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Aswath Damodaran – January 2018 Valuation Data First Update: Numbers don’t lie, or do they?

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Course Trailer. Online Learning Experience. Certificates and Credits. Download Brochure.Aswath Damodaran mentioned. Every year, sinceI have spent the first week of my year, paying homage to the numbers gods. I collect raw accounting and market data from a variety of raw data providers, and I am grateful to all of them for making my life easier, and I summarize the data on many dimensions, by geography, by industry and by market capitalization.

That summarized data, for the start ofcan be found on my websiteas can the archived data from prior years. That is pictured in the second pie chart above. Within each geographic group, I break the companies down into 94 industry groupings and the numbers in each grouping are summarized at this link. While some would prefer a finer breakdown, I prefer this coarser grouping because it allows for larger sample sizes, especially as I go to sub-groups.

Finally, I compute a range of numbers for each grouping, reflecting my corporate finance biases, and classify them into risk, profitability, leverage and cash return measures in the table below:. The links in the table will lead you to the html versions of the US data, but you can find the excel versions of this data and for the other groupings on my webpage.

Since I report more than data items, you may have to work to find what you are looking for but it or a close variant should be available somewhere on the site.

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Session 7: The Beta Regression

Thank you for reaching out. We look forward to discussing your needs and expectations and demonstrate our programs and expertise. Your Name required. Your Email required. Your Message. Register Login 0 Items. My dataset includes every publicly traded firm that has a market price available for it, in my raw dataset, and at the start ofit included 43, firms, up from the 42, firms at the start of Any decision that I make on screening the data or sampling will create biases that will color my results, and while I will not claim to be bias-free no one isI would prefer to not initiate it with my sampling.

There are countries that are represented in the data, though many have only a handful of firms that are incorporated there. That said, it is worth noting that while the companies are classified by country of incorporation, many have operations in multiple countries. The pie chart below provides the breakdown:. Finally, I compute a range of numbers for each grouping, reflecting my corporate finance biases, and classify them into risk, profitability, leverage and cash return measures in the table below: Risk Measures Cost of Funding Pricing Multiples 1.

Beta 1. Cost of Equity 1.

damodaran beta

Standard deviation in stock price 2. Cost of Debt 2. Price to Book 3. Standard deviation in operating income 3. Cost of Capital 3. High-Low Price Risk Measure 4. Net Profit Margin 1. Operating Margin 2. Interest Coverage Ratios 3.The financial press and investing websites have recently put the spotlight on firms that have large cash balances.

The primary example cited is Apple Inc. As of 30 SeptemberApple had USD billion of cash and marketable securities on its balance sheet. There are reasons why a company may want to hold a lot of cash. For example, cash gives firms a cushion during periods when cash flows are volatile, provides flexibility to make opportunistic investments, and allows firms the choice not to raise funds during disadvantageous periods. On the other hand, there are costs as well, which include the cost of carry i.

Regardless of the potential motives for holding a large amount of cash, one thing that is certain is that Apple does not need USD billion in cash to operate its business. The surplus cash beyond what the company needs for its operations is known as excess cash. When conducting fundamental valuation, excess cash is considered a non-operating asset that is added to the value resulting from a discounted cash flow DCF analysis of the operations of a business.

damodaran beta

Therefore, the appropriate discount rate used in a DCF analysis should be a rate that reflects only the risk of the operations of the firm. However, the common approach of using betas obtained by regressing historical returns incorporates the level of excess cash during the estimation period. For our illustration, we assume Rf equals 2.

The Hamada formula calculates the unlevered beta B U as follows:. The average debt-to-equity ratio for Apple over the two-year beta estimation period is Then, given the definition of a portfolio beta described above, we can represent the unlevered beta as follows:.

We are interested in finding the value of B A given all the other inputs to Equation 3, which we obtain as follows. As outsiders, it is difficult to determine how much cash a firm needs for operations. However, for the purposes of our example, we will use the amount of long-term marketable securities Apple reports in its SEC filings as an alternative proxy. Apple states that long-term marketable securities have maturities that generally range from one to five years and, as such, placing the cash in long-term marketable securities suggests that Apple does not need the cash to fund its operations, at least in the short term.

Using this assumption, we find w C for Apple equal to Next, we turn to estimating the excess cash beta. Textbooks suggest that excess cash beta is equal to 0 or virtually 0. We perform a test of the reasonableness of this assertion. Since our estimate of excess cash is based on long-term marketable securities with maturities of one to five years, we estimate B C using the beta of the Vanguard Short-Term Bond ETF, which has an average duration of 2.

We find that the beta is In general, excess cash can also be invested in short-term instruments, so we can also test the zero-excess-cash beta assertion using short-term securities. Given the above, it appears reasonable to assume that the excess cash beta is 0. The average cash-adjusted debt-to-equity ratio is Using Equation 1 and the same risk-free rate of 2.

