# Building A Better Beta

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Includes: AAPL
by: Stock Market Sherpa

## Summary

A stock's beta is a critical input when calculating its cost of equity (and weighted average cost of capital).

This in turn has a significant impact on the result of any type of discounted cash flow analysis of the security.

This article examines some of the flaws with beta and how one might go about solving them.

Determining the beta of a particular stock is not generally considered to be a fascinating topic. I can almost guarantee that this will be one of the least-read articles that I ever publish on this website. And that is a shame, because a stock's beta can have significant implications on its valuation when performing a discounted cash flow (NYSE:DCF) analysis.

A Brief Overview of Beta

The beta of a stock is a combination of its volatility and its correlation with the stock market as a whole. A beta of 1 means that a stock has risen and fallen in the same direction and amount as the market while a beta of 2 means that a stock has been twice as volatile as the market and a beta of 0.5 demonstrates that a stock has half the volatility of the market. Generally, beta (for American companies) is quoted based on daily performance compared to the S&P 500 going back one year. I have chosen to intentionally leave the mathematical equation for calculating beta out of this article as it is widely available elsewhere online or in finance textbooks.

Beta and the Capital Asset Pricing Model

So why is beta such an important metric for a stock? Well, if one is attempting to calculate the cost of equity for a certain company, the capital asset pricing model (CAPM) is the most popular type of analysis. The CAPM has three inputs:

1. The risk free rate (generally the 10-year government T-Bill rate is used, currently around 2.5%).
2. The risk premium of the stock market (the historical premium for holding stocks instead of government bonds - this page is a fantastic resource - a conservative assumption is 8%).
3. The beta of the stock in question.

The formula is simply:

CAPM Cost of Equity = Risk Free Rate *plus* (Risk Premium *multiplied by* Beta)

Therefore, a higher beta leads to a higher cost of equity (discount rate).

Discounting Future Cash Flows

I have written several articles recently where I perform a discounted cash flow analysis on a particular company. One of the key inputs in any DCF model is the weighted average cost of capital (WACC), which serves as the rate that future cash flows are discounted at. For most companies, the cost of equity is the most significant part of its WACC, and, as I have demonstrated above, beta is a key input when using the CAPM to calculate the cost of equity.

Since DCF models rely on evaluating cash flows that will occur well into the future, modifying the discount rate by a small amount can have a huge impact on the result. In my recent (base case) analysis of Apple (NASDAQ:AAPL), my model produced the following share price values based on a range of potential discount rates:

 WACC Share Value 8.0% \$198.50 8.5% \$188.24 9.0% \$179.11 9.5% \$170.95 10.0% \$163.60 10.5% \$156.95 11.0% \$150.91

In my DCF model, I always perform a sensitivity analysis to demonstrate how the model price changes if a different discount rate is used. However, the key takeaway is that beta is critical to the CAPM method of determining a cost of equity, the cost of equity is critical when determining an appropriate WACC (discount rate) and the WACC is critical when performing a DCF analysis.

Issues Identifying Beta

There are three main challenges I have encountered when trying to identify the beta of a particular stock:

1. Each Source Gives A Different Reading

Let us revisit Apple. Apple's beta according to Yahoo! Finance is: 1.45. According to Google Finance, it is 1.25. According to Nasdaq.com it is 0.81. According to Reuters.com it is 1.17. You get the picture. Each website uses a slightly different methodology and the result is that it becomes difficult to trust any individual source. If you use Yahoo's beta of 1.45, Apple's cost of equity is approximately 14%. However, if you use Nasdaq.com's beta of 0.81, Apple's cost of equity drops to 9%.

2. Beta Changes Over Time

The best way to demonstrate this is using the below graph of Apple's beta over 10 years from YCharts.com:

Would it have made sense to use a beta of 2.5 when analyzing Apple in 2009, only to reduce that to 0.8 half a decade later? Furthermore, how can one be confident that the beta he or she uses for a particular stock today will be accurate one or two months from now?

3. Beta is Backward Looking

This final point is fairly obvious. Beta is measured based on past stock performance data. A company that makes a meaningful acquisition (or divestiture) or issues (or retires) significant amounts of debt may make its stock more or less risky, but these changes will not show up fully in its beta for a year or more.

Solutions to These Problems

Below, I outline a pair of methods for solving these problems.

Problem: Each Source Gives A Different Reading

Solution: Run the numbers yourself. This is a little bit messy, but using stock data you can extract from Seeking Alpha (link for Apple) and a simple Excel formula, this can be done in less than five minutes. For Apple, the beta using one year of performance data was 0.85. Since I can see and validate the data that went into this calculation, I am more confident in the result than if I had simply cherry picked a number from a website.

Problems: Beta Changes Over Time AND Beta is Backward Looking

Solution: I find it most efficient to handle both of these issues with one adjustment. Because (by definition) the stock market has a beta of 1, I contend that the average stock also has a beta of 1. Therefore, if one believes in the concept of mean reversion, it is reasonable that a stock with a particularly high beta will likely see its beta fall toward 1 over time and a stock with an abnormally low beta will likely see its beta rise toward 1 over time.

Therefore, if one uses Excel to calculate the "raw" beta of a stock over the past year, he or she can regress it back towards the mean by using the following simple formula:

Adjusted Beta = (Beta *plus* 1) *divided by* 2

Therefore, a stock with a calculated beta of 1.4 would have an adjusted beta of 1.2 and a stock with a calculated beta of 0.6 would have an adjusted beta of 0.8.

Conclusion

Are these solutions foolproof? No. However, through my experience modeling dozens of stocks, this method provides a reasonable estimate of a stock's true beta moving forward that can be utilized successfully to determine a firm's WACC when performing a DCF analysis.

Disclosure: I am/we are long AAPL.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.