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Chapter 4 Variances and covariances

than might be anticipated If Y and Z are uncorrelated the covariance term drops out from the expression for the variance of their sum leaving var(Y+Z) = var(Y)+var(Z) Similarly if X 1;:::;X n are random variables for which cov(X i;X j) = 0 for each i6= jthen var(X 1 + + X n) = var(X 1) + + var(X n)

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Review of Mean Variance Standard Deviation Covariance and

Review of Mean Variance Standard Deviation Covariance and Correlation Coefficient Consider two stocks A and B Stock A is currently price at $10 per share and stock B at $25 per share For each tehre are four possibilities that may occur one year from now depending on how the economy performs over the next year along business cycles:

What is a covariance in finance?
Covariances have significant applications in finance and modern portfolio theory. For example, in the capital asset pricing model ( CAPM ), which is used to calculate the expected return of an asset, the covariance between a security and the market is used in the formula for one of the model's key variables, beta.
How do you calculate covariance?
Covariance is calculated by analyzing at-return surprises (standard deviations from the expected return) or multiplying the correlation between the two random variables by the standard deviation of each variable. Covariance is a statistical tool used to determine the relationship between the movements of two random variables.
Which stocks have positive covariance?
For example, if stock A's return moves higher whenever stock B's return moves higher, and the same relationship is found when each stock's return decreases, these stocks are said to have positive covariance. In finance, covariances are calculated to help diversify security holdings.
How does covariance measure the directional relationship between two assets?
This is usually expressed through a correlation coefficient, which can range from -1 to +1. While the covariance does measure the directional relationship between two assets, it does not show the strength of the relationship between the two assets; the coefficient of correlation is a more appropriate indicator of this strength.

What Is Covariance?

Covariance is a statistical measure of the directional relationship between two asset returns. Investors can use this measurement to understand the relationship between two stock returns. Formulas that calculate covariancecan predict how two stocks might perform relative to each other in the future. Applied to historical returns, covariance can hel

Covariance in Portfolio Management

Covariance applied to a portfoliocan help determine what assets to include in the portfolio. It measures whether stocks move in the same direction (a positive covariance) or in opposite directions (a negative covariance). When constructing a portfolio, a portfolio manager will select stocks that work well together. This usually means these stocks'

Calculating Covariance

Calculating a stock's covariance starts with finding a list of previous returns or "historical returns" as they are called on most quote pages. Typically, you use the closing pricefor each day to find the return. To begin the calculations, find the closing price for both stocks and build a list. For example: Next, calculate the average returnfor ea

Finding Covariance with Microsoft Excel

In MS Excel,you use one of the following functions to find the covariance: 1. = COVARIANCE.S() for a sample 2. = COVARIANCE.P() for a population You will need to set up the two lists of returns in vertical columns as in Table 1. Then, when prompted, select each column. In Excel, each list is called an "array," and two arrays should be inside the br

Uses of Covariance

Covariance can tell how the stocks move together, but to determine the strength of the relationship, look at their correlation. The correlation should, therefore, be used in conjunction with the covariance, and is represented by this equation: Correlation=ρ=cov(X,Y)σXσYwhere:cov(X,Y)=Covariance between X and YσX=Standard deviation of XσY=Standard d

The Bottom Line

Covariance is a common statistical calculation that can show how two stocks tend to move together. Investors can use it to lower their portfolio risk by selecting stocks that move in opposite directions. However, because covariance is calculated using historical returns, it can never provide complete certainty about the future. It should not be use

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What Is Covariance?

The fields of mathematics and statistics offer a great many tools to help us evaluate stocks. One of these is covariance, which is a statistical measure of the directional relationship between two asset returns. One may apply the concept of covariance to anything, but here the variables are stock returns. Formulas that calculate covariance can pred...

Calculating Covariance

Covariance in Microsoft Excel

In MS Excel,you use one of the following functions to find the covariance: 1. = COVARIANCE.S() for a sample1 2. = COVARIANCE.P() for a population2 You will need to set up the two lists of returns in vertical columns as in Table 1. Then, when prompted, select each column. In Excel, each list is called an "array," and two arrays should be inside the ...

Meaning

In the example, there is a positive covariance, so the two stocks tend to move together. When one stock has a positive return, the other tends to have a positive return as well. If the result were negative, then the two stocks would tend to have opposite returns—when one had a positive return, the other would have a negative return.

Example of Covariance

Covariance and correlation both primarily assess the relationship between variables. The closest analogy to the relationship between them is the relationship between the variance and standard deviation. Covariancemeasures the total variation of two random variables from their expected values. Using covariance, we can only gauge the direction of the...

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