To understand whether such changes are meaningful, we should tie our illustration to some form of valuation impact. The WACC is the blended rate of the after-tax cost of debt and cost of equity. Assuming a pre-tax cost of debt of 3. Note that the increased leverage has an offsetting effect i. This leads to an unadjusted WACC of 9.Specifically, firms may issue many bonds and the heterogeneity of those bonds may make identification of a representative bond difficult.

In addition, even if such a bond could be identified, the bond markets are very illiquid and finding a reliable price series for such a bond could prove challenging. The Benninga-Sarig formula was developed to arrive at a CAPM-like approach when there are different tax rates for debt and equity and this methodologyin addition to modifying the SML for debt, also requires a modified equity SML equation i.

damodaran beta

Moreover, in a later edition of the financial modeling book relied upon in the Cost of Capitaleven the author questions the usefulness of the formula he developed.

Specifically, Benninga writes:. Therefore, we have to determine whether there are any benefits to using the Benninga-Sarig formula. I obtain price data for the two market proxies from Yahoo Finance.

Corp and HY Bond Indexes from Morningstar Direct for the bond index data by credit rating and the debt betas are estimated using five years of monthly returns. The results of my test are reported in Table 1. Therefore, there appears to be no practical benefit to using the Benninga-Sarig debt betas over the CAPM that would offset the need to deviate from the CAPM and standard beta unlevering formulas.

Moreover, using the CAPM gives the added benefit of allowing the valuation practitioner to use a consistent methodology to calculate both the equity and debt betas i. To see how, note that the Fernandez formula is. First, based on the CAPM, a zero-beta asset is expected to yield the risk-free rate of return, but investors will likely not consider investing in many, or any, corporate debt if the debt were only expected to yield the risk-free rate.

Second, prior studies report debt betas for broad ratings categories that are not equal to zero. For example, inCornell and Green published a paper that reported high-grade bonds have a debt beta of 0. In the DFC Opinion, the Court implicitly suggested the use of two procedures: the Benninga-Sarig formula to estimate debt betas and the Hamada formula to unlever betas.

As shown above, debt betas estimated using the Benninga-Sarig formula require the use of a different Security Market Line and beta unlevering formula, but the ultimate results are virtually identical to debt betas estimated using the CAPM.

We also showed that the Hamada formula is the Fernandez formula when you assume a debt beta of zero, but the zero debt beta assumption required by the Hamada formula unlikely holds in practice. Therefore, using these two approaches may not be the best practice for valuation practitioners. E-mail: cang compasslexecon. Opinions expressed herein are solely those of the author and are not opinions of Compass Lexecon or its other employees. Financial Modeling, 4 th ed. MIT Press, p.

Clifford S. Ang, CFA is Vice President at Compass Lexecon, an economic consulting firm that specializes in the application of economics to a variety of legal and regulatory issues. Ang specializes in the areas of valuation, corporate finance, accounting, and damages.

He has worked on hundreds of engagements involving companies across a broad-spectrum of industries concerning issues such as valuation, solvency, market efficiency, materiality, loss causation, and damages. Ang can be reached at or by e-mail to cang compasslexecon. Save and Share: Print. National Association of Certified Valuators and Analysts The National Association of Certified Valuators and Analysts NACVA supports the users of business and intangible asset valuation services and financial forensic services, including damages determinations of all kinds and fraud detection and prevention, by training and certifying financial professionals in these disciplines.

Number of Entries : I agree with Professor's view. If beta is not the correct measure of risk, what else can be taken as risk measuring tool? If Mr. Buffet is not using beta, it is because he is gonna hold a stock for his life time. Only Mr. Buffet can do that. Not all. There is a huge difference between investment and Trading.

Investment is what Warren Buffet does he holds a huge ownership stock in the particular company. He analyses a company's future prospects by understanding the business, Market for the products produced by that company. Which is very much difficult for a person who is engaged in the activities like buying a stock for a certain period,or buying a call option, trading in Futures allowed in India etc.

Aswath sir, How an individual can analyze a stock for trading practice? The contrast between investing and trading does not really make sense. If you invested in Google long term, do you not think that you are going to be exposed to more risk than investing in Coca Cola? An investment is risky and having a long time horizon cannot make real risk go away. As for Buffet, I would not take everything he says at face value. He may not adjust his expected returns for risk but he sure does adjust the cash flows.

I'm actually in the middle of teaching Ch. Just found this blog so haven't posted here before, but many thanks for all the help you provide on your website! I'm an economist who was converted to teaching finance about 8 years ago and ended up loving it. Your books and website have been tremendous help to me. By the way, and a bit off topic, I just received my copy of strategic risk taking. Are you planning a course around this material in the future? If not, I'd be interested in hearing how you might be using it or suggest using it in the classroom.

