 In this section, I will tell you how to, what is meant by the concept of expected value of rate of return and how do we calculate it. So firstly we need to understand that what are the basic components of a total rate of return. So rate of return, your total rate of return, may have two components, the first one is the dividend income component and the other is a price change component. So dividend income component, by the end of the year, by the end of the financial year, if any company has announced dividend for its stock holders, the dividend which they have paid at the initial price, we divide it and take out one component of return which we call dividend income component. So for that, what we do is, we take into account the capital dividend and we divide it by the initial price at which the price level which was used at which that particular stock was purchased. So the initial price which was used at which the price was used at which the stock was purchased, we call that value as P0 as you can see the formula and on top of that we will keep the gas dividend in the numerator. This is the component of your dividend income. Then you have to see the price change because the prices, they keep on fluctuating, the prices of the stocks are changing day by day with time, like you see the movements of the stock market. So the next component of the total value of rate of return is calculated by taking into account the price change component. In that, what you do is, the stock which is in the market right now, or the stock which you have sold, minus the initial price which you had bought. So P1 minus P0, you will divide it from P0 which you will get the value, that will be the price change component. So the price change component will be collected in the dividend income component and you will get the total rate of return. Total rate of return, to further understand, I have taken the help of numbers here. So suppose the dividend income component is, suppose that is 3% and the price change component was 7%, so 3% will get the expected rate of return of 10%. So this is how we calculate the expected rate of return for one stock. Now there is another important thing and that is we always consider the expected value of rate of return. When I say expected value, this means I am talking about the mean. So it is not necessary. It is not that you will consider only one value of expected rate of return for your decision. That we should invest in this particular instrument or stock or we should sell this particular stock that you will consider one value of return. It is not that. So we have financial analysts, financial advisors, they look at the mean value and they analyze its dispersion. So the mean of the expected return, we need the value of returns, different time periods and their probabilities. The different values, as we saw in another example, we said that when the economy becomes very strong, then what will be the expected return? What will happen in the weak economy situation? What will happen in the normal situation? So in this way, on different time periods, the rate of return that is coming in the future is not realized yet. So we are talking about the expected value of the expected value of the expected value of the expected value of the expected value of the expected value of return. And for that, we will use the formula that is given by EE stands for expected. So remember that we have to use this concept in many other places as well. So small r stands for the rate of return. And e means expected value of rate of return, fine. And where we will say e of r, this means we are talking about mean, average. So e of r means expected rate of return. So how will this value come out? You said suppose we are doing the analysis of 6 months. We have monthly values of rate of return on January, February, March, April, May, June. We have taken the returns of these 6 months. We have named them r1, r2, r3, r4, r5, r6. So with each r value you will have to account for the chance that if we say that we will get 20% return in March on this particular financial instrument, then what is the chance of that? i.e. 10% chance, 20% chance, what is the chance of that? So we have to account for the chances or probabilities and we have written the probability of every time period in this formula p1, p2, p3, p4. So you have to multiply r1 with p1, r2 with p2, r3 with p3. And as I have given an example, suppose we have the expected return of 6 months. So we can take out our mean on the basis of 6 months. So how will we take out our mean on p1, r1, p1 with r1, p2 with r2, so on. You have to multiply 6 values and add them up. So that will be your mean. And the formula here is in rate of returns. You have been told the general formula. So in this you can see the p1, r1 with an extended pn, rn. So in this time period we can use this formula. Or you can use the sign of summation or summation. So we have expected the mean of return to be sum of sigma, p, i, r, i. So these are the two ways. And both are telling the same value. And this is what will give you the value of mean of the expected returns over a certain period of time. To illustrate this, I am going to take the genco example. We had just discussed that there is a stock. We are assuming it. Its name is genco. And genco, in the shape of three different economies, different returns are yielded. And we have their probabilities. With the help of this data, we will calculate the mean of return. You have to take the first return with the probability. You have to multiply it with the probability of the second return. And so on. We have only three observations here. After multiplying the three with their respective probability, we have to add them up. And I have the value here, 0.1, i.e. 0.1. If we convert this to percentage, then this becomes 10%. 10% means the mean of the expected rate of returns. The three expected rate of returns, their mean is 10%. This means that the stock of the genco will be a bad economy, normal or good. It can give you a 10% return. This is what I am telling you. Therefore, we do take into account the mean of the expected returns. But you don't just have to collect the returns. We will multiply them with their probabilities and then add them up. The expected rate of return, any mean of rate of return, calculators.