 Hello, and welcome to this session. This is Professor Farhad in which we would look at an example for a regression line using a single index stock market model. It doesn't matter whether we are using a single index stock market model or some other model. You'll be able to understand the single regression line. This topic is covered on the CFA exam, as well as the CPA exam BEC section, also covered in an essentials or principles of investment course, whether graduate or undergraduate. 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 1,800 plus accounting, auditing, tax, finance, as well as Excel tutorial. If you like my lectures, please like them, share them, put them in playlist. If they benefit you, it means they might benefit other people and connect with me on insti.gram. On my website, farhadlectures.com, you will find additional resources to supplement this course, as well as your other accounting and finance courses, as well as your professional certifications. I strongly suggest you check out my website. So what we're going to do, we're going to look at a regression output first, answer some questions, then we're going to run our own regression output, then answer some questions. In this way, we would learn what our regression line looks like and learn a little bit more about this process. So first thing is they're asking us, what is the regression line for XYZ company? Well, we don't have the information for stock XYZ, we have the information for ABC company. So let's take a look at the output for ABC company. This is the regression output. So first, what's the regression line for ABC? We're going to run XYZ later, shortly. So when we run the regression, we're going to have this output. Remember, the regression line, if you remember from the formula is, it's going to be alpha plus beta times the risk premium plus EFI, the residual risk that's the firm risk. Now, what is alpha? Alpha is the intercept. What's the intercept here? It's positive, it's 0.34%. So the coefficient is the alpha, so it's 0.34%. So it's less than 1%, 0.34, which is 0.003. I'm just going to put it at 0.34%. Plus the market index, the beta is 0.525, times the access return, yeah, the access return or the risk premium on the market for stock, for stock ABC, for stock ABC. So basically, we can take any of these numbers, plug them here and we'll find the expected return for the expected return for ABC company. So this is the regression line for ABC. Now, what we need to do, we need to run the regression line for X, Y, Z. So we are giving the data, we are giving the access return for X, Y, Z right here. So this is going to be the Y access and we are giving the market index, which is this is going to be the independent, the X access. So what I did, I took those two column, I'm going to transfer them to an Excel sheet, I already did and I'm going to run the regression, then we're going to have an output that's similar to this one, then we're going to compare and try to answer the questions, which of these companies, ABC or X, Y, Z, will have a greater, what's called systematic risk and which one will have less systematic risk. So I'm going to go ahead and switch to Excel to run the regression. So this is the data, this is the market index data, this is the stock X, Y, Z data and I will upload this Excel sheet to my website so you can access it if you want to. So I'm going to highlight this, go to data analysis and I'm going to, if you don't have data analysis, you've got to learn how to download the data analysis tool pack, just type for had data analysis tool pack and I will show you how to do it. I don't want to show you how in this session. So I'm going to click regression and we just make sure I have the Y access or these. Yes. So here's what's going to happen. Let me go ahead or remove everything. So you see what I'm doing. Okay, let me remove this. Okay. So you have the Y access, the Y access is the stock price and I'm going to include stock X, Y, Z, the X access is the independent variable is the market. So I have the label and I'm going to do the line fit plot. That's all what I'm going to do. I'm going to click on okay and I'm going to have this output. Yes, I'm going to have this output. Now I'm going to switch back to the Excel sheet because already I'm going to copy this output, put it on the Excel sheet. I meant to say I'm going to copy the Excel sheet to the PowerPoint slides, but here's the Excel sheet. Now here's the intercept, the coefficient for this X, Y, Z, the coefficient for X, Y, Z is 0.008 or 0.83%. If we're talking about percentages or 0.0083, this is the coefficient. So this is the regression line because the question is asking us, what is the regression line for X, Y, Z, plus the beta is 0.9914. So 0.9914 times the risk premium of the stock. So this is the regression line for X, Y, Z stock. The regression line for ABC was 0.34 plus 0.52. So it's 0.34% plus 0.525 times the risk premium. So this is X, Y, Z, and this is ABC. Now we are ready to compare and answer the question and the question is, does ABC or X, Y, Z have a greater systematic risk? Greater systematic risk. Which one has a greater systematic risk? Simply put, which one has more market risk? Well, which one will move more with the market? Remember, the market index is beta. And what does that mean? Now we need to understand beta in order to answer this question. Beta means the beta for the whole market is one. So closer the one you are, the more your stock moves with the market. So notice, X, Y, Z is almost one. X, Y, Z, beta is almost one. What does that mean? It means simply put, X, Y, Z works almost, almost. I'm not gonna say one, but almost directly with the market. So when the market goes up one point, X, Y, Z goes up 0.99. When the market goes down one point, it goes down 0.99. Let's say one, okay? Just to illustrate the point. So I would say X, Y, Z has a more systematic risk, greater systematic risk. ABC company, ABC company, their beta is 0.52, 50%. What does that mean? It means ABC company, when the market moves one point, they move half a point. When the market moves up or down, they'll move half a point. So they have less systematic risk. They have less market risk. So this is how we were able to answer the questions, whether we have greater systematic risk or less systematic risk. We measure this by the market index or beta. So this is beta and this is alpha. Alpha is the Y intercept, beta is the market index. Now, the third question is, what proportion of the variance of X, Y, Z is firm specific? Now, how do we find whether something is firm specific or how do we find the variance of a stock to find, what proportion of the variance of the stock is firm specific? How do we find this? We find this by examining the R square, R square. So let's first examine the R square for ABC company. So, whoops, the R square for ABC company, the R square for ABC company is 0.25. What does it mean? It's 0.25. If it's 0.25, it means approximately 0.75. 0.75 is firm specific. 0.75 is firm specific. So that's for ABC company. Yeah, that's for ABC company. And kind of for me, it makes sense because ABC company is not affected by the market. Notice the market is only 0.52. They only move half a point when the market moves. So it must be, if that's the case, then what really moves ABC stock is firm specific. Let's take a look at X, Y, Z. X, Y, Z with R square, okay. X, Y, Z, R square is 0.844. Well, it means the firm specific factor is only 0.55, around 15%, because if this is 85, what's left is this is 15%. Well, this kind of, this makes sense to me, but it doesn't have to, but it makes sense because X, Y, Z, we said it moves with the market. It means the firm specific is not that high. It's not that high, okay? It's not that high. So to answer the question is, what proportion of the variance of X, Y, Z is firm specific, only 15% is firm specific, only 15%. Why? Because look, the remainder is, they work with the market almost 100%. Now, also it's very important to see what the line looks like for X, Y, Z company. This is what the line would look like for ABC company. This is like the middle line, because I asked Excel to provide this for me. And notice the return for X, Y, Z lies around. And some of them, they're even like right on the line, like this point is on the line, this point is almost on the line, this point on the line. So they work directly with the market. Now, if we plot, I should have, but I did not, if we draw a plot for ABC, ABC it would look something like this. The points will be a little bit far away from the center, from the center because they are not closer to the center because the firm is, the firm risk is more, is firm specific, not based on the market. So hopefully by answering these questions and working this example, you'll have a better idea how this work, how the regression line, you wanna make sure you're comfortable by reading the formula. And I did have, I did explain the stock market index model, if that helps go back and view that recording as well. In the next session, I'm gonna start to introduce the idea of CAPM, the capital asset pricing model. Always I'm gonna ask you to like this recording if you like it, share it. And if you're still listening, I appreciate it. It means you really like this recording. And don't forget to visit my website for additional resources for this course as well as your accounting and finance courses. Good luck, study hard and stay safe.