Negatively correlated assets

Negatively correlated assets with a positive expected return can provide a sigifincantly higher probability in the expected value.

To find negatively correlated returns, we need to look at the covariance between the returns of two assets. Covariance is a statistical measure that describes the relationship between two variables, in this case, the returns of two assets. It is calculated as the average of the product of the deviations of each variable from their respective means.

If the covariance between two assets is positive, it means that the returns of the two assets move in the same direction. If the covariance is negative, it means that the returns move in opposite directions. Therefore, a negative covariance indicates a negative correlation between the two assets.

The correlation coefficient, which is derived from the covariance, is a standardized measure of the correlation between two variables. It is a number between -1 and 1, where -1 indicates perfect negative correlation, 0 indicates no correlation, and 1 indicates perfect positive correlation.

To find negatively correlated assets with a positive expected return, we need to look for assets that have a negative correlation coefficient and a positive expected return. One way to do this is to use the concept of efficient portfolios. An efficient portfolio is a portfolio that has the highest expected return for a given level of risk or the lowest risk for a given level of expected return.

To construct an efficient portfolio with negatively correlated assets, we need to find assets that have low or negative covariance. We can then combine these assets in a portfolio in such a way that the overall covariance is minimized, resulting in a portfolio with lower risk and higher expected return.

To calculate the covariance between two assets, we can use the following formula:

Cov(X,Y) = (1/n) * ∑ [(Xi - X) * (Yi - Y)]

Where Cov(X,Y) is the covariance between assets X and Y, n is the number of observations, Xi and Yi are the returns of assets X and Y, and Xbar and Ybar are the means of the returns of assets X and Y, respectively.

Once we have the covariance between two assets, we can calculate the correlation coefficient using the following formula:

Corr(X,Y) = Cov(X,Y) / (σX * σY)

Where Corr(X,Y) is the correlation coefficient between assets X and Y, Cov(X,Y) is the covariance between assets X and Y, σX is the standard deviation of the returns of asset X, and σY is the standard deviation of the returns of asset Y.

By using these formulas, we can identify negatively correlated assets with a positive expected return and construct an efficient portfolio that maximizes returns while minimizing risk. However, it is important to note that correlation is not a constant, and it can change over time. Therefore, it is important to regularly monitor the correlation between assets in a portfolio and adjust the portfolio accordingly.

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