 Hello and welcome to the session. This is Professor Farhad in which we would look at a single index stock market model This topic is covered on the CFA exam as well as essentials of investments I'm gonna try to keep the Statistics out of this as much as possible when I explain this model as always I would like to remind you to connect with me only then 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 course as well as your other accounting and finance courses I strongly suggest you check out my website. First, we need to do a quick review You just want to make sure we know the difference between systematic and firm risk because we need to use those terms in this session systematic risk Systematic risk is the macroeconomic risk that's affecting all securities not a particular company and not a particular product It's affecting the whole economy inflation interest rate the Federal Reserve so on and so forth firm Specific risk in contrast to the systematic risk it affect only one particular company or one particular firm or at most maybe a cluster of firms For example software companies now the index model that we're gonna be working with today. What is that? It's a basically a statistical model designed to estimate These two component which are what are those two component the systematic risk Which is the broad market risk and the firm specific risk as to relate to a particular security or portfolio So we're going to look at this model as a way to Study the relationship between a particular stock or portfolio and those two Risks systematic risk and firm specific risk. So why do we use this index model? Why don't we use morco? It's well, there's a reason why because of its practicality and we're going to explain this in a moment To construct an efficient frontier, which is we talked about the efficient frontier in the prior session From a universe of 100 securities only we need to estimate 100 expected return because we need to we need to figure out the return We need to figure out the variances and we need to figure out Obviously the most important is how did they interlate with each other the covariances? So we need basically 4950 covariances alone and we're only talking about 100 security. So if we are dealing with 1000 securities What's going to happen? We need to compute almost half a million variances 1000 expected return and 1000 different Factors, so that's that's that's that's impractical So the index model asserts that one common systematic factor Which is a market factor is responsible for all the co-variability of the stock return With all other variability due to a due to firm specific factors So what we're saying in this model look how a stock return varies It's we can measure this by Study in the relationship between that stock and the market itself rather than studying the stock All the variability but among the stocks just let's look at this stock and how does it vary within the market? So this assumption dramatically simplifies the analysis of what we are trying what we are trying to do So i'm going to try to illustrate this concept by looking at this diagram and going through the equation So again, i'm going to try to keep the statistics out of this as much as Possible as much as possible. So here we're looking at this diagram And each dot there's a 60 of them a few count them represent the monthly access return of five years for Ford Motor Company And what we have in addition to that we have the Access monthly market index. So this is the market index right here the x-axis And we have the access monthly return on ford on the y-axis Now how first of all, how do we read those dots because we have 60 of them? For example, if we take this dot january 2020 the return for Ford Motor Company because the return for Ford Motor Company on the y-axis is 15 0.9 percent. That's the Ford Motor Company And the market return for that month was 5.4 So this is where this point intercept 5.4 on the market. Let's assume the market the s&p 500 And 15.9, which is let's say 16 percent. So january 20 seconds. So this is how we read those returns So so basically you could look at this return this return this return so on and so forth now What else do we need to know? What else do we need to know is this? the The line this line right here line of best fit this line and we're going to talk about how we draw this line later This line supposedly passes in the middle of all these dots. So it is in the middle So this this line is the the line of best fit like in the middle of all these dots Okay, now this is a regression line And what does it show if you know anything about regression? We saw a positive relationship between Ford and the market I mean we can look at just look at the Look at the scattered and we see that as As we have more return as we have more return as we have more return for the market We have more return for Ford motor stocks. It means there's a positive relationship now. We're going to measure this positive relationship We're going to measure it and you look at the equation, but that's the first thing you want to know And also we have you remember every time we have a line we can we can show that we can compute the slope of the line And what's the slope of the line? Rise over run or rise over run So you could also compute the slope of the line. It reflects the sensitivity of Ford return to the market how much Ford changes with every one percent of change in the market again We're going to look at actual numbers, but this is what we can do from this information. Okay now Notice these points are scattered all over. Okay Now the more scattered they are so if they are scattered all over the place if they were scattered more than this Then what we can say is there is no relationship between Ford and the market So the more the closer they are to this line And if they all if they are if all these dots are on this line, what does that mean? Let's assume that all are on this line Okay, so it means with for example, this is two percent market return. Maybe this is two percent ford five percent five percent notice 10 percent 10 percent of all these dots so the closer to the dot it means there is a perfect relationship So in other words ford and ford motor company and the stock market or whatever market We are using as as as a proxy of the market. They work hand in hand the more scattered they are Okay, it means Ford has firm specific condition that explain the stock not the market So hopefully this is the overall picture now We're going to look at specifically about the equation that form this line and understand the component of it So let's take a look at it. Take a look at this. So how do we how we might determine the line of best fit? Well, we estimate the line using a single variable linear regression using this formula Now we need to explain everything in this formula So the return is a function of the