Is the size of the covariance larger than the absolute value?

Absolute value. The larger it is, the more random the variable is.

The smaller the independence of , the greater the covariance of the absolute value if the interrelationships of the random variables are not taken into account.

The larger. If two variables change in opposite directions, one of them is greater than its own expected value.

If the other is less than its expected value, then the covariance between the two variables is negative.

Covariance represents the overall error of two variables, unlike variance, which represents the error of only one variable. If the two variables have the same trend, that is, if one of them is greater than its expected value, and the other is greater than its expected value, then the covariance between the two variables is positive.

Properties: If two random variables x and y are independent of each other, then e[(x-e(x))(y-e(y))]=0, so if the above mathematical expectation.

If they are not zero, then x and y must not be independent of each other, that is, there is a certain relationship between them.

There is a relationship between covariance and variance as follows:

d(x+y)=d(x)+d(y)+2cov(x,y)d(x-y)=d(x)+d(y)-2cov(x,y) The covariance is related to the expected value as follows:

cov(x,y) = e(xy)-e(x)e(y) properties of covariance:

1）cov(x，y)=cov(y，x)

2) CoV(ax,by)=abcov(x,y),(a,b is constant)3)CoV(x1+x2,y)=cov(x1,y)+cov(x2,y) is defined by the covariance, it can be seen that cov(x,x)=d(x), cov(y,y)=d(y).

Covariance reflects the relationship between two variables.

What you are referring to here is the relationship between the changes in risk between the two investment methods.

When the covariance is positive, the risk of the two investment methods is in the same direction, that is, the risk of one investment method increases and decreases, and the risk of the other investment method also increases and decreases.

When the covariance is negative, the risk of the two investment methods is reversed, that is, the risk of one investment method increases and decreases, and the risk of the other investment method decreases and increases.

When the covariance is zero, there is no mutual influence between the risks of the two investment styles.

Moreover, the greater the covariance, the stronger the strength of the relationship, and the more obvious the synergy of the risk intensity in the same direction or in the opposite direction, and the less obvious the vice versa.

Therefore, the covariance you are talking about here is small, indicating that the impact of risk changes between two or several investment methods is not very important, and such a portfolio can reduce or even eliminate unsystematic risk (the risk caused by a special factor, which is not systematically and comprehensively connected with the entire market, but only has an impact on individual or a small number of returns).

The covariance has a plus or minus sign, so the plus or minus sign represents the direction of the interrelationship between the two sets of random variables.

In addition, the absolute value of the covariance represents the strength of the relationship between the two sets of random variables. The larger the absolute value, the less independent the two groups of random variables, or the stronger their correlation with each other.

Therefore, if the covariance size comparison does not consider the direction of the relationship between the two groups of random variables, it can be said that the absolute value is larger.

Covariance and variance are both commonly used concepts in statistics to measure the relationship between random variables and the degree to which variables are discrete.

Variance is a measure of how discrete a random variable is. For a random variable x, its variance represents the degree of dispersion between the observed value and its mean. The variance is calculated as:

var（x）=e[（x-e[x]）²

where var(x) is the variance of the random variable x, e[x] is the expected (mean) of x, and e[.].] indicates to take expectations.

Covariance is a measure of the correlation between two random variables. For the two random variables x and y, their covariance indicates the degree to which the observed values of x and y deviate from their respective means and the relationship between x and y. The covariance is calculated as:

cov（x，y）=e[（x-e[x]）*y-e[y]）]

where cov(x,y) represents the covariance of x and y, e[x] and e[y] represent the expectation (mean) of x and y, respectively, e[.] indicates to take expectations.

There is a certain relationship between covariance and variance. If we consider the covariance of a random variable x and itself, i.e., cov(x,x), this is equivalent to the variance of x. This is because variance measures the distance between a random variable and its mean, while covariance contains a measure of the distance between the means of two variables, and when the two variables are the same, the mean is equal, so the covariance is equal to the variance.

In summary, variance and covariance are used to describe the degree of dispersion of variables and the relationships between variables. Variance is a measure of how much a single variable is discrete, and covariance is a measure of the correlation and dispersion between two variables. In certain cases, the covariance can also be equated to the variance, i.e., the covariance of a single variable and the self-proclaimed bureau is equal to the variance.