Portfolio theory is used to maximize an investment's expected rate of return for a given level of risk, or minimize the level of risk for a given expected rate of return.
For the purpose of investing, risk is defined as the variation of the return from what was expected (volatility). It is represented by a measure such as standard deviation.
Diversification is used to reduce a portfolio's overall volatility. By building a portfolio out of many unrelated (uncorrelated) investments total volatility (risk) is minimized. The idea is that most assets will provide a return similar to their expected return and will offset those in the portfolio that perform poorly. The diversification ratio is the ratio of the standard deviation of an equally weighted portfolio to the standard deviation of a randomly selected security.
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