alpha of i Plus the beta of i plus the risk premium for that particular period plus E of i and we're going to explain each one of them separately starting with rm this function here We use r of i to to donate the excess return. So the market index m has an excess return Which is the basically the risk premium. What's the risk premium? It's the risk the return on ford minus the risk free rate This is the risk premium for if we're looking at ford security. So this is this one here Okay, this one here alpha. What is alpha? This is alpha alpha of i alpha of i is the intercept of the equation You know, it's alpha of y and what's the intercept of the equation? This is so you can see it. Hopefully i'm sure you know what the intercept of the equation This is the intercept of the equation where this line hits the y axis and it's going to be negative point Approximately negative point nine, but this is what the alpha intercept is. What does it represent? It represent the security's expected return when the market access return Equal to zero think about it when this is when if this equal to zero if you take zero times beta even though You don't know what beta is this is going to give you zero. So simply put alpha alpha tells you what is the return On this stock. What's the return on ford motor stock if the access return is zero that means We cannot have any risk premium To can we still have some sort of return for this for the stock? So can be thought of as the expected return on the stock and access of the treasury rate above the risk free rate Beyond any return beyond above any return induced by movement in the broad market So simply put you want this to be if this is positive if this is positive That's good. Why good positive because what we're saying is although you have no And no access return because this is zero you still have some return The stock still earns something even without the risk premium Okay, so investors naturally will be attracted to stocks with positive value of alpha It implies a higher average access return without the cost of any additional exposure to the market So simply put you're gonna you're gonna earn you're gonna you have a return Even without any exposure to the market. So that's why you want this alpha to be positive So investors would always look at alpha but alpha overall in the market If we compute all the alphas from different people the the alpha market is zero Now, let's take a look at beta. So let's take a look at this function here beta Beta is the slope of the line beta is the slope of the line, which is again rise Over run. Hopefully we all know what how to compute the slope of the line It's the amount by which the security return tend to increase or decrease increase or decrease for every 1% increase or decrease And return on the index and therefore measure the security sensitivity to the market wide economic shocks Simply put when the market goes up 1% what happened to your stock when the market goes down 1% what happened to your stock So this beta Measures it so it's it's the beta is the natural measure It is a natural measure of the systematic of the market risk. How does the market risk affect your stock? What's the relationship between the two and the term is e of i at you know at monthly It's the firm specific surprise in the security return in the monthly. It's often called the residual Basically, this is the risk that's specific to the company itself Think about it. This is we said this is the market risk And this is gonna be the firm risk Okay So the greater the residual positive or negative the the wider is the scatter of the return around this straight line So if you have if you have greater residual risk Okay, the the numbers will be scattered. Why it means if you have a greater residual risk It means the this firm this firm risk is not based on the market This if this number is large at positive or negative it's based on the firm itself Therefore, it's not explained by the market and that's what we have to measure when we get the numbers We're gonna see the measurement of the numbers. Is it explained by the market or is it explained by the firm? This scatter reflect the impact of firm specific or what we call residual risk now Remember both residual risk and systematic risk both of the market and residual Contribute to the volatility of the return. Of course, that's the case, you know the stock your stock is Is dependent upon the volatility of the market as well as the volatility of the company itself of the of the news of the company itself So let's talk about this line and call it now the security characteristic line This is the line that we draw plot of the security is predicted access return given the access return of the market This is the return and for Ford Motor Company. What we have is Alpha is 0.98 percent, which is negative beta is 1.32 now. We need to know The risk premium plus This residual so this is what we can find out So to look at the security characteristic line It tells us on average that ford stock roses an additional 1.32 percent for every 1 percent in the market So 1.32 it means for every 1.32 percent it goes up for one for every 1 percent change in the market Ford will go up 1.32 percent. That's what it's that's what this beta is telling us If we take these numbers and plug the january in january when the market access return Was 5.4 so this is the market we would have predicted ford return to be negative 9.8 plus 1.32 times 5.4 percent which is equal to we would expect ford to have a return of 6.2 But ford had a return of 15.9 again. This is a formula What does that mean? It means the difference between what we expected and 15.9 Resulting in the residual In a large positive residual return of 9.7 so in this for the month of for the month of January we had a positive Residual return it means in january the stock was not influenced by the market The stock was influenced by factors maybe ford reported good numbers while the market wasn't doing well This is what we can this is how we can interpret this if we go back here and look at this number here And we notice let's take a look graphically at it because it's very important. We see it's far away It's far away from the market. Do you see this now if we compute if we compute for this number It's going to be closer So if we compute this number the residual Will be lower if we compute this number the residual will be close to zero for these numbers What does it mean residual close to zero? It means That that for that particular month Ford return was exactly Explain 100% if it's zero by the market return. There is no residual It means if if the market went up 3% if the market was up 4% the return for Ford was 4% do you see this it will be the same So the closer to the line those points are the closer to the line. It means they are the Systematic factors explain Ford's stock not firm specific