RESEARCH PAPERS | CORPORATE VALUATION

EQUITY RISK PREMIUMS (ERP): DETERMINANTS, ESTIMATION, AND IMPLICATIONS – THE 2024 EDITION
Aswath Damodaran
2024
The equity risk premium is the price of risk in equity markets, and it is not just a key input in estimating costs of equity and capital in both corporate finance and valuation, but it is also a key metric in assessing the overall market. Given its importance, it is surprising how haphazard the estimation of equity risk premiums remains in practice. We begin this paper by looking at the economic determinants of equity risk premiums, including investor risk aversion, information uncertainty and perceptions of macroeconomic risk. In the standard approach to estimating the equity risk premium, historical returns are used, with the difference in annual returns on stocks versus bonds, over a long period, comprising the expected risk premium. We note the limitations of this approach, even in markets with an abundance of data, like the United States, and its complete failure in emerging markets, where the historical data tends to be limited and volatile. We look at two other approaches to estimating equity risk premiums – the survey approach, where investors and managers are asked to assess the risk premium and the implied premium approach, where a forward-looking estimate of the premium is estimated using either current equity prices or risk premiums in other markets. In the next section, we look at the relationship between the equity risk premium and risk premiums in the bond market (default spreads) and in real estate (cap rates) and how that relationship can be mined to generate expected equity risk premiums. We close the paper by examining why different approaches yield different values for the equity risk premium, and how to choose the “right” number to use in analysis. >more

EQUITY RETURN EXPECTATIONS AND PORTFOLIOS: EVIDENCE FROM LARGE ASSET MANAGERS
Magnus Dahlquist, and Markus Ibert
2023
Collecting large asset managers' capital market assumptions, we revisit the relationships between subjective equity premium expectations, equity valuations, and financial portfolios. In contrast to the well-documented extrapolative expectations of retail investors, asset managers' equity premium expectations are countercyclical: they are high (low) when valuations are low (high). We find that asset managers' portfolios reflect their heterogeneous expectations: allocation funds of asset managers with larger US equity premium expectations invest significantly more in US equities. The pass-through of expectations to portfolios seems to be muted by investment mandates and is smaller than the one predicted by a standard portfolio choice model. >more

EQUITY RETURN EXPECTATIONS AND PORTFOLIOS: EVIDENCE FROM LARGE ASSET MANAGERS
Magnus Dahlquist, and Markus Ibert
2023
Collecting large asset managers' capital market assumptions, we revisit the relationships between subjective equity premium expectations, equity valuations, and financial portfolios. In contrast to the well-documented extrapolative expectations of retail investors, asset managers' equity premium expectations are countercyclical: they are high (low) when valuations are low (high). We find that asset managers' portfolios reflect their heterogeneous expectations: allocation funds of asset managers with larger US equity premium expectations invest significantly more in US equities. The pass-through of expectations to portfolios seems to be muted by investment mandates and is smaller than the one predicted by a standard portfolio choice model. >more

THE USE OF ASSET GROWTH IN EMPIRICAL ASSET PRICING MODELS
Michael J. Cooper, Huseyin Gulen, and Mihai Ion
2023
We show that the performance of the new factor models of Hou, Xue, and Zhang (2015) and Fama and French (2015) depends crucially on how their investment factor is constructed. Both models use growth in total assets to measure investment. Their ability to price the cross-section of returns decreases significantly when the investment factor is constructed using traditional investment measures, or measures that also account for investment in intangibles. In contrast, we find that factors based on growth in inventory and accounts receivable contain the bulk of the pricing information in the asset growth factor. We show evidence that the superior performance of the asset growth factor seems to be attributable to its ability to capture aggregate shocks to equity financing costs. >more

