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The strength of the relationship between X and Y is sometimes expressed by squaring the correlation coefficient and multiplying by 100. The resulting statistic is known as variance explained (or R2). Example: a correlation of 0.5 means 0.52×100 = 25% of the variance in Y is “explained” or predicted by the X variable.
How can portfolio variance be reduced?
Modern portfolio theory says that portfolio variance can be reduced by choosing asset classes with a low or negative correlation, such as stocks and bonds, where the variance (or standard deviation) of the portfolio is the x-axis of the efficient frontier.
How to calculate the correlation of two random variables?
Consider two random variables X and Y: – If ρ (X, Y) = 0, we say that X and Y are uncorrelated. – If ρ (X, Y) > 0, we say that X and Y are positively correlated. – If ρ (X, Y) < 0, we say that X and Y are negatively correlated.
How are mean and variance related in statistics?
[In this module we will discuss estimates of sample mean and variance, and also discuss the definition of covariance and correlation between two sets of random variables] Statistics like the sample mean, variance, skewness, and kurtosis are intimately related to the moments of a sample .
What are some examples of positive correlation coefficients?
The closer the value of ρ is to +1, the stronger the linear relationship. For example, suppose the value of oil prices are directly related to the prices of airplane tickets, with a correlation coefficient of +0.8. The relationship between oil prices and airfares has a very strong positive correlation since the value is close to +1.
What’s the difference between positive and negative correlations?
Positive correlation is a relationship between two variables in which both variables move in tandem—that is, in the same direction. Negative correlation or inverse correlation is a relationship between two variables whereby they move in opposite directions.