 In continuation to our core area, we are starting financial risk management and in that we are discussing introduction, definitions and evaluating portfolios. So when we have portfolios, there is a question coming in, suppose you have two options to select. Now which portfolio will be better or if you have two assets, which asset to invest in, there should be some mechanism to work it out. In this module, we will be specifically looking at how we can select portfolios given the facts. So it's like ranking the portfolio, it's like evaluating them and selecting the best out of it. So ranking portfolios, they are multiple ways and one of the most renowned and famous way of ranking a portfolio is through some ratios and one of the common ratio in that is sharp ratio. We can also call it sharpie but we will be calling it sharp so both ways it's fine. So sharp ratio. Sharp ratio was developed by Nobel laureate William Sharpie and that's why it's referred to as sharp ratio in that. It's used to help investor understand return of investment and compare the returns. The main point here is comparisons, when you have alternates which route this ratio will help you in doing that. We'll be learning its background, we'll be learning how to calculate it and we'll be also having practice of this. Ratio is the average return in excess of the risk period because if we are earning a risk-free return, that means we are not taking any kind of risk. For taking the risk, what excess we're going to get out of it, that is being gauged by this ratio. When we deduct our return, portfolio expected return from risk-free rate and then we divide it with the portfolio's risk, that will give you the sharp ratio. I'll just show you the formula as well. So it will help investors to gauge how the risk has added to their returns in the portfolio. So the sharp ratio is a measure of excess return over the risk-free rate relative to its standard deviation. We have discussed standard deviation previously as well but a brief recall, standard deviation is a measure of risk. So we take care of the total risk applicable to portfolio. So if we discuss it in the mathematical way, it's the return less the risk-free rate divided by the standard. I will just show you the formula as well. It's also having two types of sharp ratio calculation. As we have seen, we have some historical data and then we have some future data. So in finance term, we call it X post. X post is that's the past performance. So it's referred to as things which have been already done. So we take the data of what has been actual outcome and based on that we calculate. But remember, it's already passed but it will be an indicator used to gauge it. Then we have X ante. X ante as I just initially told, it's about future. So in this, we look at expected portfolio performance. That what we are expecting from this and based on those expectations, we are going to rank it. Because mainly when we are deciding for future, our main concern is which will be better for the future. So formula for sharp ratio, as we just discussed, it's RP minus RF divided by standard deviation, where RP is your return of the portfolio. RF is the risk-free return and that's the standard deviation of the portfolio. That means the risk you are going to take for this particular portfolio. Let's do a small example. Suppose that asset has an expected return of 15% in excess of risk-free. We typically don't know if the asset will have the return because it's future we are not sure, but again it's an expected part. And the standard deviation is 10%. So when risk-free rate is same. In this context, we have seen we are earning 15% divided by 10%, so it gives you a sharp ratio of 1.5. Sharp ratio in its absolute term does not tell clearly what it is about, but it makes more sense when we compare two portfolios or when we compare from one period to another. So this we have 1.5. Calculating more commonly used exposed as we have just discussed, it's the past data to which it relate. For example, we have asset returns, we have S&P total return and that's the excess return what we are going to gauge out of it. So this table reflects that any excess return or excess negative return, that could be the case as well. So if we don't need to have always the same benchmark, we can have multiple benchmarks to relate to calculate its impact. Benchmark asset caps means that we have return over and above the benchmark rate and then we have standard deviation for this particular risk. So the sharp ratio that comes out to be say this 0.29, this indicates for this particular portfolio, we have this given number. This number as I've just told you in isolation, they are not the true indicator, but for the detailed comparison, they'll have a compact when we compare the two. Currently you have $250,000 to invest, expected return 12, volatility is 10% and tangent portfolio is 17%. Risk-free rate is 5%. So we have to see what we are gauging over and above the risk-free rate to come out of it. So sharp ratio is 12% that is expected return minus risk-free rate of 5% divided by the risk factor that is 10.1. So it is 0.7. So conclusion is as I've just mentioned, when we are having two sharp ratios, the one which is higher is better than the other. So that means if we have two portfolios and one is having a sharp ratio of 1.2 and other is having a sharp ratio of 1.6. So we based on the expectation will recommend portfolio with a higher sharp ratio that is 1.6. So this is basic about sharp ratio. Thank you.