whose values aren't highly correlated. At the same time, he laid down some basic principles for establishing an advantageous relationship between risk and return. This has come to be known as diversification of assets. In other words, don't put all your eggs in one basket.

A key to understanding the Markowitz model is to be comfortable with the statistic known as the variance of a portfolio. Mathematically, the variance of a portfolio is:

Variance is a measure of the expected fluctuation in return--the higher the variance, the riskier the investment. The covariance is a measure of the correlation of return fluctuations of one stock with the fluctuations of another. High covariance indicates an increase in one stock's return is likely to correspond to an increase in the other. A covariance close to zero means the return rates are relatively independent. A negative covariance means that an increase in one stock's return is likely to correspond to a decrease in the other.

The Markowitz model seeks to minimize a portfolio's variance, while meeting a desired level of overall expected return. In this model, you're considering investing in three stocks. From historical data, you have clculated an expected return, the variance of the return rate, and the covariance of the return between the different stocks. You want to reduce variability, or risk, by spreading your investment wisely amongst the three stocks. You have a target growth rate of 12 percent. As an additional safety feature, you decide to invest no more than 75 percent in any single asset.


Financial | Portfolio | Stocks | Markowitz |