LBO VALUATION USING FLOWS TO EQUITY
Ian A. Cooper, and Kjell G. Nyborg
2023
The flows to equity method is commonly used in leveraged buyouts and other highly levered transactions. These flows are hybrid flows, mixing expected operating cash flows with promised debt payments under a planned debt schedule. Because of this, it is difficult to accurately estimate the appropriate discount rate, a difficulty that is compounded by the typically changing leverage over time under the planned debt schedule. We show how the flows to equity approach works and discuss its benefits and drawbacks as compared with other, ‘more standard’ methods. >more

COUNTRY RISK: DETERMINANTS, MEASURES AND IMPLICATIONS – THE 2023 EDITION
Aswath Damodaran
2023
As companies and investors globalize, we are increasingly faced with estimation questions about the risk associated with this globalization. When investors invest in China Mobile, Infosys or Vale, they may be rewarded with higher returns, but they are also exposed to additional risk. When Siemens and Apple push for growth in Asia and Latin America, they clearly are exposed to the political and economic turmoil that often characterize these markets. In practical terms, how, if at all, should we adjust for this additional risk? We will begin the paper with an overview of overall country risk, its sources and measures. We will continue with a discussion of sovereign default risk and examine sovereign ratings and credit default swaps (CDS) as measures of that risk. We will extend that discussion to look at country risk from the perspective of equity investors, by looking at equity risk premiums for different countries and consequences for valuation. In the fourth section, we argue that a company’s exposure to country risk should not be determined by where it is incorporated and traded. By that measure, neither Coca Cola nor Nestle are exposed to country risk. Exposure to country risk should come from a company’s operations, making country risk a critical component of the valuation of almost every large multinational corporation. In the final section, we will also look at how to move across currencies in valuation and capital budgeting, and how to avoid mismatching errors. >more

EQUITY RISK PREMIUMS (ERP): DETERMINANTS, ESTIMATION AND IMPLICATIONS - THE 2023 EDITION
Aswath Damodaran
2023
The equity risk premium is the price of risk in equity markets, and it is not just a key input in estimating costs of equity and capital in both corporate finance and valuation, but it is also a key metric in assessing the overall market. Given its importance, it is surprising how haphazard the estimation of equity risk premiums remains in practice. We begin this paper by looking at the economic determinants of equity risk premiums, including investor risk aversion, information uncertainty and perceptions of macroeconomic risk. In the standard approach to estimating the equity risk premium, historical returns are used, with the difference in annual returns on stocks versus bonds, over a long period, comprising the expected risk premium. We note the limitations of this approach, even in markets with an abundance of data, like the United States, and its complete failure in emerging markets, where the historical data tends to be limited and volatile. We look at two other approaches to estimating equity risk premiums – the survey approach, where investors and managers are asked to assess the risk premium and the implied premium approach, where a forward-looking estimate of the premium is estimated using either current equity prices or risk premiums in other markets. In the next section, we look at the relationship between the equity risk premium and risk premiums in the bond market (default spreads) and in real estate (cap rates) and how that relationship can be mined to generate expected equity risk premiums. We close the paper by examining why different approaches yield different values for the equity risk premium, and how to choose the “right” number to use in analysis. >more

A COMPREHENSIVE 2021 LOOK AT THE EMPIRICAL PERFORMANCE OF EQUITY PREMIUM PREDICTION II
Amit Goyal, Ivo Welch, and Athanasse Zafirov
2023
Our paper reexamines whether 29 variables from 26 papers published after Goyal and Welch (2008), as well as the original 17 variables, were useful in predicting the equity premium in-sample and out-of-sample. Our samples include the original periods in which these variables were identified, but end in 2021. Much of the extant literature seems obsolete, with a majority of variables no longer having empirical support even in-sample. A small number still perform reasonably well. >more

