# Capital Asset Pricing Model (CAPM) Definition, Assumptions and Calculation

**Capital Asset Pricing Model (CAPM)**

**What is CAPM?****CAPM Assumptions****CAPM Formula****How to calculate CAPM?**

## Capital Asset Pricing Model

**CAPM stands for** Capital Asset Pricing Model. Capital Asset Pricing Model (CAPM) defines the relationship between risk and required returns in the security market and it is used in the pricing of risky securities.

## CAPM Model Assumptions

1. **Mean-Standard Deviation Analysis:** We started out by assuming that individual’s preferences can be represented in terms of the mean and standard deviation of returns.

2. **Investors’ Identical Believes:** All investors are rational, have identical subjective estimates of the means, the variances, and covariance of returns of all assets.

3. **Unlimited borrowing and lending:** All investors can borrow or lend an unlimited amount at an exogenously given risk-free rate of interest.

4. **Perfect markets:** Markets are friction-less and there are no transactions costs. All assets are perfectly divisible, perfectly liquid so that they can be sold immediately at the market price.

5.** Same after-tax returns:** Taxes must be such that after-tax returns ensure that everybody faces the same efficiency locus.

6. **Perfect Information:** All investors have access to same information and analyze the information in the same manner.

#### How to Calculate CAPM?

As an analyst, you could use CAPM to decide what price you should pay for a particular stock. If Stock A is riskier than Stock B, the price of Stock A should be lower to compensate investors for taking on the increased risk.

**CAPM Formula**

The **Capital Asset Pricing Model** is given below:

**ra = rrf + βa (rm-rrf)**

where:

• **rrf** = the rate of return on risk-free securities

• **rm** = market’s expected rate of return

• **βa** = beta of the asset

So let us start with the expression of the CAPM. The expression is the one that you see on the screen, and we are going to define what each of those things actually means. One the left-hand side, we have the required return on equity or the cost of equity. And you see that there are two subscripts there. The i is for any company, any company i. So if, if we look at two companies that i would go from one company to the other, Re as we said before, is the required return or the cost of equity. And the subscript i plays an important role. And we’ll clarify that in just a second. Now on the right-hand side, we have basically, what we need to calculate the cost of equity on the left-hand side. And what we need is Rf. And that stands for the Risk-Free Rate, we’ll get back to that in just a second. MRP and that stands for Market Risk Premium, which some people would call the Equity Risk Premium. Market Risk Premium and Equity Risk Premium, those two things are the same. And the last term is the beta. The same beta that we discussed in session two, is actually in session one. And we also talked a little bit about it in, in session two. It is the same beta that we talked about before, and we will have a couple of more things to say about it in just a minute. So, what is Rf? What, what is this risk-free rate? Well, the idea of the risk-free rate is, remember what we’re trying to calculate is a required return on equity, and what the risk-free rate basically tells you is the least that you would require to part with your money is, to get a compensation for the expected loss of purchasing power. Inflation erodes the purchasing power of your money. And you would not invest in anything, from which you would expect at least to be compensated for that expected loss of purchasing power. That is exactly what the risk-free rate is. If you actually look at the long-term short-term risk-free rate government bond yields, and inflation rate these two are very closely correlated. That means that the risk-free rate is simply a compensation not for bearing risk. But for the expected loss of projection power. Now you would say, and you would be right if you say, but wait a minute I am investing in a company, and, and a company is risky. I may lose my money. Well, that is why we have a second term. The second term if we put MRP times beta.

