 and welcome to the session. This is Professor Farhad in which we would look at the efficient frontier. This topic is covered on the CFA exam as well as an essentials and principles of investment scores. As always, I would like 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 tutorials. If you like my lectures, please like them and share them. 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 supplement and complement your finance courses, accounting courses, this course as well. So what is the efficient frontier theory? It's a theory that was introduced by the Nobel laureate Harry Morcovitz in 1952 and it's the cornerstone for the modern portfolio theory. Now we looked at the modern portfolio theory in a prior recording. So if you understand what the modern portfolio theory, the efficient frontier theory should not be any surprise to you. And the assumption in investment is the higher risk that we take, the higher expected return. And conversely, investors can take a low degree of risk. And as a result, they can experience, you should expect a lower return. So risk and return go hand in hand. And if you're listening to my course, I've been saying this all along. So according to this theory, to the frontier theory, there's an optimal portfolio that could be designated with a perfect balance between risk and return. Actually, we looked at it, we just would not call it the efficient frontier theory, but that's what it's called. So the optimal portfolio that we looked at earlier, we're going to see in a moment, does not simply include securities with the highest potential return or the lowest securities. So what it is then? The optimal portfolio aimed to balance securities with the greatest return with an acceptable risk. So give me the best return with my risk, with my risk, my acceptable degree of risk, or securities with the lowest risk for a given level of return. Or you can find it the other way. And we're going to look at, we're going to look at the graph in a moment. The points on the plot of risk versus expected return, where the optimal portfolio lies are known as the efficient frontier. And this is what we are looking at. This is the efficient frontier. But for now, imagine that this frontier does not exist for now, just kind of so we can start this example. So if you have individual assets, what you can do, we learn from the portfolio theory that if you combine different assets with different covariances, you might be able to reduce your risk for the portfolio for the combination and really improve your return. So here's what we do. If we take those different assets, this is asset A, asset B, asset C, asset D, all the more the better and the more covariance there is between them, the better they are. And what we do is we build different portfolios. And what's going to happen when we build different portfolios, they're going to give us those portfolios, they're going to start to give us a line. For example, this is the risk, the standard deviation, and this is the return. And what we do, we can eventually draw this line based on the portfolio that we created from these different assets. Okay? Now, here's what we can say about this line. Any investments that lies on this line, this is called the efficient frontier risky asset, any portfolio that falls on this line is better than any individual inside the line. What do I mean by this? Well, let's take this point and this point and compare them. Let's see why this one is better. Look, let's assume this is 5, 10, 15, 20. This is 5, 10, 15, 20. So notice here, these two assets, they have a degree of standard deviation of 20%. So the risk level is 20. But notice the one on the, the one on the, the one on the efficient frontier risky asset has a return. Let's see 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22. So this one has a 22 return and this one has an 18% return. So you'd always, if you have to choose between those two, you will choose the one on the risky, the one on the efficient frontier of risky assets. Or we can look at this asset, this asset and this portfolio here. Well, notice here, they both have 15 standard deviation, but this asset has a higher return. Or we can compare or we can compare this, this, this asset return to this point here. They both have the same return, 10%. This one on the frontier has a standard deviation, let's say of 13. And this one has a standard deviation of 22. Obviously you'll prefer this one. They both have the same return, but they have a lowest risk. So this is what we mean by the efficient frontier of risky asset. When you build the portfolio from these, all these assets, draw that weekend line, it's called the efficient frontier. Anything inside the line is considered suboptimal to the efficient, to the efficient frontier line. And anything outside here is considered impossible, giving the risk and return that we are, that we are giving. Now you have to understand on this efficient frontier line, there is the minimum variance portfolio. And this is the portfolio, this is the point where the portfolio has the minimum risk, which is 11%, 11%. This is the minimum risk portfolio. So this is where this, this point is the closest to the Y-axis, to the expected, to the expected return. It has the lowest risk. Kind of it's the safest investment. Now anything below this, notice these dotted blue lines here, you don't want to invest in here. You don't want to select anything in here because look, if you select any asset, any investment option here, if you compare it to here, if we're giving, let's assume, let's assume this is 14 standard deviation. If this is, oh, oh, let's say this is 13, let's assume this is 13 standard deviation. This one will give you a 7% return. This one will give you a 15% return. So really the efficient frontier is only, let me just highlight it in yellow. It's only this part here, this is the efficient frontier. Okay. So what else can we say about this efficient frontier? Remember, any investment on this line on the efficient frontier is acceptable. Now, maybe a young individual will choose this area here. High risk, high risk, high return. And another individual who's closer to retirement or the retire, they prefer this point here. They're both on the efficient frontier. So an old individual will invest in this portfolio. A young individual, they will invest in this portfolio, but they're both considered efficient frontier. Now, if we introduce the risk-free asset to the portfolio, and let's assume the risk-free asset is 4%, and we draw a line where this line called the capital allocation line tangently hit the efficient frontier at one point. Tangent, I mean, just imagine we hit it only in one point. This is the tangent line. This is the line where we have the highest sharp ratio. And what's the sharp ratio? Risk to return. You're getting the most return for your risk, the most return for your risk. So this is important. And this is considered the optimal portfolio, the optimal portfolio as well. So basically, we're looking at return, you put the basically risk premium, which is the expected return minus the risk-free asset divided by the standard deviation. This is the sharp ratio. And it exists when this capital allocation line tangently hit the efficient frontier, the highest means you're getting the most for your risk. This is where investors, they love this, they love this point here, because it gives them the highest return for the risk taking. Hopefully you have an idea about what the efficient frontier is. In the next session, we would look at a single index stock market and look at the variance characteristic of that. As always, I'm going to remind you to please like this recording. If you like it, share it. Don't forget to visit my website, farhatlatchers.com to supplement and compliment this course as well as your other courses. Good luck and study hard.