## Mean, Variance and Covariance

The computation of mean, variance and covariance statistics allow portfolio managers to compare the return-risk characteristics and potential portfolio impact of underlying securities. These metrics are quantitatively determined and rely on historic price or return data. While we can compute the historic profile, this does not necessarily mean the relationship between assets, or their return-risk profile will remain the same in the future.

## Mean

Refer to the section on measures of return for detail on the computation of arithmetic and geometric returns. A mean return provides us an indication of the most likely return based on the historic returns delivered by the security.

## Variance

Variance is a measure of dispersion around the mean and is statistically defined as the average squared deviation from the mean. It is noted using the symbol ?². The standard deviation is the square root of the variance and is commonly referred to as the volatility of the asset.

## Covariance

Covariance is a measure of how closely two assets move together. Covariance is the product of the correlation between two assets and the standard deviation of those two assets. It is an important concept within the context of a portfolio as ideally, a portfolio should comprise of assets that are not perfectly correlated. A perfect correlation implies a correlation coefficient equal to +1 whereas perfect negative correlation returns a correlation coefficient of -1.

## Question

In a two-asset portfolio, which combination of assets would result in the most diversified portfolio?

A. Correlation coefficient = 0.75

B. Correlation coefficient = -0.2

C. Correlation coefficient = 0

Solution

The correct answer is B.

Within a two-asset portfolio, by combining negatively correlated assets, a diversified portfolio is produced and portfolio risk is lowered.

Reading 41 LOS 41c:

Calculate and interpret the mean, variance, and covariance (or correlation) of asset returns based on historical data

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