 Hello and welcome to this session. This is Professor Farhad and which would look at examples that deal with risk aversion and the sharpie ratio. Every time I hear I mentioned the word examples it means in the prior session I already explained the topics of risk aversion and sharpie ratio. Those topics are covered on the CFA exam as well as an essentials of or principles of investment course. As always I'm going to remind you to connect with me on LinkedIn if you haven't done so. YouTube is where you would need to subscribe. I have 1800 plus accounting, auditing, tax, finance, as well as Excel tutorial. If you like my lectures please like them, share them, put them in playlists. If they benefit you it means they might benefit other people. Connect with me on Instagram. On my website farhadlectures.com you will find additional resources to complement and supplement this finance investment course as well as your other courses. I strongly suggest you check out my website. So let's take a look at the first example. An analyst forecasted the return of the market index over the coming year will be 10%. The one year T-bill rate is 5%. The T-bill rate represents the risk-free. The market portfolio, the market index represents the market. Examination of the return of the S&P suggests that the standard deviation is 18. So the standard deviation is 18. What does this information suggest about the degree of risk aversion of the average investor? Assuming the average portfolio resembled the market index. So simply put what we're trying to calculate is the risk aversion for this typical portfolio. Well first of all you need to know the formula. What is the formula? It's the index fund return which is 10% minus the risk-free rate 0.05 divided by the standard deviation. But here we're giving the standard deviation. We have to turn the standard deviation into the variance. Therefore we have to raise it to the second power. So simply put the risk premium of this portfolio is 5%. 10 minus 5 equal to 5%. Now what we have to do, we have to take 0.18 and multiply it by 0.18. So let's take 0.18 times 0.18. That's going to give us 0.324, 0.324, not 324, 0.0324. Now all we have to do is take 0.05, 0.05, which is the risk premium divided by 0.0324 and that's going to give us approximate risk aversion of 1.54. So that's the A, that's the risk aversion for your typical investor giving this portfolio. Now what is the sharpie ratio of the index portfolio in A? So what's the sharpie ratio? Here they're asking us about the risk aversion. What's the sharpie ratio? Basically the numerator is the same. It's the risk premium divided by now. We're going to divide this by the standard deviation 0.18 and that's going to give us 0.28 for the sharpie ratio. So this is how you compute the risk aversion. This is how you compute the sharpie ratio. What do they mean exactly? Well go to my previous recording or go to my website to get the understanding. This is just an example to illustrate the point. Let's look at another example. Suppose you forecast that the standard deviation for the market is 20%. If the risk measure of the risk aversion equal to four what would be the reasonable expected market risk premium? Okay so what are we given here? Here we are giving the A the risk aversion equal to four. We are giving the standard deviation of 0.2, the standard deviation and we are asked basically to compute the expected risk premium. So we're looking to compute the risk premium. And basically what we have here is basically a formula with one unknown, formula with one unknown. But remember we have to turn the standard deviation into the variance because so we're going to raise to the second power. And basically what we have is four times 0.2 times 0.2 is 0.04 and that's equal to the risk premium. Now basically we just have to find out what is 0.4 times 0.04 that's equal to 16.16 or 16%. Simply put the risk premium for the portfolio is 16%. What value of A is consistent with the risk premium of 9%? Well what they're saying is change the 16 to 9.04 in the denominator what will be A under those circumstances? Well if we do this computation if we take 9% times the risk premium it's got divided by the 0.04 will give us 2.25. So let me ask you this which portfolio would you prefer? Well obviously I'll prefer this portfolio because my variance is the same 0.04 but for this portfolio here my risk aversion is 4 and my return is 16 obviously I'll prefer this one. What will happen to the risk premium if the investor become become more risk tolerant? So what they're asking is what would happen to this number here to the numerator if the investor if the investor now is risk is more tolerant toward risk it means they have less risk aversion. Well think about it what happened when you have more risk tolerance? So if your risk tolerance goes up now you want to take more risk because you have more risk tolerance. When you when you are willing to take more risk it means your risk aversion is going down your risk aversion is going down you no longer avoiding risk you don't care about risk. Well as a result if risk doesn't if risk doesn't bother you if in other words you are not asking for extra return against the risk because risk doesn't bother you because if you are risk aversion the assumption is if you're risk averse every time you want to take more risk you expect more return now you are more risk tolerance which is the opposite kind of a risk aversion what happened is you don't care about the risk premium you tolerate lower risk premium why because you are risk tolerance you're okay you don't care you don't want to be compensated for the risk because you're comfortable with the risk if you are not comfortable with the risk in order to take the risk you would ask for a higher a higher return. So hopefully those exercises will help you understand the risk aversion and the sharpie ratio because those are examples I already explained them look in the description if you'd like to about the link for this playlist. In the next session we will start to take a look at asset allocation across risky and risk free portfolio because we kind of now we explain what is risk premium we explain risk aversion we explain how to measure the the price of the risk in the market and look at the sharpie ratio now we are ready to kind of start to build a portfolio and allocate asset between risk free and risky asset based on your risk tolerance as always I'm going to remind you to like this recording and if you're still watching it means you like it please share it put it in your playlist let other people know about it and don't forget to check out my website farhatlectures.com for additional resources for this course as well your other courses good luck study hard and stay safe