The main function of covariance is to indicate that whether the association between variables in negative, positive or zero.The correlation coefficient and the covariance are related in the following way.The equation indicates that the covariance standardized by dividing the product of the two standard deviations of returns is simply equal to the correlation coefficient.In the light of this definition of correlation coefficient, the covariance can be as followSo the covariance can be calculated from the known element of correlation coefficient because the standard deviations of the rates of return of assets will already be provided.
Whether you can extrapolate that to make a broader statement I’ll leave open to interpretation.This is a similar concept that you’ll see in many great books about investing and stocks, and while not a profound statement it’s still worth mentioning.Markowitz explains here that the “right kind of diversification” includes doing so across different industries, especially when those vary in their “economic characteristics”.I’ll add that industries within the same country or geographical region can have very different microeconomics or capital structures and/or cyclicality or exposure to various macroeconomics. But the risk-averse investors are interest only in those portfolios that offer minimum risk for a given level of return. Covariance is referred to as the extent to which two random variables move together over time. After the calculation of covariance, it is easy to calculate the risk of the entire portfolio. The portfolio percentages or weights of investable funds to be invested in every security are utilized to provide solution to the Markowitz model.
The measure of covariance does this.The extent of association between the returns for a pair of securities is measured by absolute measure of covariance. The investors knew that diversification is best for making investments but Markowitz formally built the quantified concept of diversification. This means that the portfolio risk is a function ofThe weighted covariance among entire security pairsIt should be remembered that portfolio risk is actually determined by the following three pairsWhen there are two securities in portfolio, there are two covariances and weighed covariance term is multiplied by the two because the covariance of A with B is similar to the covariance of B with A. By combining assets with less than perfect positive correlation, portfolio risk can be reduced. But the most suitable portfolio for the investor is the efficient portfolio.Attainable set of portfolios are generated by the available assets or securities. Under these assumptions a portfolio is considered to be efficient if no other portfolio offers a higher expected return with the same or lower risk. The covariance can bePositive which highlight that the returns on two securities try to move in one direction at the same time. However, that math becomes irrelevant if assumptions are incorrectly made, and I’ll leave it to the astute investor to determine the validity of the assumptions, and additionally to investigate the math behind the portfolio theory if the conclusion is made that the assumptions seem reasonably valid.Perhaps one of the curses of establishing a theory whose ideas are so widely spread is the vast misunderstandings that come with it.Personally, I’ve seen so many diluted opinions on Markowitz’s portfolio theory, and it becomes like that childhood game of telephone—wherein a message is passed from one person to the next until the 20Not to mention that Markowitz gets lumped in and confused with various other academic theories and ideas, like the CAPM model (and its assumptions), the definition of beta, modern applications of the ideas, the list goes on and on.Here, I attempt to present an honest and straightforward summation of important clarifications that I believe are missed when it comes to Markowitz’s portfolio theory as presented in his I don’t mean to start with my own criticism but this is an important, albeit overlooked, assumption baked into this statement.This is something expanded on much more thoroughly the book Many critics of Modern Portfolio Theory (and Markowitz) use this exact argument to debunk the theory—I’ll admit to having doing this myself in the past too.
Whether you can extrapolate that to make a broader statement I’ll leave open to interpretation.This is a similar concept that you’ll see in many great books about investing and stocks, and while not a profound statement it’s still worth mentioning.Markowitz explains here that the “right kind of diversification” includes doing so across different industries, especially when those vary in their “economic characteristics”.I’ll add that industries within the same country or geographical region can have very different microeconomics or capital structures and/or cyclicality or exposure to various macroeconomics. But the risk-averse investors are interest only in those portfolios that offer minimum risk for a given level of return. Covariance is referred to as the extent to which two random variables move together over time. After the calculation of covariance, it is easy to calculate the risk of the entire portfolio. The portfolio percentages or weights of investable funds to be invested in every security are utilized to provide solution to the Markowitz model.
The measure of covariance does this.The extent of association between the returns for a pair of securities is measured by absolute measure of covariance. The investors knew that diversification is best for making investments but Markowitz formally built the quantified concept of diversification. This means that the portfolio risk is a function ofThe weighted covariance among entire security pairsIt should be remembered that portfolio risk is actually determined by the following three pairsWhen there are two securities in portfolio, there are two covariances and weighed covariance term is multiplied by the two because the covariance of A with B is similar to the covariance of B with A. By combining assets with less than perfect positive correlation, portfolio risk can be reduced. But the most suitable portfolio for the investor is the efficient portfolio.Attainable set of portfolios are generated by the available assets or securities. Under these assumptions a portfolio is considered to be efficient if no other portfolio offers a higher expected return with the same or lower risk. The covariance can bePositive which highlight that the returns on two securities try to move in one direction at the same time. However, that math becomes irrelevant if assumptions are incorrectly made, and I’ll leave it to the astute investor to determine the validity of the assumptions, and additionally to investigate the math behind the portfolio theory if the conclusion is made that the assumptions seem reasonably valid.Perhaps one of the curses of establishing a theory whose ideas are so widely spread is the vast misunderstandings that come with it.Personally, I’ve seen so many diluted opinions on Markowitz’s portfolio theory, and it becomes like that childhood game of telephone—wherein a message is passed from one person to the next until the 20Not to mention that Markowitz gets lumped in and confused with various other academic theories and ideas, like the CAPM model (and its assumptions), the definition of beta, modern applications of the ideas, the list goes on and on.Here, I attempt to present an honest and straightforward summation of important clarifications that I believe are missed when it comes to Markowitz’s portfolio theory as presented in his I don’t mean to start with my own criticism but this is an important, albeit overlooked, assumption baked into this statement.This is something expanded on much more thoroughly the book Many critics of Modern Portfolio Theory (and Markowitz) use this exact argument to debunk the theory—I’ll admit to having doing this myself in the past too.