Matt Cullen-Meyer | Sept. 26, 2021

Beta is a key component to analyzing stock opportunities and is easily calculated in Excel. When used as an input to the **Capital Asset Pricing Model (CAPM)**, it helps determine a company's estimated cost of equity. This can then be used as a hurdle rate against which to compare expected returns of different stock opportunities. The resultant cost of equity can also be used in discounted cash flow (DCF) models to estimate the intrinsic value of a company by discounting future cash flows back to the present.

But what is the beta of a stock? Beta is an **indicator of risk**. It measures the degree to which a stock's value fluctuates relative to the overall stock market. Beta values less than 1.0 indicate that a company's stock price moves in less-than-perfect correlation with the market (ie low risk). These tend to be conservative or counter-cyclical stocks, which provide diversification benefit. A beta value of 1.0 means that a company's stock price moves up and down in line with the broader stock market (ie average risk). Companies with beta values greater than 1.0 amplify market movements (ie high risk). They skyrocket in value when the stock market goes up, but collapse hard when the market enters a downturn.

The precise method for calculating the beta of a company's stock differs by practitioner, though there are certainly some common practices.

- Step one calls for
**picking a stock market index**representative of the overall market, like the S&P 500. - Step two requires
**downloading historical daily stock prices**over the past three years for both the market index and the stock ticker of interest. - Step three involves
**merging the closing stock prices**for the selected company and the index into a single spreadsheet. - Step four entails
**calculating the daily rates of return**over the last three years. - Step five covers calculating the beta coefficient for the stock by
**running a linear regression**.

Each of these steps are covered in detail below.

The Capital Asset Pricing Model (CAPM) Beta is a measure of risk relative to the broad stock market. Determining an appropriate market proxy, however, is not a straightforward choice. Most texts and practitioners choose the **S&P 500 index (^GSPC)** since it is representative of the overall US market and simple to use. Thankfully, the index choice is unlikely to make a significant difference in most cases since stock indexes are weighted by market capitalization. This means that small and micro cap stocks have only a marginal impact on the overall market index.

Many websites are available for retrieving historical stock prices, the most common one being **Yahoo Finance**. These same sites usually have a way to download the data into a spreadsheet format. The two primary choices that practitioners must make when pulling historical prices are the time frame and the time interval of the returns. A **three-year time frame** is a popular choice since it generally represents a business cycle. A stock's beta is unlikely to shift significantly over a three-year period, thereby minimizing the standard error. Betas calculated using different time intervals, however, are generally not statistically significant from each other. For the time interval, most investment practitioners use **daily returns** when calculating a stock's beta. Daily return intervals tend to increase the precision of beta calculations, especially for estimation periods of three years or less.

A | B | |

1 | Date |
^GSPC |

2 | 9/24/2021 | 4,455.48 |

3 | 9/23/2021 | 4,448.98 |

4 | 9/22/2021 | 4,395.64 |

5 | 9/21/2021 | 4,354.19 |

6 | 9/20/2021 | 4,357.73 |

A | B | |

1 | Date |
MSFT |

2 | 9/24/2021 | 299.35 |

3 | 9/23/2021 | 299.56 |

4 | 9/22/2021 | 298.58 |

5 | 9/21/2021 | 294.80 |

6 | 9/20/2021 | 294.30 |

Stock and index prices are usually downloaded separately on different spreadsheets, which must then be joined side by side. The resultant worksheet should have three columns: (1) date, (2) adjusted closing prices for the stock, and (3) adjusted closing prices for the market index. (Please note that the dates of the two datasets you download may not match and must therefore be aligned in certain cases, though the issue is far less common for weekly and especially monthly intervals).

A | B | C | |

1 | Date |
^GSPC |
MSFT |

2 | 9/24/2021 | 4,455.48 | 299.35 |

3 | 9/23/2021 | 4,448.98 | 299.56 |

4 | 9/22/2021 | 4,395.64 | 298.58 |

5 | 9/21/2021 | 4,354.19 | 294.80 |

6 | 9/20/2021 | 4,357.73 | 294.30 |

The last bit of data wrangling required before estimating beta is to calculate the **daily percentage price change**. This is calculated as the current price minus the previous price, all divided by the previous price [=(price(t) – price(t-1)) / price(t-1)]. This should be calculated for each period in the time series for both the stock and the index. Using the natural logarithm [=ln(price(t) / price(t-1))] to calculate the percentage change makes little difference in the end result.

A | B | C | D | E | |

1 | Date |
^GSPC |
^GSPC %∆ |
MSFT |
MSFT %∆ |

2 | 9/24/2021 | 4,455.48 | 0.15% | 299.35 | (0.07%) |

3 | 9/23/2021 | 4,448.98 | 1.21% | 299.56 | 0.33% |

4 | 9/22/2021 | 4,395.64 | 0.95% | 298.58 | 1.28% |

5 | 9/21/2021 | 4,354.19 | (0.08%) | 294.80 | 0.17% |

6 | 9/20/2021 | 4,357.73 | 294.30 |

Historical beta is found by regressing the index’s returns against the stock’s returns. In practice, this is done using the **SLOPE function in Excel**, where the first argument (known y’s) is the range of values for the daily stock returns and the second argument (known x’s) is the range of values for the daily index returns. The resultant output is the slope coefficient or beta (denoted by β).

F | |

1 | Beta |

2 | =SLOPE(E2:E5,C2:C5) |

There are many videos and articles available on the internet that provide helpful walkthroughs on how to calculate the beta of a stock with Excel. What they often omit, however, is clarification on what to use as a market proxy, how far back to retrieve historical prices, and whether to use daily, weekly, or monthly returns. This is likely because there aren’t straightforward answers. That doesn’t mean that there aren’t good places to start. Try calculating beta using different parameters and read up on the economic rationale behind the different choices. I've linked a couple of academic papers below that are especially helpful on this topic.

It is also useful to see how a stock’s beta has changed over time by graphing historical betas on a rolling basis. Beta estimates can additionally be improved by using industry betas (e.g. using a sector or industry index) or taking the median beta of several industry competitors since an individual company's beta over the last, say, three years might not be representative of its typical risk. This requires un-levering the raw betas of competitors [βu = βe / (1 + D/E)] and then re-levering them to reflect the company’s own leverage profile [βe = βu * (1 + D/E)].

Aswath Damodaran. *Estimating Risk Parameters*.

Daves, Ehrnhardt and Kunkel. *Estimating Systematic Risk: The Choice of Return Interval and Estimation Period*.

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