TRADING ON TALENT: HUMAN CAPITAL AND FIRM PERFORMANCE
Anastassia Fedyk, and James Hodson
2022
How is skilled human capital reflected in firm performance? By directly observing the monthly career migration patterns of 37 million employees of US public companies, along with their education, demographics, and skills, we explore firm-level "skill premia." Our key empirical finding is that, contrary to the individual-level patterns documented by the labor economics literature, technical and social skillsets negatively forecast both financial and operational performance at the firm level. We explore several potential mechanisms for this finding. Social skillsets display counter-cyclical performance, suggesting that their negative premia reflect their risk profiles. Meanwhile, negative premia on technical skillsets show patterns consistent with over-exuberance regarding contemporaneous popular technologies: IT and Mobile Networks skillsets carry negative premia in the early 2000s, while Data Analysis, Software Engineering, and Web Development display negative premia during the 2010s. >more

COUNTRY RISK: DETERMINANTS, MEASURES AND IMPLICATIONS - THE 2022 EDITION
Aswath Damodaran
2022
As companies and investors globalize, we are increasingly faced with estimation questions about the risk associated with this globalization. When investors invest in China Mobile, Infosys or Vale, they may be rewarded with higher returns, but they are also exposed to additional risk. When Siemens and Apple push for growth in Asia and Latin America, they clearly are exposed to the political and economic turmoil that often characterize these markets. In practical terms, how, if at all, should we adjust for this additional risk? We will begin the paper with an overview of overall country risk, its sources and measures. We will continue with a discussion of sovereign default risk and examine sovereign ratings and credit default swaps (CDS) as measures of that risk. We will extend that discussion to look at country risk from the perspective of equity investors, by looking at equity risk premiums for different countries and consequences for valuation. In the fourth section, we argue that a company’s exposure to country risk should not be determined by where it is incorporated and traded. By that measure, neither Coca Cola nor Nestle are exposed to country risk. Exposure to country risk should come from a company’s operations, making country risk a critical component of the valuation of almost every large multinational corporation. In the final section, we will also look at how to move across currencies in valuation and capital budgeting, and how to avoid mismatching errors. >more

SURVEY: MARKET RISK PREMIUM AND RISK-FREE RATE USED FOR 95 COUNTRIES IN 2022
Pablo Fernandez, Teresa García de Santos, and Javier Fernandez Acin
2022
This paper contains the statistics of a survey about the Risk-Free Rate (RF) and the Market Risk Premium (MRP) used in 2022 for 95 countries. We got answers for 99 countries, but we only report the results for 95 countries with more than 6 answers. Many respondents use for European countries a RF higher than the yield of the 10-year Government bonds. The coefficient of variation (standard deviation / average) of RF is higher than the coefficient of variation of MRP for the Euro countries. The paper also contains the links to previous years surveys, from 2008 to 2021. >more

PRIVATE COMPANY VALUATIONS BY MUTUAL FUNDS
Vikas Agarwal, Brad M. Barber, Si Cheng, Allaudeen Hameed, and Ayako Yasuda
2022
Mutual fund families set and report values of their private startup holdings, which affect the fund net asset value (NAV) at which investors buy/sell fund shares. We test three hypotheses related to the valuation practice: (i) information cost/access, (ii) litigation risk, and (iii) strategic NAV management. Consistent with (i), families with larger PE holdings and/or stronger information access update valuations more frequently in the absence of public information releases, their updates co-move less with other families, and their fund returns jump less at follow-on financings. We find no support for hypotheses (ii) or (iii). We also find that high-PE-exposure funds are subject to greater financial fragility. >more

THE SOCIAL MEDIA RISK PREMIUM
Amin Hosseini, Gergana Jostova, Alexander Philipov, and Robert Savickas
2020
We show that social media risk is priced in the cross-section of stocks and bonds. New social media stock and bond factors, based on firms' presence on Twitter, earn annual premiums of 7.2% and 3.3%, respectively. Their contributions to explaining the cross-section are significant when tested both with classical and recent machine-learning asset pricing methodologies. The social media risk premium is traced to both retail and institutional investors and is higher in low sentiment. Unlike other risk factors, the social media factor origins are clearly identified: prior to the age of social media their premiums did not exist. >more

