 Covariance and correlation are the two statistical measures that are used to determine directional relationship between the return series of two individual assets in a portfolio and the strength of this relationship between these two individual assets. First we have covariance of portfolio returns. Covariance basically is a measure of directional relationship between the returns of two risky assets. We have positive covariance and negative covariance. Positive covariance we mean the return for two individual assets tend to move in the similar direction with relation to their individual means over time. And by negative covariance we mean the return for the assets tend to move in opposite to the individual main of the individual assets. The magnitude of the covariance depends on two factors. The first is the covariance of the individual assets returns and the second is the relationship between the returns of the individual assets. Covariance provides an absolute measure of how two assets move together over a certain period of time. To determine covariance between two assets for example asset i and asset j we have a certain formula. Basically we determine the individual main deviation of returns for individual assets and then we multiply the individual main deviation of an asset with the individual main deviation of another asset and the sum of these multiplications is then termed as the covariance. We divide the covariance over n minus 1 because in fact we are using the sample mean so this means that with the actual sample data the sample mean or the R bar is used as an estimate of the expected returns and the values are then divided by n minus 1 rather than by n and this is done basically to avoid the statistical bias. For a given period of time if the returns of any two assets are above or below their individual means then the product of deviations from their individual means would be positive. This means that the larger positive covariance of returns between these assets will be experienced over time. Similarly for a given period of time if an asset's returns are above its mean and the returns of other assets are below its mean then the product of deviations from their means would be the negative value. This means that the larger negative covariance of returns between these assets would be observed over a certain time period. Similar students on the screen we have certain data we have basically the individual returns for Dow Jones stock market index and the Barclays capital treasury bonds. So we have an index value for stock and the index value for bonds we have these monthly values for a year. We have mean deviation for stock market similarly we have mean deviation for the bond market and when multiply these two mean deviations we have their multiplication and the sum of these values is known as the covariance. If we observe this covariance then this negative value of covariance shows a negative relationship between the stock market and the bond market and it is difficult to decide whether this minus 5.06 as a covariance is high or a low value as we have no predefined benchmark to determine this relationship we have a scattered graph that we have paired values of RIT and RJT. By RIT we have the stock market values and by RJT we have the bond market values these are plotted against each other and this demonstrates the linear relationship between these two values and here we have also the strength of this relationship that is measured by covariance. If we observe these multiplications of the main deviations we can see that we have nine negative values in the 12 total values and this means that during nine of the 12 months the two asserts moved opposite to each other as per the product of their individual means so this clearly states a negative covariance between these two different asserts. The second mirror we have the correlation it is basically the standardized covariance when we divide a covariance over the product of the individual standard deviations of the two asserts i and g as the formula we can see to determine correlation or R we divide covariance between two asserts over the individual asserts standard deviation this R-R correlation may range from negative one to positive one if the correlation is positive one this means a perfect positive correlation this means that returns for the two asserts moved together completely in a linear manner this means that if returns of an asset i are increasing then the returns of an asset j would also be increasing and if the value of R comes to negative one we can say that we have a perfect negative correlation between two asserts this means that returns for two asserts have same percentage movement but in the opposite direction means if the returns of an asset i are increasing then the returns of an asset j are decreasing and if the value of R comes to zero this means there is no correlation between the individual individual two individual asserts we can also say that there is no the returns of two individual asserts are statistically uncorrelated on the screen we can see a sample of the correlation between two individual asserts in the left panel we have a perfect positive correlation because the same direction shows that the returns of two individual asserts are moving in same direction and on the right panel we can see there is a perfect negative correlation because if the returns of an asset are decreasing on the same time the returns of an other asset are increasing so for every increase in an asset we have a corresponding decrease in an other asset's return so there is a perfect negative correlation among the asserts i, a and b and in the below panel we have a zero correlation as we see that the returns on asset b are increasing on the same time the returns on asset b are decreasing and increasing many times in the same cycle so apparently there seems no relationship between the returns of asset a and asset b so this is the example of zero correlation we can have an example of this relationship for the year 2010 that we have already seen we have a total stock market index on monthly basis we have the bond index on monthly basis we have the scared deviation and the sum of these deviations we have divided the sum over n-1 as we have already seen that this is n-1 because we are using the sample mean and using this values we are determining the standard deviation for stock market index which is 5.56% and the standard deviation of bond index which is 1.22 this standard deviation of both the asset shows that the stock market is relatively higher risky than the bond index market when we use these values in the correlation model we have a correlation of 0.746 which is a negative value so there is a negative correlation between stock market index and the bond market index similarly rearranging this model we can determine the value of covariance which we have already seen and that is minus 5.06 so covariance model and correlation model we can interchange these values provided we have at least two values in each model