Together that is what we call the risk premium and the risk premium is well of course beyond, expecting compensation for the expected loss of purchasing power. If I am going to bear some risk, I want some extra compensation so the CAPM. Is basically a model that tells you, how you actually calculate the raised premium for a specific company. Now, what is the MRP times beta? Well, the MRP is the market risk premium, as we said before. And that is sort of a historical difference, between the return of the equity and the return of debt. And so year over year, you look at the return of equities in the market, you look at the return of government debt, and you subtract one from the other. And if you do that over, and over, and over, and over again, you can calculate in some sort of average of that. What is that average? Well, it gives you an idea. Of how much more return, have investors required from investing in equity than from investing in debt? And that number as we’ll see, you know, in the U.S. the typical number is somewhere between five and 6% and the typical interpretation is that. Historically people have required about five percent of or six percent more, to invest in equities as opposed to in investing risk free at government debt. That is what market risk premium is. But now you could say well but wait a minute. I am not investing just in equities. I am investing in this particular company, and that’s where beta actually comes in and that’s why, as you see, the beta has an i because now we’re talking about a specific company. And that company, remember what beta is all about. That company might magnify or mitigate, the markets fluctuation. So everything else equal. The more that a company magnifies market fluctuations, the more return that you are going to require. And the more a company mitigates market fluctuations, the less return that you’re going to require. Now look again at the expression, and notice that Rf and MRP, they don’t have a subscript i, that basically means that if you look at the cost of equity, of Oracle, Microsoft, Apple, GE, all those companies will, will be using the same Rf. And we will be using the same MRP. The only thing that is going to change as we go from company to company is the beta of the company, so on the right-hand side of the CAPM expression. What we have only one component that is a specific for the company that we are looking at. The other two are common to all the companies that we may be looking at. So at the end of the day, the CAPM is a very intuitive model that says, that the required return on putting your money in this specific company, is going to depend on, first requiring a return from not losing purchasing power, but on top of that, requiring a return from bearing risk. First of investing in equities and second from investing in the equity of this specific company, when you put all that together then you get the expression from the CAPM. Now this brief intuition of the CAPM that I just gave you very quickly is, is developed a little, a little bit more detail in one of the technical notes that is going to accompany this particular session. But you, you, you see where we’re going with this. What we are going to require in return. That the depends on not losing purchasing power, and depends on bearing risk. And that is what the CAPM is at the end of the day. Now, this seems to be very clear. And it seems that well it’s going to be easy to calculate this with a CAPM, because I just need to throw three numbers into that expression and I’m done. But as they say the devil is in the details once we ask the question. So what is RF? What is MRP, and what is beta that are very many different ways in which we. We, we, we could actually these numbers. That is where, remember from the very beginning of the session. When we said that there are some arguable issues. This is a very arguable one. And I’m going to show you some possibilities now. But, there are many different ways of thinking how, what number we can put into RF, what number we can put into MRP, and what number we can put into beta. Whereas, on the side of debt, the fact that we need to use the yield to maturity, as opposed to the interest rate. And that is one of those undisputable issues. Just about, everybody would agree that that is the way to go. Not everybody agrees on what the exact numbers that we need to be put on a CAPM expression. That is why this is just an article that was published in the Harvard Business Review not long ago and it is asking executives the question of, whether you know your cost of capital? And it is posing that question simply because, there so many uncertainties on the way of calculating. Not only the cost of capital, but also particularly the, the cost of equity. Just to give you a glimpse of this and I do not want to confuse you. Just want to give you an idea that this is less a stride forward than it seems to be. This is when you ask people around, again these are surveys of practitioners using the model. Look at the possibilities for the risk-free rate. Some people use gov, everybody uses government bonds. But the question is for how long, what is the maturity of those government bonds. So there you have a people that use three-month treasury bonds. Some other people that use one year, five years, ten years, 20 years, or 30 years. As you see, they are the most popular option with 46% of users, almost 50%. It is a ten-year bond. And that is typically indeed the most typical option. But as you see you know, there are people that actually beg to disagree. And there are people that use longer maturities, and people that use shorter maturities. That is what I mean. By saying well it is very easy to understand to rationalize what the risk-free rate means in the context of the require rate on an equity, and in the context of the CAPM, but it’s much more difficult to put a specific number to that most people would agree. That ten ten year bond yield to maturity is the number we should use, but, as you see many other people would use other possibilities. And again this is not to confuse you. This is just to show you that, that our differences of opinion and that this is much more arguable than many of the things that we discussed before. This is for the. Market risk premium or the equity risk premium. And as you see there these are specific number for the U.S. market. Let me make just a quick point here. When you look at different numbers, these numbers might change dramatically. In other words, remember what the market risk premium is. Is the extra compensation required by investors for investing in equity as opposed to investing risk free government debt? Well that extra compensation does not have to be the same across countries. And the data actually showed that maybe very different across countries. So the numbers that you’re seeing there are from the U.S. and as you see there, the range between five and six percent is very popular. About half the people, use that range. But as you also see, some people actually use higher numbers. And some people actually use lower numbers. Again. It’s very difficult to argue that you’re right and I’m