Co-Variance

Examples of Co-Variance in the following topics:

• Portfolio Risk

  • In order to calculate the variance of a portfolio of three assets, we need to know that figure for apples, bananas, and cherries, and we also need to know the co-variance of each.
  • Co-variances can be thought of as correlations.
  • If every time bananas have a bad day, so do apples, their co-variance will be large.
  • If bananas do great half of the time when cherries do bad and bananas do terrible the other half, their co-variance is zero.
  • The formula to compute the co-variance between returns on X and Y:

• Regression Analysis for Forecast Improvement

  • The errors are uncorrelated, that is, the variance– co-variance matrix of the errors is diagonal, and each non-zero element is the variance of the error.
  • The variance of the error is constant across observations (homoscedasticity).

• Implications for Variance

  • A diversified portfolio containing investments with small or negative correlation coefficients will have a lower variance than a single asset portfolio.
  • Although risk is reduced as long as correlations are not perfect, it is typically forecast (wholly or in part) based on statistical relationships (like correlation and variance) that existed over some past period.
  • A diversified portfolio containing investments with small or negative correlation coefficients will have a lower variance than a similar portfolio of one asset type.
  • This is why it's possible to reduce variance without compromising expected return by diversifying.
  • Diversifying asset classes can reduce portfolio variance without diminishing expected return

• Variance

  • In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out.
  • This table shows how to calculate the variance of an investment outcome .
  • You may not need to calculate variance yourself, but you should still notice how we got it.
  • We get the variance from adding up the numbers in the orange column.
  • Calculating variance is a 3 step process once expected return has been calculated.

• Approaches to Assessing Risk

  • From the average cost per employee over time, or cost accrual ratio, a project manager can estimate: the cost associated with the risk, if it arises, estimated by multiplying employee costs per unit time by the estimated time lost (cost impact, C where C = cost accrual ratio * S), the probable increase in time associated with a risk (schedule variance due to risk, Rs where Rs = Probability * S).
  • This is intended to cause the greatest risks to the project to be attempted first so that risk is minimized as quickly as possible.This can be slightly misleading as schedule variances with a large P (probability) and small S (estimated time lost) and vice versa are not equivalent.
  • The probable increase in cost associated with a risk (cost variance due to risk, Rc where Rc = P*C = P*Cost Accrual Ratio*S = P*S*CAR): sorting on this value puts the highest risks to the budget first, which can raise concerns about schedule variance.

• Measuring and Protecting against Economic Exposure

  • We assume the random error term, ($\varepsilon$) equals zero with a constant variance while ($\alpha$) and ($\beta$) are the estimated parameters.
  • Covariance measures the variation of the asset's price to the exchange rate while the variance shows the variation of the exchange rate.

• Inputs to COGS

  • This also gives rise to variances.

• Beta Coefficient for Portfolios

  • Beta is a normalized variable, which means that it is a ratio of two variances, so you have to compare the volatility of returns to the benchmark volatility.

• Impact of Diversification on Risk and Return: Unsystematic Risk

  • Remember, we talked about every particular investment having an expected return and a variance.

• Announcements, News, and Returns

  • Some stocks tend to fluctuate more than others on a day-to-day basis, and the metric called Beta describe's the variance of a stocks day to day price.