1. What is a discount rate?
In the previous exercises, you were given the discount rate that you used to discount the free cash flows or dividends. In this chapter, you will learn how to calculate the cost of equity.
2. Capital Asset Pricing Model (CAPM)
The CAPM is the most common approach used to estimate the cost of equity. Mathematically, the CAPM tells us that the expected return on a stock i is equal to the risk-free rate plus the product of stock i's beta and the equity risk premium. The equity risk premium is the extra return investors demand from investing in stocks over bonds and is measured as the difference between the return on the S&P 500 Index less the return on a US Treasury security.
We now go through each of the components of CAPM.
3. Beta
We all heard the saying: "Don't put your eggs in one basket." If you select the stocks in your portfolio properly, you will be able to substantially reduce firm-specific risk. Examples of firm-specific risk are management departures and plant closures. That is, things that only affect one firm and not the industry or market as a whole. The CAPM tells us that investors would not be compensated for taking on firm-specific risk because investors can invest in a portfolio of securities and eliminate firm-specific risk. Therefore, only risk that the investor cannot diversify away, which is known as systematic risk or market risk, matters when determining the cost of capital. Beta is the measure of the stock's systematic risk.
4. Using Regression Analysis to Estimate Beta
How then do we estimate beta? The most common way to estimate betas is through regression analysis. You regress the security's return on the market's return. This is known as the market model. It is a simpler model than the CAPM, but the results are virtually identical in almost all instances.
5. Using Regression Analysis to Estimate Beta
The regression is performed over an estimation period of 2 to 5 years in length and using either weekly or monthly returns.
6. Estimating Beta
The steps to estimate beta are as follows. First, obtain price data. In the code, we assume you already did this. There are a variety of ways to do this. A common approach is to use getSymbols in the quantmod library.
Second, calculate the stock and market's return. The code shows how to use the Delt() command to calculate the returns.
When we combine the two, we end up with an odd variable name for the firm's return. So we have to use the names() command to rename the first variable to something more appropriate.
Next, we need two prices to calculate a return. So we remove the first observation because the Delt() command calculates its first return beginning with the second observation.
We then run a regression using the lm() command.
Beta can then be extracted using the last line of the code by applying the summary() command on the regression dataset.
7. Let's practice!
Now it's time for you to practice estimating betas.