 We are doing introduction to financial risk management. In this module, we will be studying how to calculate returns and risk because there are many ways in which returns can be calculated and many ways which risk can be calculated. So we need to know that. You might have learned a bit of these in your basic statistics knowledge, but here we will be applying in the terms of finance, specifically with respect to portfolios and assets investment. So when we say my year of return, returns can be calculated in many ways. One of the most important way of measuring return is a holding period return. Let me clarify it in the beginning. Returns are normally quoted as per annum. Like if you say I'm depositing money in bank, they'll offer me 8%. So here, it is assumed that 8% per annum. But when we say holding period return, this is not to do with per annum. It could be for one week. It could be for one year. It could be even for more than one year. So what was the holding period return of three years? What was the return of two years? So the exception of the holding period is the return of per annum. How can we calculate the normal return? We take it at the end period value divided by the beginning period value. Like in the period we entered, and then at what level the investment goes to. It could be positive. It could be negative. It's not necessary that the investment goes up. It can fall several times in the investment. Reducting with one will give you the return which we are getting. For example, we have also placed it in the formula. Pt is the price at time t divided by P0 is the price at time 0. Plus any Cf. Cf means talking with cash flow here. When you take a share, you can get cash flow like in form of dividend. Or if you take a bond, you can be getting some form of interest. So those cash flows are adding in the closing value. And then you deduct a 1 from it and you'll get the returns out of it. For example, we took a share of 100. And after the holding period, it turns out to be 105. So 105 divided by 100. And in this period, we also got a dividend of 2 rupees. So we add that 2 to the 105. So 107 divided by 100 minus 1. This is our return. That is 7%. Now if this 7% holding period is given to us, then we'll know if it happened in a month or a year. So we should appreciate this point that the holding period is not linked with year. It's linked with the period to which it relates. And we can also calculate holding period returns for a multi-period. Like you can give small periods of returns. And then you are required to calculate returns for the whole period. For example, what is the 3-year holding period return if annual returns are 7%, 9% and a minus 5%. As I told, it could be minus as well. So now these 3-year different returns have come. Now we want to see how much our over-the-period return has come. So what we do is, we'll calculate it. We'll take 1 plus the return for the first period. Then times 1 plus the return of the second. And then times and 1 return of the third. Minus the 1, formulas 1. So 107 plus 1 plus 109 plus 105 will come here with minus. So this tells us that over the period we have earned a return of 10.8%. This is the total span of the return. That is, the 3-year holding return is 10.8%. So there are many ways in which this average could be done. So when we look at the average return in the previous example, this was one way of calculating. It has a simple, arithmetic mean. We take the values and divide by number. Then it is geometric mean, which we just did, in which we took it along with the multiple effect. Because it captures the compounding factor. Another way is money weighted return. That's beyond our specific scope because for that, you need a proper financial calculator or a spreadsheet to calculate. It doesn't have normal calculations, but this method also exists. So in average return, as I just told you, we take the returns of the whole period. That could be n number of period, divided by n, that will give you the average return. This is a simple average which we normally calculate in math. So here, if we have minus 50, then we have plus 35 and plus 27. These are three period returns. So divide that with 3 and you get the return of 4%. That's the average return. Whereas when we move to geometric, because that has a compounding effect, this will take you to different, then we have 1 plus r, as we just did in the example. We'll take the respective returns and that will be taking it. In this case, return fall or come out to be minus 5. Because in the beginning, we had a major fall. So rather than an average of 4, we have a negative 5% average return. That's geometric return because we are having a compounding effect of what is being done. My year of return. We are also given situations where we are given returns for a short period, like holding period returns for a very short period. But for comparison, we have to anvilize it. Because suppose one bank is offering you per annum rate and one bank is offering you a quarterly rate, you cannot easily compare. So for comparison purposes, we have to bring it to the anvilized return mechanism. Supposedly, we have a weekly return of 0.2%. So I am asked to compare it with some other measure where we have annual return. So what I'll have to do is I have to convert it to anvilized rate. So here, as you can see, what we'll do is we add 1 plus 0.02% and take the power of 52. Because we know that in a year, we are 52 weeks and one week's return is 0.2%. So when we take the power and deduct the formula 1, this turns out to be 10.95% annualized return. So now we can easily compare with some other instrument which is giving annual rate or a semi-annual rate. So we should bring them to all the annualized. So here, we increased it. Let's see how we decrease the period. We have an 18-month return of 20%, not a standard period for comparison. Then what we do is we take 1.02, that is the rate of the return added with a formula, and we take power of 2 by 3. Because in 18 months, we have one whole year and a six month. So we take 2 over 3, that is 0.667, and that turns out to be 12.92%. So here, we can easily compare the two instruments with this mechanism. Another way of looking at return is how are the returns being presented? So there are gross returns and there are net returns. This is more applicable in the case of asset management companies or where some fees or expenses are charged. So we have a gross return, then we deduct that period expenses, and then that's the net result what we are getting out of this period. And then we have a pre-tax and after-tax nominal rate, because that is another factor because some investments, our returns are definitely taxed at different jurisdiction at different rates. So we might be earning a high gross rate, but when tax is applied, that tax factor is taking care and we get after-tax return, that is what the investor will actually gain through the investment. Though they are earning a bit more, supposedly they are earning 10%, minus the tax factor 3%, they are actually getting 7%. So here we keep it till here and then we'll add on how these will be practiced more and how they'll be applied in a later period. Thank you.