wrong, depending on what our views are the only thing that we can do when it comes down to the CAPM, is just look at us. And see what people tend to do, what are the most popular options as opposed to saying this is the way it should go, and everything else is actually wrong. Finally on the beta, and, and beta remember this is, we need to look back to estimate beta. And one of the questions. There are many questions on the estimation of beta, but one of the questions is, so how many years are we going to go back? And as you see there, you know, the, the five year estimation period is very popular. But, it’s not the only one. Some people estimate betas with one year, some people with two years, some people with three years, and some people do something else altogether different, so again, five years seems to be a popular estimation period, but it doesn’t have to be and it’s not actually the only one. Where does five years come from? Well, some people will tell you, ideally we would like to go more years back to capture whether the company magnifies or mitigates other markets’ fluctuation. But here is where, you know, a practitioner can help you a little bit thinking about these issues. Because the company might have changed a lot over time, and if the company did change a lot over time, and you go back many, many years you are picking up information that is no longer relevant. Case in point think about telecommunication companies in Europe in the early nineties that was when all the telecommunications market was being deregulated. So if I had stood here in 1995, and I had looked at the beta of Deutsche Telekom, or France Telecom, or Telefonica Spain, and I would have gone back 20 or 30 years to calculate that beta. But, I would use that beat looking ahead than I would be basically picking up information that is totally relevant. Because 20, 30 years before 19 95 all the telecommunications companies were monopolies, were a state owned, they had only one product. And back in 1995, and looking ahead then, the, the business changed completely. There was competition, there was different lines of business with cellular phones and so forth, and so, you know, if you go many years back, you’ll run the risk of picking up a lot of information that data, that is no longer relevant when you start looking ahead. And at the end of the day we always want to look ahead. Now the, the other alternative is to look just a little bit back. But of course, the problem with looking just a little bit back with a few months, or one year, or maybe even two, the problem is that the company might have done spectacularly well or spectacularly awful. And you don’t want to actually take that little bit of information and predict it maybe five, ten, 15, 20 years forward. Therefore, you know, between not going too far back, and not going too little back appears this sort of compromise of going back five years, and that is why it is a popular option. Now all that being said, what is important about these graphs that I just showed you, is that there are differences of opinion. Not everybody agrees, on what is the best way to estimate a risk free rate, a market risk premium, and a beta. Now we have one final thing and we are done. Then we will actually get to on the next session to to estimate an actual cost of capital, but remember. We call it technically the weighted average cost of capital, and that means that we need to take into account the proportions. How much we are using each of the different sources of financing. How much debt we are using, and how much equity we are using? And those proportions are the one that in terms of notation we said before that we’re going to denote with x. So xD is a proportion of debt. xE is the proportion of, of equity. And remember we’re also calling D and E stand for debt and equity. So xD and xE, if there are the only two sources of financing that a company’s going to use, if we use part of debt and part of equity, when we put them together, that’s all the capital that we have to invest. In other words, we are mathematically putting that, is that xD plus xE must be equal to 1. And so the question now is a question of proportions. Of all my capital, what proportion I am using in terms of debt, and what proportion I am using in terms of In terms of equity. So these are very simple definitions. D divided D plus E is xD. E divided D plus E is xE. And the sum of these two things must be equal to 1. And then we’re going to put specific numbers, in the next session to these two proportions. One final thing and we will be done with this. Sometimes a question comes up, what type of debt we need to consider? And here this is more or less quote unquote undisputable. That most of the time we do not look at short term debt. We do not look at the debt that a company uses to run the day-to-day operations. We are looking when we estimate the cost of capital; we are looking at long-term debt, the debt that we will raise in order to make long-term investments. And sometimes that’s not exactly, I mean, there’s sort of a gray line here. But typically that is interest bearing debt. So some people would tell you, well what you need to take into account is interest bearing debt. What you need to take into account is long-term debt. Most of the time these two things are the same. There may be some examples, or some specific cases in which that is not the case. But debt for which we pay a, a specific interest. A, an explicit interest. And long term debt. These two things actually have a lot of overlapping, and that is the type of debt that we consider to estimate the cost of capital. Final thing and we will go back to this, when we estimate the numbers in session four. Now we could use book values or market values to calculate the proportions of debt and equity. How much debt, how much equity, and what proportions we have? Well typically here that is one of those sort of almost undisputed issues that we need to use market values as opposed to book values. And if you think for a minute. About what we discussed about the cost of debt you realize why. And if, if you remember the market prices that people are willing to pay for those bonds fluctuate with the riskiness of the company. So if we want to properly reflect, how much we have capital in terms of capital invested today, that is going to be depending on market values as opposed to book values. In other words, if I wanted to get rid of my debt by buying the debt in the market, then what I pay in the market is the market value, and is not the book value of the debt. So because the market value, is the one that is going to reflect everything we know about the company today, when we calculate how much debt we have, how much equity we have and the proportions of the two, we use market values not book values. So, this is just about it for session three. We are going to, before we start session four, we are going to do a little review of the main concepts that we have discussed today and then we are going to jump right on, and estimate the cost of capital of Starbucks by the end of the year 2030.

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