Hi, This brings me to another question that was very often asked in placement interviews in B-Schools by some of the equity research companies. Can there be companies with negative beta?

And if yes then is CAPM an invalid framework? I have never quite got a convincing answer for this from most people. I know there are companies with negative beta in the market. But isn't that because of our narrow understanding of index being a true representation of the market.Beta is a measure of market risk.

Unlevered beta or asset beta measures the market risk of the company without the impact of debt. Unlevering a beta removes the financial effects of leverage thus isolating the risk due solely to company assets. In other words, how much did the company's equity contribute to its risk profile. Levered beta measures the risk of a firm with debt and equity in its capital structure to the volatility of the market.

The other type of beta is known as unlevered beta.

Corporate Finance

Unlevering the beta removes any beneficial or detrimental effects gained by adding debt to the firm's capital structure. Comparing companies' unlevered betas gives an investor clarity on the composition of risk being assumed when purchasing the stock.

Take a company that is increasing its debt thus raising its debt-to-equity ratio. This will lead to a larger percentage of earnings being used to service that debt which will amplify investor uncertainty about future earnings stream.

Consequently, the company's stock is deemed to be getting riskier but that risk is not due to market risk. Isolating and removing the debt component of overall risk results in unlevered beta. Systematic risk is the type of risk that is caused by factors beyond a company's control. This type of risk cannot be diversified away. Examples of systematic risk include natural disasters, political events, inflation and wars. To measure the level of systematic risk or volatility of a stock or portfolio, the beta is used.

Beta is a statistical measure that compares the volatility of the price of a stock against the volatility of the broader market. If the volatility of the stock, as measured by beta, is higher, the stock is considered risky. If the volatility of the stock is lower, the stock is said to have less risk. A beta of one is equivalent to the risk of the broader market. That is, a company with a beta of one has the same systematic risk as the broader market.

A beta of two means the company is twice as volatile as the overall market, but a beta of less than one means the company is less volatile and presents less risk than the broader market. The level of debt that a company has can affect its performance, making it more sensitive to changes in its stock price.

Note that the company being analyzed has debt in its financial statements, but unlevered beta treats it like it has no debt by stripping any debt off the calculation. Since companies have different capital structures and levels of debt, to effectively compare them against each other or against the market, an analyst can calculate the unlevered beta.

As of Novemberits beta is 0. Unlevered beta is almost always equal to or lower than levered beta given that debt will most often be zero or positive.I am a teacher first, who also happens to love untangling the puzzles of corporate finance and valuation, and writing about my experiences. As a result, I happen to be at the intersection of three businesses, education, publishing and financial services, that are all big, inefficiently run and deserve to be disrupted.

I may not have the power to change the status quo in any of these businesses, but I can stir the pot, and this website is my attempt to do so. Broadly speaking, the website is broken down into four sections. The first, teaching, includes all of my classes, starting with the MBA classes that I teach at Stern and including the shorter 2-day to 3-day executive sessions I have on corporate finance and valuation. You will find not only the material for the classes lecture notes, quizzesbut also webcasts of the classes that you can access on different forums.

I also have classes specifically tailored to an online audience on valuation, corporate finance and investment philosophies. The second, writing, includes links to almost everything I have written and continue to write, starting with my books and extending to my practitioner papers on equity risk premiums, cash flows and other things valuation-related.

The third, data, contains the annual updates that I provide on industry averages, for US and global companies, on both corporate finance and valuation metrics including multiples. It is also where I provide my estimates of equity risk premiums and costs of capital. The fourth, toolsincorporates the spreadsheets that I have developed over time to value and analyze companies and short in-practice webcasts on how to analyze companies.

I have been told that my website is ugly, and I apologize for its clunky look and feel. While some of you have offered to make it look better for me, and I thank you for your kindness, I need to be able to tweak, modify and adapt the website as I go along and to do that, I have to work with what I know about website design, which is not much.

You can try the search engine below and if that does not work, try this guide to the site. Implied Equity Risk Premium Update. Downloadable datasets For more data, go here. Other Updates. Teaching: The Spring Corporate Finance class, now fully archived, can be found here and the archived Spring Valuation class is linked here. The online versions of these classes can be found here and NYU is offering certificate versions here. I amd teaching three classes in the spring ofand you can find the ongoing links here: Corporate Finance and Valuation to the MBAs and Valuation to the undergraduates.

Download the latest version of my annual equity risk premium update by clicking here and the latest version of my annual country risk update by clicking here. I also have a paper on valuing userssubscribers and members.