Covariance as a diversification tool
Covariance can increase diversification in the asset portfolio. Adding assets with negative covariance to the portfolio reduces the overall risk. Initially, these risks decrease rapidly; As additional assets are added, they slowly decrease. Diversified risk cannot be significantly reduced by more than 25 different shares in the portfolio. However, including more assets with negative covariance means that risk decreases more quickly.
Covariance has some limitations. While covariance can show
the trend between two assets, it cannot be used to calculate the strength of
the relationship between prices. Determining the coefficient of correlation
between assets is a better way to measure the strength of the relationship.
An additional disadvantage of using variance is that the
measurement is subject to skew due to the presence of outliers in the
underlying data. Thus, large price movements in one period may skew the general
volatility of the price chain and provide an unreliable statistical measure of
the nature of the trend among assets.
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Use of the modern portfolio theory of heterogeneity
Modern portfolio theory (MPT) uses covariance as an
important component in constructing portfolios. MPT assumes that investors are
risk averse yet still seek the best possible return. Thus MPT attempts to
define efficient limits for the mix of assets in the portfolio, or the optimum
point at which the risk-return relationship is most beneficial. Effective Limits
Calculates the maximum return for a portfolio against the amount of risk for
the underlying asset group. The goal is to create a group of assets with a
general standard deviation less than the standard deviation of individual
securities. The graph of the effective limits is curved, which shows how high
volatility assets can be mixed with low volatility assets to maximize return
but minimize the impact of large price fluctuations. By diversifying the assets
in the portfolio, investors can reduce risk while obtaining returns on their
investment.
Covariance is a statistical measure of how two assets move
in relation to each other. It provides diversification and reduces overall
portfolio volatility. A positive covariance indicates that two assets move in
tandem. Negative covariance indicates that two assets are moving in opposite
directions.
When creating the portfolio, it is important to try to
minimize overall risk and volatility while striving to achieve a positive rate
of return. Analysts use historical price data to determine which assets will be
included in the portfolio. By including assets that show negative covariance,
the overall volatility of the portfolio will be reduced.
The covariance between two specific assets is calculated
through an equation that includes returns to historical assets as independent
and dependent variables, plus the historical average of each individual asset
price over an equivalent number of trading periods for each asset. The formula
takes the daily return minus the average return for each asset, multiplied by
each other, and then divided by the number of trading periods for the
respective timeframes that have been measured.
