 In this section, I will explain the concept of efficient frontier in detail. So, efficient frontier concept was developed by Harry Markowitz in 1952 due to which he got Nobel Prize, he presented Modern Portfolio Theory. Modern portfolio theory is an important part of efficient frontier or efficiency frontier. In this, we take the returns on the vertical axis and take the risk that you have used. Usually, we take the standard deviation as the indicator of risk, we take that on horizontal axis. So, when we take the return on the vertical axis, usually the return is taken in which form? That is the compound annual growth rate which is abbreviated as CAGR. We take the return as the indicator of risk on the vertical axis. As I mentioned earlier, we take the standard deviation as the indicator of risk on horizontal axis. Then, we take the combinations which have a maximum return. We get certain assumed, pre-assumed values of risk. So, we take the combinations of portfolio which have a maximum possible return. Then, you connect all those points and make a frontier which we call efficiency frontier or efficient frontier. When we are looking at this particular dimension, it is important to consider the values of the covariance and correlation also. So, we account for the covariance and correlation values. When we develop the efficiency frontier, you can see in this graph that the expected rate of return is taken on the y-axis. The standard deviation is taken on the x-axis. Here, you can see two capital allocation lines. One is labeled as CALB. Then, we have CALA. Now, we have discussed this already. These are the risk-reward trade-off lines. We also call them capital allocation lines. In this particular graph, you get to see one more thing apart from these two capital allocation lines. That is the Markovitz efficient frontier of risk assets, which I was talking about. So, you get to see this curve of thick black color. After a certain point, you get dotted line here. This certain point which you have defined, this is the minimum variance portfolio. What is the minimum variance? The portfolio which you have made has the lowest variance of the portfolio. You keep that particular thing as your starting point. After that, you have taken all those portfolios which have maximum expected rate of return at a certain risk level. These are the different risk levels. What can be the maximum rate of return available according to the available situation? You have different funds, securities and stocks. On the basis of which, you are defining the portfolio. What is the risk of that? According to the available situation, you can generate the maximum expected rate of return. What is the combination? You have defined these black thick lines by taking all those combinations. We call this an efficient frontier. Now, if we further digress on it, if we pay attention to it, we can see that all those combinations which are falling below this black thick line, it could be any combinations. All those combinations which are representing inefficient portfolios, this means that either, for example, I have taken this point, this means that suppose there is a 6% standard deviation value at a risk level, then you are getting this level of expected return from this portfolio, suppose that is 12%. And on the 6% risk, you will get 12% expected return if you invest in this particular portfolio. But an efficient frontier is telling you that the information which you have collected, the different financial instruments or financial assets which you have in the data, with the help of which, you have developed this black line, there is a combination which is at the same level of risk, that is, on the 6%, you can get a much higher expected rate of return. And from this combination, you came to know that this is the maximum expected rate of return which you can generate, which you can earn at this particular given risk level of 6%. So, efficient frontier is based on all those combinations which will yield maximum expected return on a given risk. Right? So, this helps us with the efficiency frontier to select the best combination. Now, when we look into the detail of efficiency frontier, we see that basically when we move on, in this particular thing, what combination we have to go to, we think that when you discussed the trade-off line of risk and return, we said that this line will represent all the combinations which you can develop on the basis of which you can develop your portfolios by allocating your money, total investment in the risk-free and risky assets. So, we assumed that if we put all the money in the risk-free asset, then this will be the value of the intercept. This will be the return which you will be earning in this case. What will be your expected return? Okay? So, now, after this particular thing, you have taken different combinations of risk-free and risky assets, like you were increasing the risk of your expected return, and you will get this CEL, for example, B, different combinations. Now, CELA is another line, another trade-off line which shows the link between risk and reward. And it tells you that if you take more risky and risky assets, then there is a possibility that you can go to a higher level of expected return. So, now, the decision is that we have seen the efficiency frontier. We have seen which different combinations are possible for us. We get to know from the CEL. But eventually, we will select all the portfolios from all these portfolios. So, for the selection, what we do is that we move our CEL as far as possible. Eventually, we get a point where CEL means that those combinations which you can take and efficiency frontier means that those combinations which you can take and which are efficient. So, eventually, we will continue pushing the CEL upwards until and unless we reach a point where your CEL, capital allocation line becomes tangent from the efficiency frontier. So, the point where it becomes tangent, like in this diagram, this M is written. This is the point where your optimal allocation is achieved. So, in the next sections, we will further discuss this in detail that what is the work of efficiency frontier? This gives us the optimal allocation for those portfolios which we can take with the help of our given resources which CEL represents and what will be the most efficient frontier and efficient portfolio which you can achieve as per the maximum level given resources. That can be achieved at a point where the capital allocation line is tangent to the efficient frontier. So, we are going to discuss it in detail in the subsequent sections. So, this is basically the introduction to this particular thing that helps us in understanding the significance of efficiency frontier.