and the wider they are From the line for those particular period It means there was something specific the Ford Motor Company There was something specific the Ford Motor Company that affected the stock price not not the market It's not explained by the market So this is this is this whole thing about this index model is to just show you the difference between those two Factors between those two factors So let's talk a little bit more about beta The average beta of all stocks in the economy is one the average response think about it If all the stocks are combined together and we compute a beta They all work the same like I mean they they cancel each other out The average response of the stock to changes of the market index composed of all the stocks is one to one If we combine everything so the beta of the market index is by definition one So what does that mean? It means when you compute your beta you can you compare your beta to one if your beta is one It means your stock works Perfectly with the market if your beta is higher than one. It's more It goes it's more it's on average It's more sensitive to the market if it's less it goes less than one It means it is it's a defensive stock So cyclical or aggressive stocks have higher than average sensitivity to the broad economy and therefore they will have a beta greater than one So they are on average. They have a lot of sensitivity The the market moves one point. They move 1.5. They move 1.7 Defensive stocks, they will have a beta less than one So the return on so when the market goes up one they go up by 0.75 They go up by 0.3 Now the best way is to show you actual beta because once you see the actual beta Hopefully it will make sense to you So if we look at the beta for amazon, and this is uh, what's the day's data at closing date august 7th The beta for amazon is 1.33. What does that mean? It means amazon moves More than the market now this is up and down when the market goes down. Also, it's going to move down 1.33 That's the relationship between beta amazon and the market if we look at walmart walmart for the same date The beta is 0.32. It means walmart doesn't move because walmart Comparing to amazon walmart is considered a defensive stock amazon. I don't know what it's considered technology stock E-commerce. I don't know amazon is basically everything. Okay, but it's definitely cyclical aggressive In comparison, hopefully we can all see this to walmart and beta clearly shows it now How do we compute this beta notice here? They took five years of data and they compare amazon to some index I don't know what the index is they could compare it to s and p 500 nasdaq I don't know they ended they did the same thing for walmart So this is how they computed beta and this is what they find out walmart doesn't move as aggressively as As as amazon and hopefully this makes sense The other thing we want to learn is about the variance because the firm specific component of the stock return is uncolorated unc Correlated with the market return We can write the variance of the access return as the stock s follow Basically, it's the variance of that formula except that basically alpha doesn't have a variance So what we're left with is the variance of the market Which is the systematic risk in the variance of the firm specific and I told you the total variance is the variance of The market plus the variance of the So why would your stock varies well because of market conditions or firm specific conditions? That's basically it therefore the total variance of the rate of return for each security is the sum of two Component what are those two component the variance attributed to the uncertainty of the entire market? Which is this component here, which is the systematic market? That's the systematic risk that's measured by the beta Measured by the beta and the risk premium and the variance of the form specific firm specific Which is the independent of market performance One more thing we could compute is r square and hopefully we all know what r square is is the correlation coefficient between the market And the stock return and this is a good measurement of how you know How can we explain the market versus the the firm specific? The dispersion of the scattered of the actual return About the regression line is measured by the variance of the residual So this is basically this shows us the magnitude of the firm specific risk And because they vary across different securities So one way to measure this is the relative importance of the systematic risk Is to measure the ratio of systematic variance to total variance remember what is total variance? Total variance. This is total variance systematic risk and firm risk So what we need what we need to know now is how much is the systematic risk in relationship to total variance? What we do is we take systematic risk And we divide systematic risk by the total risk, which is the variance the variance is Same thing as total risk and this is basically r square. So how much How much market risk explained the total risk? How much of the market risk explained the total risk? That's basically what we're saying explained risk, which is Systematic risk divided by the total variance now you could look you can look at the statistical formula But again, I'm going to try to keep stay away from those If r square equal to 1 it means there are no firm specific variants It means all the variance. So if we have a variance of 100 We have systematic risk of 100 100 divided by 100 equal to 1 So if we have r square of 1 and r square would goes from negative 1 to 1 by the way So if that's the case, it means this stock is works perfectly with the market It's all the risk is explained by the market. So the market explained the variance Low r square. It means market plays an unimportant role in explaining the variance and if we look at the the Ford the Ford stock in the january 2002 We can see if we computed most likely the the r square. It will be a low r square So the variance is firm specific the variance the risk is Because low r square. It means firm specific specific Let's assume an r square for a particular company is 0.3 for abc company It means 0.7 0.7 of abc is firm specific variance 0.7 If for example another company has an r square of 0.85 It means only 0.15 Is firm specific variance firm specific variance So which one is which one works more closely with the market? Obviously xyz more work Would work or based on statistical data or based on historical data Will match the market performance very much more much more closely In the next session we would look at an example that deals with a single index stock market As always if you like this recording, please like it and share it And I would like to remind you to visit my website farhatlectures.com If you are looking for additional resources to supplement or complement the scores Good luck and study hard