[MUSIC] Let's look at this measure of expected return, standard deviation and correlation for these two financial securities. So in this table, we look at the average monthly return and the monthly standard deviation. The monthly return, the mean, and the average return indicate the tendency. You see that from Microsoft and IBM, they're both positive. If you remember from the first graph, the prices were moving up and ending at the end of the period at a higher level, than at the beginning of the period. So, we were expecting a positive return. We see that the monthly return for Microsoft is slightly higher than the monthly return for IBM. Also confirming what we've seen in the two histograms we can see that the standard deviation of Microsoft is larger than the standard deviation of IBM. And finally the level of correlation which indicates how these two stocks move together is positive. So they do tend to move in the same direction, but the correlation is far from perfect. We can see here that the correlation is equal to zero point three. This information summarized here in this graph gives a lot of characteristics that are essential in constructing portfolios. Here they are backward-looking in the sense that we have looked at historical prices in the past. And we've computed these quantities of mean, standard deviation, and correlation. When we want to construct a portfolio we want to use the same type of information, mean, standard deviation, and correlation, but in a forward looking way. One way of doing so is to assume, for example, that the history will repeat itself. And that past information is a good indication of the future realizations of return. But we could also integrate other type of information if, for example, we have some very optimistic forecast about one particular stock. We could increase the expected return that we intend to see in the future. But this information, expected return, standard deviation and correlation is all we are going to need to construct optimally our portfolios. There are other measures that we will be using in the next lessons that relates to these quantities of risk and dependence. And they simply are transformation of the original quantity that I have just presented. One that is very often used to measure risk is called variance. Variance is actually the same, contains exactly the same information as standard deviation. It is the square of the standard deviation. A measure of dependence that is related to correlation is called covariance. The way this is computed is by using both the standard deviation of the individual stock and their correlation. The product of the three quantities, correlation, times standard deviation of the first asset times standard deviation of the second asset, gives the covariance. While the correlation is always between -1 and 1, the covariance can take any value. It is important for us to actually focus on correlation because it allows us to compare pairs of stocks between each other. Because all levels of correlations are going to be between minus 1 and 1. We can say that if two stocks have higher correlation, they tend to move more in the same direction. And using covariance to make this type of comparison is more complicated. Because, as I was explaining before. the covariance level can take any value. It's not necessarily between minus 1 and 1. So to summarize, when we construct our portfolios, we need information. The most important information pertains to the anticipated return. The average return. The direction or the tendency that we expect to see in stocks. This is measured by expected return. The second notion is a measure of risk. This tells us about the dispersion that we expect to see or that we have observed and returned. This is measured by standard deviation. The third type of metric that we want to use is a measure of dependence and the measure will be using is correlation. It takes value between -1 and 1. In the next videos, we're going to use these quantities to construct your training. [MUSIC]