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Home > Asset Management Checklists > Mean–Variance Optimization: A Primer

Asset Management Checklists

Mean–Variance Optimization: A Primer


Checklist Description

This checklist describes the principles of mean–variance optimization and how they are applied in investment.

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Definition

Mean–variance optimization (MVO) is a quantitative tool used to spread investment across different assets within a portfolio by assessing the trade-off between risk and return in order to maximize the return while minimizing any risks. The concept was devised by economist Harry M. Markowitz, who developed an algorithm to calculate optimized returns over a specified period. MVO is part of Markowitz’s modern portfolio theory (MPT), which assumes that investors will optimize their investment portfolios through diversifying their investments on a balanced risk–return basis. Markowitz’s concept of efficiency as laid out in MVO contributed to the development of the capital asset pricing model (CAPM).

The Markowitz algorithm relies on inputting three data sets on a graph: expected return per asset, standard deviation of each asset (a metric for risk), and the correlation between the two. Together these produce what Markowitz named the “efficient frontier,” or those assets expected to produce better returns than others that carry the same or fewer risks, and, conversely, a smaller risk than those expected to produce the same or a higher rate of return. Investors should ensure the three data sets, or inputs, represent their expectations of probability for the specified period, as well as include possible outcomes, each with a return per asset and probability of occurrence. The expected return, standard deviation, and correlations can then be calculated with standard statistical formulae.

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Advantages

  • Because MVO assumes that investors are risk-averse and will choose a less-risky investment among any assets that offer similar expected returns, it is a useful tool for identifying assets that have the most favorable risk–return profile.

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Disadvantages

  • MVO treats return as a future expectation and uses volatility as a proxy for risk, the flaw being that volatility is a historical parameter and you cannot assume that today’s prices provide an accurate forecast for the future.

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Action Checklist

  • Be aware of the risks of using only historical data for your inputs—you

  • may prefer to use your own estimates for a given asset’s future performance in the specified period.

  • Watch out for something called mean reversion. This occurs when an asset performs extremely well for a period and then performs spectacularly badly in the following period, or vice versa. If you have used historical data for your inputs, your outputs will indicate a strong (weak) future performance, but if mean reversion occurs, you will have results opposite to what you expected in the specified period.

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Dos and Don’ts

Do

  • Make careful decisions about which data sets to use as inputs.

  • Pay extra attention when calculating the expected returns, as your choices will determine the actual returns that you assign to each asset in the investment portfolio.

Don’t

  • Don’t assume that historical data are an accurate reflection of future performance.

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Further reading

Book:

  • Markowitz, Harry M. Portfolio Selection. 2nd ed. Malden, MA: Blackwell Publishers, 1991.

Article:

Website:

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