What is mean-variance portfolio optimization?

A mean-variance analysis is a tool that investors use to help spread risk in their portfolio. In it the investor measures an asset’s risk, expressed as the “variance,” then compares that with the asset’s likely return. The goal of mean-variance optimization is to maximize an investment’s reward based on its risk.

What does the variance of a portfolio mean?

Portfolio variance is a measure of the dispersion of returns of a portfolio. It is the aggregate of the actual returns of a given portfolio over a set period of time. Portfolio variance is calculated using the standard deviation of each security in the portfolio and the correlation between securities in the portfolio.

What is maximum diversification?

The Maximum Diversification (MD) portfolio, introduced by Choueifaty and Coignard (2008), aims to maximise a metric which defines the degree of portfolio diversification and thereby create portfo- lios which have minimally correlated assets, lower risk levels and higher returns than other, “tradi- tional” portfolio …

What is minimum variance frontier?

Graph of the lowest possible portfolio variance that is attainable for a given portfolio expected return.

What is mean-variance rule?

Mean-Variance Analysis is a technique that investors use to make decisions about financial instruments to invest in, based on the amount of risk that they are willing to accept (risk tolerance). This theory is based on the assumption that investors make rational decisions when they possess sufficient information.

Why is the minimum variance portfolio important?

A minimum variance portfolio is one that maximizes performance while minimizing risk. It can hold investment types that are volatile on their own, but when combined, create a diversified portfolio with lower volatility than any of the parts.

Is minimum variance portfolio the optimal portfolio?

Minimum variance weighted portfolios are optimal if all investments have the same expected return, while Maximum Diversification weighted portfolios are optimal if investments have the same Sharpe ratios.

What is maximum diversification portfolio?

Thus, the maximum diversification portfolio is the tangent (highest Sharpe ratio) portfolio on the efficient frontier, if average asset returns increase proportionally with risk.

What is the most diversified portfolio?

You receive the highest return for the lowest risk with a diversified portfolio. For the most diversification, include a mixture of stocks, fixed income, and commodities. Diversification works because the assets don’t correlate with each other.

How do you interpret a minimum variance portfolio?

Definition: A minimum variance portfolio indicates a well-diversified portfolio that consists of individually risky assets, which are hedged when traded together, resulting in the lowest possible risk for the rate of expected return.

Are minimum variance and maximum diversification portfolios mean-variance efficient?

Both the Minimum Variance and Maximum Diversification portfolios are mean-variance efficient under intuitive assumptions. Minimum Variance is efficient if assets have similar returns while Maximum Diversification is efficient if assets have similar Sharpe ratios.

Should you switch to a minimum variance portfolio near retirement?

Because there’s an infinite number of security combinations producing varying levels of return, the efficient frontier represents the best of those combinations. One school of thought suggests investors pivot from an efficient portfolio to a minimum variance portfolio as they near retirement.

Can covariance knowledge be leveraged to construct minimum variance portfolios?

If expected return is hard to measure, covariance knowledge can be leveraged to construct minimum variance or risk parity portfolios. If we have no knowledge at all about the market, a naive equal-weighting portfolio will be a default option, which is also served as benchmark in our backtest.

Does the maximum diversification optimization substitute asset volatilities for returns?

Consistent with the view that returns are directly proportional to volatility, the Maximum Diversification optimization substitutes asset volatilities for returns in a maximum Sharpe ratio optimization, taking the following form. where σ and Σ reference a vector of volatilities, and the covariance matrix, respectively.