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# What is Minimum Variance Portfolio?

In a study done to link the variance with returns, it was found that both genres of portfolio construction measures – minimum volatility and low volatility – deliver market return more than the average. Their information ratios (IRs) also are not statistically significant. It was also found that both strategies let investors assume palpable risk, in relation to the market prices, for which investors were not compensated.

## Minimum Variance Portfolio (MVP)

The concept of Modern Portfolio Theory (MPT) has been the milestone for finance professionals for portfolio construction since Harry Markowitz introduced the idea into finance in 1952. Every finance student has now to learn the start and source of portfolio volatility, the good factors associated with diversification and the concept and ideas of the efficient frontier.

The portfolio comprised of risky assets at the initial point of the efficient frontier is known as the Minimum Variance Portfolio. It is not need to forecast an expected return to derive the MVP. It just needs an estimation of risk and the correlation for each of the risky assets. The MVP is generated by solving a quadratic equation, which uses the universe of all risky assets and produces the portfolio with the lowest volatility −

## Formula and Calculation of Portfolio Variance

The quality of portfolio variance and its value being weighted in combination of the individual variances of each of the assets adjusted by their covariances is an important factor for portfolio variance. This means that the net portfolio variance is lower than any simple weighted average of the singular variance.

The formula for portfolio variance in a two-asset portfolio is as follows −

$$\mathrm{Portfolio\:Variance = (π€_{1})^{2}(σ_{1})^{2} + (π€_{2})^{2}(σ_{2})^{2} + 2 π€_{1}π€_{2}\:Cov_{1,2}}$$

Where −

$π€_{1}$ = the portfolio weight of the first asset

$π€_{2}$ = the portfolio weight of the second asset

$σ_{1}$ = the standard deviation of the first asset

$σ_{2}$ = the standard deviation of the second asset

$Cov_{1,2}$ the covariance of the two assets, which can thus be expressed as $ρ_{(1,2)}σ_{1}σ_{2}$ where $ρ_{(1,2)}$ is the correlation coefficient between the two assets

In general, construction of investment portfolio is done with the Modern portfolio theory (MPT). MPT usually relies on the fact that serious investors need to maximize returns while also minimizing risk, which is sometimes measured using volatility. The investors actually seek what is called an efficient frontier, which means the lowest level of risk and volatility at which a required return can be achieved.

In MPT, risk is lowered by making a portfolio by investing in non-correlated assets. Assets that are risky individually can actually lower the total risk of the overall portfolio by making an investment that will go up when other investments drop. This artificial addition of reduced correlation can reduce the variance of a theoretical portfolio.

Therefore, the individual return on investment is less important than the overall contribution of each asset’s contribution to the portfolio, in terms of return, risk, and diversification.

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