We can add the riskfree rate and the equity risk premium to determine how much the market, or an average risk stock, will return. But what if our stock is more or less risky than the market? For that, we need a measure of relative risk.
Most analysts use beta as a measure of relative risk. Sometimes you’ll see the shorthand for beta in the form of the lowercase second letter of the Greek alphabet: β
What Is Beta?
Beta measures how volatile an equity is compared to the market, which for practical purposes, is usually the S&P500 index for US stocks. Beta is convenient because the market’s beta is centered around 1.0. A stock with a beta of 2.0 should move up twice as much as the market in good times and down twice as much in bad times. The expected returns are the same, but they’re twice as volatile. A stock with a beta of 0.5 would move up and down half as much as the market. The former is considered twice as risky as the market while the latter is regarded as half as risky.
Beta can be classified depending upon how it’s calculated:
 Regression beta
 Bottomup beta
Regression Beta
Most analysts and services calculate beta using a regression. Regression betas are computed using a linear regression comparing the returns of the market with that of a stock. This is what a Bloomberg terminal or Yahoo Finance displays as beta, and it’s a terrible way to think about risk both technically and conceptually.
Regression Beta Technical Issues
Regressionbased betas have three problems inherent in how they are calculated:
 High standard error
 Backwardlooking
 Subject to bias
High Standard Error
Regression betas are very noisy. Most have a high standard error. For instance, if the beta of a stock is 1.25 with a standard error of 0.5, the actual beta could be .25 or 2.25 using two standard deviations. Check the error next time you’re using a regression beta and be prepared to be shocked.
Additionally, if your stock makes up a significant portion of the comparison market, the beta can look great but it is fundamentally flawed.
Backward Looking
Regression betas look at a single slice of history. If a stock drops significantly while the market is going up, it will be less correlated with the market and its beta measure will go down. If a stock is plummeting, is it really less risky?
Subject to Bias
With regression betas, you can pretty much come up with any number you want if you cherrypick the index and time period.
Regression Beta Conceptual Issues
Beta is a statistical measure that tries to estimate risk. Risk comes from the choices a company makes regarding:
 Nature of revenue sources
 Operating leverage
 Financial leverage
Nature of Revenue Sources
Companies that sell discretionary products will have less predictable earnings as customer purchases will fluctuate more due to market cycles.
Operating Leverage
Companies that have higher cost structures will have earnings that vary more in good and bad times than companies that have a less rigid cost structure. While accountants don’t break out financials into variable and fixed costs, you can use the following to get an idea of operating leverage over a period of time.
ebitv = ebit / r
Where:
 ebitv: EBIT Variability Measure
 ebit: Change in Earnings Before Interest and Taxes
 r: Change in Revenues
Financial Leverage
When you borrow money, you create a fixed expense that you have to pay in good times and in bad. This will magnify earnings in good times and subtract from them in notsogood times.
lbeta = ubeta _ (1 + (1 – tr) _ (d/e)
Where:
 lbeta: Levered Beta
 ubeta: Unlevered Beta
 tr: Tax Rate
 d: Debt
 e: Equity
Bottomup Beta
A bottomup beta, sometimes called a fundamental beta, is both technically and conceptually more sound than a regression beta. It inherently incorporates the revenue and leverage risks causing increased earnings volatility. You can then adjust the financial leverage, and potentially the operational leverage, to match that of the firm you’re valuing.
Bottomup betas have several benefits:
 They are more precise.
 They’re not shackled to the past. You can select the businesses, weights, and financial leverage that a business has today or may have tomorrow.
 They can be estimated for a nontraded asset or business.
If you’re not interested in calculating the bottomup beta for yourself or you don’t have access to the resources needed, Aswath Damodaran makes our lives easier once again by calculating the bottomup betas by sector .
How to Calculate a Bottomup Beta
 Find the businesses that your firm operates in
 Find the publicly traded firms in each of these businesses and obtain their regression betas. Take the median of the betas for these companies
 Estimate how much value your firm derives from each different business it is in
 Compute the weighted average of the unlevered betas
 Compute a levered beta (equity beta) for your firm using the market debt to equity ratio of your firm
An example of a steel and chemical company:
 Your company is in the steel and chemical businesses

Find the median unlevered regression betas
 Find the median regression beta for as many steel companies as you can
 Find the median regression beta for as many chemical companies as you can
 Remove the effects of debt (unlever):
usb = bas / (1 + (1 – tr) * (adr/aer)
Where:
 usb: Unlevered Steel Beta
 bas: Beta Across Public Steel Firms
 tr: Tax Rate
 adr: Average Debt Ratio Publish Steel Firms

aer: Average Equity Ratio Public Steel Firms
 Remove the effects of cash: usb = usb / (1CashPercentage)
 Estimate how much value the business derives from the steel and chemical business using the weights that make the most sense, generally revenue weights.
 Compute the weighted average from the unlevered betas:
wb = sub _ (sr/tr) + cub _ (cr/tr)
Where:
 wb: Weighted Beta
 sub: Steel Unlevered Beta
 sr: Steel Revenue
 tr: Total Revenue
 cub: Chemical Unlevered Beta
 cr: Chemical Revenue
 Compute the levered beta (equity beta) for the firm:
lb = (1 + (1 – tr) * (d/e)
Where:
 lb: Levered Beta
 tr: Tax Rate
 d: Debt
 e: Equity
Adjusting The Market Risk for a Private Company
For a private company, we need to add back the risk that the model assumes to be diversified away. r^2 is a statistical measure of how close the data fits the regression line. By dividing by r^2, we are adding back that risk.
ndpcoe = mb / square_root(r^2)
Where:
 ndpcoe: NonDiversified Private Cost of Equity
 mb: Market Beta