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When he drastically modified the risk theory of financial markets, Markowitz reasoned in terms of a portfolio. A portfolio is a whole group of financial assets. Its overall profitability is the sum total of the return on each asset weighted in terms of the proportion represented by its value with regard to that of the entire portfolio. Portfolio profitability is the weighted average of returns on the securities included in it. Yet the risk incurred is another story entirely. A portfolio’s volatility is less than the average volatility of the securities from which it is constituted; that is why diversification is basically praiseworthy.
Markowitz’s singular contribution consisted in providing precise instruments to measure diversification. These instruments allow for the constitution of a portfolio supplying optimal returns for minimal risk; Markowitz terms this an efficient portfolio. No efficient portfolio is superior to any other. Each is simply the best in its category of risk; it offers the highest expectations of returns for a given risk. And in a rigorously equivalent manner, it offers minimal risk for a given expectation of returns. If an efficient portfolio offers comparatively higher returns, it must also present more risks.
Instances of random deviation have a tendency to cancel each other out in a portfolio. This is called diversification. There is an important parameter known as the correlation coefficient, whose role is to assess the benefits obtained through diversification. The correlation coefficient measures the degree of correlation between two variables. The greater their tendency to move in concert at the same time, the higher their correlation coefficient. The range of values this takes is between – 1 and + 1. If the phenomena are perfectly correlated, the coefficient is +1. If they are inversely correlated, the coefficient is – 1. If they are not correlated at all, the coefficient is equal to 0. As for two positively correlated shares, the periods of strong returns for the first correspond to the periods of strong performance for the second; the same for poor performance. When the shares are negatively correlated, underachievers accompany overachievers. When there is no correlation at all, A’s performance has nothing to do with B’s.
Diversification brings together two random variables that are not strictly correlated and thereby diminishes average risk. The interest of Markowitz’s theory basically consists in his having mathematically expressed the fact that the important parameter is the correlation coefficient and that what matters is to estimate correlations involving multiple phenomena.