Investments Formula #8 Flashcards
(17 cards)
What is this formula?
COVij= ρif σi σf
Covariance
When do you use the covariance formula?
When the question asked to solve for the covariant or correlation coefficient (ρ)
What do you do if you need to solve for “ρ”(correlation coefficient)?
Use ρif =COVij / σi σf
Isolate the factor you were trying to identify
What do you do if you need to solve for “σi ”(standard deviation of stock i )?
Use σi= COVij / (σf ρi)
What does “ρ” represent?
Correlation coefficient
What does “σ” represent?
Standard deviation
Security A has a standard deviation of 4.1% and security B has a standard deviation of 9.3%. If the covariance of the returns returns is 19.37 what is the correlation coefficient?
.5080
Use ρif =COVij / σi σf
What is the definition of covariance?
Covariance is a statistical tool that measures how two random variables in a data set change together. It indicates the direction of their relationship, whether they move in the same or opposite directions, and the strength of their correlation. Positive covariance Variables move in the same direction.
What is the definition of standard deviation?
Standard deviation is a statistical measure that indicates the amount of variation or dispersion within a set of data. It essentially tells you, on average, how far each data point is from the mean of the data set. A low standard deviation means the data points are clustered closely around the mean, while a high standard deviation means they are more spread out
What is correlation coefficient?
A correlation coefficient is a statistical measure that describes the strength and direction of a linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation
What is the difference between covariance and correlation coefficient?
Covariance measures the direction of the linear relationship between two variables, while correlation coefficient measures both the STRENGTH and direction of that relationship. Correlation is essentially a standardized version of covariance, making it easier to compare across different datasets and scales.
What is the range for correlation coefficient?
-1 to +1
What does +1 mean?
Securities are perfectly positively correlated and expose the portfolio to maximum risk.
What does a correlation coefficient of zero mean?
There is no relationship between the securities
What does a -1 correlation coefficient mean?
They are perfectly negatively correlated, they move opposite to one another, risk is completely eliminated
Why use the covariance formula?
In finance, covariance is used to understand the relationship between different assets in a portfolio. It helps assess how the returns of different assets move together, which is crucial for diversification and risk management
What determines the strength of coefficient correlation?
The closer the data points are to the line of best fit on a scatter graph, the stronger the correlation. It can be measured numerically by a correlation coefficient.
