## Calculating Value-Step 1: Calculate the Capital Asset Pricing Model (CAPM) (Post 5)

The first step in determining a company’s fair price is to calculate the Capital Asset Pricing Model (CAPM). Before you get scared of this term and run away I should tell you that it is a very simple calculation that requires easily accessible numbers.

Before I show you how to calculate the CAPM I want to give you a bit of history on its origins and some theory behind it; this will help you to better understand what it is and why it’s important.

The CAPM was developed by William F. Sharpe way back in 1964 as his dissertation research for his PhD. He demonstrated in his research that a stock portfolio’s risk can be broken into two parts. The first is unsystematic risk or diversifiable risk which is measured by alpha. This risk is business specific; meaning it is specific to the company in question. A portfolio can diversify away from this risk by diversifying the holdings in the portfolio and can effectively reduce unsystematic risk to zero.

The second type of risk is systematic risk or non-diversifiable risk which is measured by beta. Beta is the market risk which a portfolio cannot diversify away from since it affects the market as a whole. These risks include such things as interest rates and inflation risk. Since alpha can be reduced to zero, he decided that the only relevant risk is Beta.

From this conclusion he discovered an equation called the Capital Asset Pricing Model that measures quantitatively the amount of return that a portfolio must earn in order to fairly compensate the investor for the risk incurred.

So your first step is to calculate the amount of return you must earn for the level of risk you are undertaking.

Here is the exact formula to calculate the CAPM. I will be explaining this formula one step at a time until you understand how it is calculated.

CAPM: Required Return= Rf + [Beta * (Expected Market Return – Rf)]

Rf= Risk free rate of return

Beta=Market risk as it pertains to the stock

Expected Market Return=Overall expected market return

**Risk free rate of return**

This number is a percentage derived from a “risk-free” investment, ie: if you were to invest your money into a risk free asset what would your return be? Your next question is probably what is considered a risk free investment? The answer: US Treasury bills. As you know there is theoretically no such thing as a risk free investment, but for the most realistic assumption that we can make US T-Bills are our best bet. Historically for calculating the risk free rate for the CAPM we have used the 3-year yield on US T-bills. Conditions have drastically changed over the past decade and the current yield on 3-year T-bills is too low for a realistic calculation of the CAPM. Instead we use the 10-Year T-Bill. For the most part we want the risk free rate to be around 2% for a realistic calculation.

So where do we get this number?

Go to Google and type in the search phrase “10 year treasury bill”. The first link should be www.treasury.gov which will take you directly to the table of treasury bills. Look under the “10 Yr” column. The default setting on the time period is going to be the current month’s rates.

Take the most recent percentage as this is updated daily

**BETA**

As I mentioned earlier Beta is market risk as it pertains to the individual stock that you are analyzing. In more specific terms Beta measures a stocks’ sensitivity to market conditions. The higher the Beta the more sensitive the stock is to changes in overall market conditions and vice versa. Finding Beta on a stock is very simple. Almost any website that has the option to enter a ticker symbol will display the stock’s Beta in the profile. If you go to Yahoo! Finance and type in any ticker symbol the Beta will be displayed in the profile. Here is YHOO’s stock profile.

**Expected Market Return (EMR)**

Finally we need to get the Expected Market Return (EMR). This might trouble some of you who are thinking you can’t estimate the expected market return. The good news is that you don’t have to. We will be using the historical average percentage return over the past 20 something years. Calculating the expected market return for a given year is somewhat very difficult if not impossible. I have found that the best and most accurate number to put in our CAPM calculation should come from many years being averaged out. What you will be doing to get this number is downloading a spreadsheet directly from the S&P website.

1) Go to the Standard and Poor’s website at www.standardandpoors.com

2) From the homepage, click on “S&P Indices” (You will be redirected to the S&P indices site)

3) On the homepage of the indices site you will see 4 featured indices, and one of them should be the S&P 500. Click on the white lettering where it says “S&P 500”

4) This will take you to the S&P 500 page. You will look to left hand side and hover your mouse on the drop down arrow of “Additional info”

5) This will give you drop down options and you will click on the link “Monthly and Annual Returns”

6) This will open the download for an excel spreadsheet. Download and open the spreadsheet

7) Click on the “Annual Total Returns” sheet in the bottom left corner of the spreadsheet

8) From this sheet we are going to get the number that we need. Select all the numbers under the column “TOTAL RETURN CHANGE” Select only the numbers and not the actual heading

9) You want the average of all these numbers. If you are using the latest version of excel you should have the average of the range displayed in the bottom right corner.

If you don’t then you can just use an average function. =AVERAGE (select range).

You get the idea; you just need the average of all the numbers under that column. How you calculate them is up to you. This percentage will be your expected market return

That is how we get these numbers. The next step is what we actually do with them….

**Putting the numbers to work**

Before you put any of these above numbers into your formula you first have to change all of your percentages into decimals (change Rf and EMR to a decimal). This is easy to do; just divide the number by 100 and it will convert it into a decimal instead of a percentage.

Examples:

10.45%=10.45/100=0.1045

1.86%=1.86/100=0.0186

12%=12/100=0.12

2.01%=2.01/100=0.0201

How it all comes together….

For this example I am going to use the following numbers:

Rf=1.98%

Expected market return=11.28%

Beta=1.11

The first thing I have to do is change Rf and EMR from percentages into decimals:

Rf=1.98/100=0.0198

EMR=11.28/100=0.1128

The next thing to do is to plug these numbers into our formula

CAPM: Required Return= Rf + [Beta * (Expected Market Return – Rf)]

CAPM = 0.0198 + [1.11 * (0.1128 – 0.0198)]

CAPM= 0.0198 + [1.11 * (0.0930)]

CAPM= 0.0198 + [0.1032]

CAPM= 0.1230

Take this final number and convert it back into a percentage by multiplying it by 100. (0.1230*100)=12.30%

Your required return is 12.30%

You will see later why this number is important once we start calculating present value. We won’t be using it until we get to step 8. For now we are going to put our CAPM formula and our required return on our worksheet. It will look like this:

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