It is often supposed that investors do not like risk; they are convinced that the good surprises fail to compensate for the bad ones. They would consequently prefer the same returns while incurring a lower degree of risk.
The more the correlation coefficient is negative, the more one endeavors to diminish average risk by applying negatively correlated instruments. If the investor is indeed ‘‘risk-averse’’, he will make sure that the latter are as negatively correlated as is feasible. Then again, the mere fact that the financial instruments are not strictly correlated enables diversification to play an appreciable role.
The correlation of two financial instruments takes on a value between – 1 and + 1. The lower the correlation between a financial asset and a portfolio, the more the volatility of the latter is diminished once the former is added to the portfolio. If one adds securities that are negatively correlated with the portfolio, then the volatility of the latter will be very much diminished. If the new financial assets have no correlation with the portfolio (its coefficient correlation is 0), adding such a security will nonetheless reduce the volatility of the portfolio. Even with a positive correlation coefficient, provided that it is less than 1, adding a supplementary asset diminishes the risks incurred by a portfolio. If we limit ourselves to stock portfolios, studies show that maximal risk diversification is attained with at least 20 shares of firms operating in heterogeneous industrial sectors. Needless to say, if you specialize in stocks for skis, ice skates, fur jackets and 17 shares in industries related to cold weather, your portfolio will be poorly diversified notwithstanding your 20 shares! In contrast, you must try to introduce shares that are not positively correlated. It is also necessary for the probability distributions and the degrees of correlation between them to remain stable for a sizable length of time. The more we study long periods of time, the less reliable are the available statistics. How long is long enough? During calm spells studies by institutional investors analyze and survey the degrees of correlation that may exist between the different categories of financial assets: the stocks of large-scale groups, medium-sized companies, government bonds, corporate bonds, junk bonds, real estate, hedge funds and so on. One must remember that securities that are riskier than a portfolio when taken individually may, in spite of everything and provided that they are not correlated with the portfolio, reduce the overall risks of the latter.
Such factors help to explain the interest in international diversification; it can be expected that economic crises will not take place simultaneously in every country. This approach is supported by the observation that in each country, stocks evolve as a function of the ups and downs of the local economy. Money flows likewise introduce negative correlations between stock market performances and exchange rates. Lowering risk through international diversification largely compensates for the risk linked to exchange rates. Yet with the ongoing internationalization of the activities of quoted companies, the impact of purely local or national factors tends to diminish. A French economist, Bruno Solnik, has shown that for an internationally diversified firm, asset returns are determined to a significant extent by non-domestic (rather than domestic) factors. Moreover, the sensitivity of individual company returns to non-domestic factors is integrally linked to the scope of their international activities, as represented by the relative importance of foreign sales in relation to total sales.

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.