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A diversified portfolio will definetely minimise the risk but up to a certain level. After a certain level of diversification risk will not decrese but remains constant.
In1977 Elton and Gruber worked out an empirical example of the gains from diversification. Their approach was to consider a population of3290 securities available for possible inclusion in a portfolio, and to consider the average risk over all possible randomly chosen n-asset portfolios with equal amounts held in each included asset, for various values of n. Their results are summarized in the following table. It can be seen that most of the gains from diversification come for n≤30.
Number of Stocks in PortfolioAverage Standard Deviation of Annual Portfolio ReturnsRatio of Portfolio Standard Deviation to Standard Deviation of a Single Stock1 49.24% 1.00 2 37.36 0.76 4 29.69 0.60 6 26.64 0.54 8 24.98 0.51 10 23.93 0.49 20 21.68 0.44 30 20.87 0.42 40 20.46 0.42 50 20.20 0.41 400 19.29 0.39 500 19.27 0.39 1000 19.21 0.39
i only write one thing lower the correlation higher the diversification higher the correlation higher the risk.
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