Can the variance of a portfolio be smaller than the variance of any individual stock?

The most important quality of portfolio variance is that its value is a weighted combination of the individual variances of each of the assets adjusted by their covariances. This means that the overall portfolio variance is lower than a simple weighted average of the individual variances of the stocks in the portfolio.

Can the minimum variance portfolio be the optimal risk portfolio?

Revisiting the Portfolio Optimization Machine. 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.

How the relationship between assets in a portfolio affects the portfolio risk?

Adding assets with a negative covariance to a portfolio reduces the overall risk. At first, this risk drops off quickly; as additional assets are added, it drops off slowly. Diversifiable risk cannot significantly be reduced beyond including 25 different stocks in a portfolio.

Why variance is not a good measure of risk?

Using variance as a risk measure has some deficiencies due to its symmetry property and inability to consider the risk of low probability events. If returns are not normally distributed and investors exhibit non-quadratic utility functions, alternative ways are needed to express the riskiness of an investment.

Can portfolio variance negative?

Should I just assume it’s zero? A negative variance is troublesome because one cannot take the square root (to estimate standard deviation) of a negative number without resorting to imaginary numbers.

What does minimum variance portfolio mean?

Minimum Variance Portfolio is the technical way of representing a low-risk portfolio. It carries low volatility as it correlates to your expected return (you’re not assuming greater risk than is necessary).

What does the minimum variance portfolio tell us?

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.

What does portfolio variance tell us?

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 does low variance mean in statistics?

A small variance indicates that the data points tend to be very close to the mean, and to each other. A high variance indicates that the data points are very spread out from the mean, and from one another. Variance is the average of the squared distances from each point to the mean.