# Capital Asset Pricing Model (CAPM) – Part 2 (Equation)

This video dives deep into understanding the CAPM. Enjoy!

VIDEO SUMMARY

In this video we are going to continue our discussion of the capital asset pricing model. We are going to walk through the equation twice. The first time we are going to do a general overview to give you a sense of what this equation is about. The second time we are going to dig deep into what these variables mean.

We are going to start by looking at the first variable. This is the return of your investment and this is what we are trying to solve for. The key to remember here is that risk and return are related concepts. You are trying to determine what return you should expect to receive to be compensated for holding this risk. What we are really dealing with is risk rates.

The next variable is the risk-free rate. This is the rate for the most risk-free asset available in the market. If you go out into the market and you say “I’m going to buy the investment that is the most risk-averse investment out there” you get some return. That is your benchmark. Any other opportunity is going to be some premium above that benchmark.

To the risk-free rate, you are going to add the market risk premium. The market risk premium tells you how much riskier the market is over the risk-free rate. If you are investing in a stock market index fund that represents the overall market, the market risk premium tells you how much riskier that is over the risk-free alternative.

Ultimately, we are not interested in the overall market. We are interested in the individual opportunity. For that, we are going to look at the beta of our investment. Beta compares the variability of your individual opportunity versus the overall market. So if we are looking at stocks, we are going to say, “My company has a variability that is going to be greater than the market or less than the market” If it was the same as the market, you would get a beta of 1.0. That means you would expect it to follow the market or perform similar to a market index fund. If it is riskier than the market you would expect a beta higher than 1.0 and this means it would fluctuate greater than the market beta. Beta less than 1.0 means it would be less variable than the market.

In this equation, we are starting with the risk-free rate. We are adding the market risk premium which we are multiplying by the beta of your investment and this tells us how much we should be compensated for the risk we are holding for this individual investment.

So why do we calculate risk this way? I have to say, this equation is genius. This is genius because what it does is it acknowledges that the financial world is interrelated. So we are not just taking our individual investment opportunity and considering it by itself and saying this is how risky the investment is. It compares the riskiness of your investment versus the market, which is compared to the risk-free rate. So you are saying it is all interrelated and the reason why this is important is… let us say you have invested in a stock. And let us say the overall market does really well this year. Well if you have a riskier investment than the market, you should have expected even greater variability than the market. So for holding that risk you should have achieved a higher return than the market. If you did not, you need to look at that investment because you might not be compensated for the risk that you took on. The reason why that is, is because you know the market generally does well in times of economic prosperity. Good economies lead to better profits for businesses that lead to higher stock prices. So in this time of good economic activity, why didn’t the company stock for your individual investment perform accordingly? This equation is acknowledging that everything is interrelated in this economic sense.

Let us go back to the equation again and really look at these variables. What I want you to understand is the assumptions we are making. Because we are making some pretty significant assumptions. We start with the risk-free rate. The risk-free rate presents us with an interesting question. What is the actual rate that we plug in to the equation? Most people take guidance by looking at the US Treasury. They consider that the least risky alternative out there. But even if you use that assumption, the US Treasury is a market that fluctuates over time. So in that range of numbers, what is the actual number you should use? Not only that, what we are really wanting here is we are wanting the “future” risk-free rate. So we are going to perform some historical analysis, but we are going to use that to inform our decision of where we think risk-free rates will be in the future. That is a huge assumption.

Next we look at the market risk premium. Here again you have the same issue. You know you can do an analysis and look at market rates over time. But history is no guarantee of what is going to happen in the future. You have to make a judgment call to say what you think the market risk premium will be in the future. That is an assumption. But that is not the only assumption we are making here. The other big assumption is deciding what the market is. Are we going to use as the market an individual sector? Are we going to use the overall stock market? Are we going to use the NASDAQ? The S&P 500? The DOW? US stocks? World stocks? There are a lot of assumptions that are made just determining the market.

Then you have beta. Now beta is a whole lot of assumptions by itself. We said that beta is the variability from the individual stock opportunity versus the market. We calculate that out using a regression analysis. A regression analysis is you take two columns of numbers. In one column, you have the daily changes in stock price for the individual stock and in the second column, you have the daily changes in stock price for the market. Then you can compare the two and you can say statistically what the variability is. Greater variability than the market is higher than 1.0. Lower than the market is less than 1.0. Well we have the problem again of history versus the future. You need to take your beta and then make a determination whether your beta is going to be staying the same in the future. Not only that, we are making an assumption based on what period of time we are looking at. Are we going back and looking at stock prices over the last five years, or over the last 25 years. It makes a difference. It is interesting if you go to different financial websites, you will get different results for beta for the same stock. It is because people are using slightly different assumptions and they are generally pretty close.

It is important to realize what assumptions you are making when you are using this formula. You might be asking yourself, “if there is so many assumption, how is this even useful?” What happens in a practical sense, is you sit down and you do a lot of analysis. You do a lot of hard work going through mountains of data and you start to get a sense of your market. You start to get a sense of what are reasonable values that you can plug in to the equation.

I would like to do an example where we are actually plugging in values into the equation. I am going to use some numbers, and these are just hypothetical numbers. We are going to use 4 percent for the risk-free rate. We will use 8 percent for the market risk premium. We will use 2.0 for beta. Starting with the risk-free rate of 4% tells us the risk-free alternative, our benchmark, would be that we should expect a return of 4%. When we add the market premium, that is 8 plus 4 equals 12. So for an investment in the market index we should expect a return of 12%. Now when we multiply by the beta which is 2.0, we get 16 plus 4 equals a return of 20%. That is pretty high. That is a pretty risky investment, but we should be expecting a pretty high return to be compensated for holding that risk. So if we invested \$100 in this risk at 20%, we should be expecting a return of 120.

I would like to take a step back and think about what we are accomplishing here with the capital asset pricing model. This is really a process for making good financial decisions. It might be a business decision or an investment decision. But we are making some decision about some assumption we have about a future opportunity. That future cash we expect to receive, we are going to discount by some assessment of the risk involved. We can get this understanding of the risk involved by using some process like the capital asset pricing model and comparing the risk of individual opportunities versus the riskiness of the market compared to the risk-free rate. As a business person, the better you can get at going through this process and being really thoughtful about your assumptions, the better your financial outcomes will be.

Neither Zach De Gregorio or Wolves and Finance Inc. shall be liable for any damages related to information in this video. It is recommended you contact a CPA in your area for business advice.

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