 In this session, I will explain the framework that is used by the professional asset managers when they decide the combinations of risky and riskless assets to form a portfolio. So this particular framework is based upon the principle of the tradeoff between the expected rate of return and the risk. So we know that we are forcing in future that if we invest in a certain financial asset, we will be able to generate a certain rate of return. So based upon this information, we calculate the expected rate of return and then we also consider the values of the standard deviations of the expected rate of return in order to make a decision whether or not we are going to invest in that risky asset or riskless asset or if we want to go for a combination of the risky and the riskless assets in order to form a portfolio, then we are going to consider the tradeoff because we all know that higher return, if you want to take it through any investment, then you have to take a higher risk. So if you take a low risk, then obviously you will get a low return. So when we develop a portfolio or a professional asset manager, then we use this tradeoff as a framework. So in order to explain this particular concept or the framework which is used by the professional asset managers, I am going to take an example. So suppose you have 100,000 rupees which you want to invest and you have a choice that you want to put these 100,000 rupees in riskless asset or risky asset. So it is always safer and better to invest in multiple assets whose risk levels are different from that you can generate better expected returns in a safer way. So therefore, we just thought that we have choices, we have a risky asset and a riskless asset. Riskless assets are usually your T-bills, those who do not want to take a risk or a risk more than risk, they invest in tri-ribbles. You get very little return on that but your investment is secure, your money does not go to waste. But those types of investors who want to take a higher return have to take a higher risk. So we assume that the risk-free asset will give you 6% interest and the risk-free asset will give you 14% interest and the expected rate of return of 14% will be 0.14. So you can see that they have been riskless asset, which is 0.06 and the risk-free asset that you are investing in is 14% which can be written as 0.14 and these are the yearly values. So then we have to look at the standard deviation also because the risk-free asset is risk-involved. So you will not get this 14% return, expected rate of return of 14% will not be there. In this, there can be a shortage, we also have to make a standard deviation to make it less. So standard deviation means that on average, your mean return, expected return, on average how much variation or variability can come to your hand. So in this particular example, we assume that our standard deviation will fluctuate by 14% that is given by 0.2 and when we consider all this information, then there could be a question that according to this situation, how much money I am going to invest in the risk-free asset and how much money I am going to invest in the risk-less asset. So for that, we are going to discuss a framework which is used by professional asset managers. So I will be explaining that using different options, if you put your entire lakh rupees in the risk-free asset, then what will happen? If you put your entire lakh rupees in the risk-less asset, then what will happen and what would be the outcome, the expected rate of return if according to different combinations, you invest your investment in these two different assets. So I am going to explain this particular framework using this data which you can see in this table. So we have got multiple portfolios, you have portfolio F, G, H, I, and J. What is the difference between these? You can see that first of all, we have invested 1 lakh in the risk-free asset, we have accounted for them. Then in the risk-less asset, the amount of your 1 lakh per portion that you are investing, you have taken different options and defined these portfolios. Then we have expected rate of return and then we have accounted for the standard deviation. So these two things are going to play an important role when we have to decide. So let's look at the values in detail. So suppose, as a starting point, we have portfolio F in which we have invested 1 lakh in the risk-less asset. And by doing this, we have assumed that you will get 6% expected rate of return for which we use capital E, small r symbol. And I had told you that when we invest in risk-less asset, the standard deviation means the risk, the dispersion is zero. So you can see it is zero. Now if we invest, instead of 100% in the risk-less asset, we invest 75% of the total money which we have, i.e. 1 lakh per portion, we have put 75,000 in the risk-less asset and 25,000 in the risk-less asset. So in this case, you are getting 14% over 25% and you are getting 6% over 75%. So if you take the average of 6% and 14%, then your 8% expected rate of return has come out. If you define the variation in this, then we have discussed formulas of standard deviation. By using that, we have taken the value that is 0.05. So you can see that if we invest 75% in the risk-less asset and 25% of 1 lakh in the risk-less asset, then our return has increased by 0.02 or 2% but our risk has also increased. So if instead of 75, 25, if we invest 50% of the total investment amount in the risk-less asset and 50% in the risk-less assets, as a result, we will be able to earn or generate 10% expected rate of return with a risk of 0.10. And then similarly, if we increase the investment in the risky asset, we will be able to generate a higher expected rate of return but at the same time you can see that the risk has also gone up from 0.10 to 0.15. Now if we invest all the money in the risky asset and don't invest any money in the risk-less asset, then in this context, you can see 14% expected rate of return but at the same time the risk of standard deviation has gone to 0.2. So with this data set, we can see that as you go for a higher rate of expected rate of return, at the same time you have to see the rate of return and your risk is also increasing which we can see with the help of standard deviation. Now if we want to see this diagrammatically, then we can look at this particular risk-reward rate of line which is also known as the capital allocation line. We also call this risk-reward rate of line as the capital allocation line. Now what I have shown you is portfolios starting from FGH8JS. You saw that when we were investing all the money in our portfolio in risk-less asset, then we were earning 6% rate of return and our risk was 0. So with these portfolios, the expected rate of return and the standard deviation values are taken to these points and when you connect these points, you will get the risk-reward rate of line which is also known as the capital allocation line. When you have to draw the capital allocation line or the risk-reward rate of line graphically, then we always take the standard deviations on x-axis and the expected rate of return on the vertical axis. So in this way, you can see that through this line, we can represent the various combinations of risk-less assets with the help of graphically line in the form of different portfolios. So basically, when we are looking at the framework that is used by the professional asset managers, that is solely exclusively based upon the principle or the trade-off between the risk and the return. So whatever data we have used in developing or drawing the line which I have just shown you, which is called the expected rate of return and risk-rate-off line, or we also call it the capital allocation line that is developed based upon the information we have discussed in the table earlier. So you look at the various combinations of the total investment being invested in the different assets and then on the basis of that, what is then you calculate the possible expected rate of returns along with their standard deviation. So when you look at these values, the different portfolios with respect to the expected rate of return and the standard deviation values are when drawn in the graphical form, then you get the expected rate of return risk-rate-off line or the capital allocation line.