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Computerized Investing > Third Quarter 2012

Portfolio Optimization Program Finds Efficient Frontier

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by Joe Lan, CFA

Modern portfolio theory (MPT) attempts to use relationships between securities to maximize the return obtainable for a given amount of risk. The theory is based on the premise that through diversification, it is possible to achieve a combination of assets that has a lower risk than any of the individual assets. The theory states that for each portfolio of stocks, an efficient frontier exists that contains combinations of stocks within the portfolio that provide the highest return for a given level of risk, or the lowest risk for a given return.

It is fairly simple to conceptualize how a collection of holdings can have lower risk than any individual holding. Consider an overly simplified example of two assets that are perfectly negatively correlated (e.g., as one variable increases, the other decreases by the same amount). In this case, the two assets when held together provide some weighted return but their collective risk, measured by volatility, is zero. Due to their perfectly negative correlation, when one asset appreciates, the other will depreciate by the same amount.

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