One effective tool for investment advisors to determine the amount of diversification necessary for a portfolio is modern portfolio theory (MPT). MPT is used to determine an efficient frontier for portfolio optimization and uses diversification to achieve this goal. The efficient frontier provides a maximum return obtainable for a certain amount of risk taken.
MPT states that for a given portfolio of assets, there is an optimized combination of stocks and assets to provide the greatest return for a given level of risk. MPT uses diversification, asset allocation and periodic rebalancing to optimize portfolios. MPT was first created by Harry Markowitz in the 1950s, and he eventually won a Nobel Prize for it. Further innovation of MPT has added the calculation of Treasury bonds (Tbonds) and Treasury bills (Tbills) as a riskfree asset that shifts the efficient frontier.
Correlation
MPT uses the statistical measures of correlation to determine the relationship between assets in a portfolio. The correlation coefficient is a measure of the relationship between how two assets move together and is measured on a scale from 1 to +1. A correlation coefficient of 1 represents a perfect positive relationship whereby assets move together in the same direction to the same degree. A correlation coefficient of 1 represents a perfect negative correlation between two assets, meaning they move in opposite directions from each other.
The correlation coefficient is calculated by taking the covariance of the two assets divided by the product of the standard deviation of both assets. Correlation is essentially a statistical measure of diversification. Including assets in a portfolio that have negative correlation can help to reduce the overall volatility and risk for that mix of assets. (For related reading, see "How Can You Calculate Correlation Using Excel?")
Achieving Optimal Diversification to Reduce Unsystematic Risk
MPT shows that by combining more assets in a portfolio, diversification is increased while the standard deviation, or the volatility, of the portfolio is reduced. However, maximum diversification is achieved with around 30 stocks in a portfolio. After that point, including more assets adds a negligible amount of diversification. Diversification is useful for reducing unsystematic risk. Unsystematic risk is the risk associated with a certain stock or sector.
For example, each stock in a portfolio has risk associated with negative news impacting that stock. By diversifying into other stocks and sectors, the decline in one asset has less impact on the larger portfolio. However, diversification is unable to reduce systematic risk, which is that risk associated with the overall market. During times of high volatility, assets become more correlated and have a greater tendency to move in the same direction. Only more sophisticated hedging strategies can mitigate systematic risk.
There have been some criticisms of MPT over the years. One major criticism is that MPT assumes a Gaussian distribution of asset returns. Financial returns often do not follow symmetrical distributions such as the Gaussian distribution. MPT further assumes that the correlation between assets is static, when in reality the degree of correlation between assets can fluctuate. The efficient frontier is subject to shifts that MPT may not accurately represent.
(For related reading, see: "How to Diversify Your Portfolio Beyond Stocks.")

How is correlation used in modern portfolio theory?
Modern portfolio theory looks for correlation between expected returns and expected volatility of different investments. Read Answer >> 
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How are negative correlations used in risk management?
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