EQUITY RISK PREMIUMS (ERP): DETERMINANTS, ESTIMATION, AND IMPLICATIONS – THE 2022 EDITION
Aswath Damodaran
2022
The equity risk premium is the price of risk in equity markets, and it is not just a key input in estimating costs of equity and capital in both corporate finance and valuation, but it is also a key metric in assessing the overall market. Given its importance, it is surprising how haphazard the estimation of equity risk premiums remains in practice. We begin this paper by looking at the economic determinants of equity risk premiums, including investor risk aversion, information uncertainty and perceptions of macroeconomic risk. In the standard approach to estimating the equity risk premium, historical returns are used, with the difference in annual returns on stocks versus bonds, over a long period, comprising the expected risk premium. We note the limitations of this approach, even in markets like the United States, which have long periods of historical data available, and its complete failure in emerging markets, where the historical data tends to be limited and volatile. We look at two other approaches to estimating equity risk premiums – the survey approach, where investors and managers are asked to assess the risk premium and the implied approach, where a forward-looking estimate of the premium is estimated using either current equity prices or risk premiums in non-equity markets. In the next section, we look at the relationship between the equity risk premium and risk premiums in the bond market (default spreads) and in real estate (cap rates) and how that relationship can be mined to generate expected equity risk premiums. We close the paper by examining why different approaches yield different values for the equity risk premium, and how to choose the “right” number to use in analysis. >more

POLITICAL BETA
Raymond J. Fisman, April M. Knill, Sergey Mityakov, and Margarita Portnykh
2021
Using a portfolio theory framework, we introduce the concept of political beta to model firm-level export diversification in response to global political risk. Our model predicts that firms are less responsive to changes in political relations with lower beta countries – those that contribute less to the firm’s total political risk. We document patterns consistent with our model using disaggregated Russian firm-by-destination-country data during 2001-2011: Trade is positively correlated with political relations, though the effect is far weaker for trading partners whose political relations with Russia are relatively uncorrelated with those of other partners in a firm’s export portfolio. >more

PEER SELECTION AND VALUATION IN MERGERS AND ACQUISITIONS
Gregory W. Eaton, Feng Guo, Tingting Liu, and Micah S. Officer
2021
Using unique data, this paper examines investment banks’ choice of peers in comparable companies analysis in mergers and acquisitions. We find strong evidence that product market space is amongst the most important factors in peer selection, but we provide evidence indicating that Standard Industrial Classification (SIC) codes, particularly three- and four-digit codes, do a poor job of categorizing related firms in this setting. Banks strategically select large, high growth peers with high valuation multiples, factors that are also positively related to premiums. Our evidence is consistent with target-firm advisors selecting peers with high valuation multiples to negotiate higher takeover prices. >more
 

TESTING FOR ASSET PRICE BUBBLES USING OPTIONS DATA
Nicola Fusari, Robert Jarrow, and Sujan Lamichhane
2021
We present a new approach to identifying asset price bubbles based on options data. We estimate asset bubbles by exploiting the differential pricing between put and call options. We apply our methodology to two stock market indexes, the S&P 500 and the Nasdaq-100, and two technology stocks, Amazon and Facebook, over the 2014-2018 sample period. We find that, while indexes do not exhibit significant bubbles, Amazon and Facebook show frequent and significant bubbles. The estimated bubbles tend to be associated with high trading volume and earning announcement days. Since our approach can be implemented in real time, it is useful to both policy-makers and investors. As an illustration we consider two case studies: the Nasdaq dot-com bubble (between 1999 to 2002) and GameStop (between December 2020 and January 2021). In both cases we identify significant and persistent bubbles. >more

IS FINANCIAL GLOBALIZATION IN REVERSE AFTER THE 2008 GLOBAL FINANCIAL CRISIS? EVIDENCE FROM CORPORATE VALUATIONS
Craig Doidge, George Andrew Karolyi, and René M. Stulz
2020
For the last two decades, non-US firms have lower valuations than similar US firms. We study the evolution of this valuation gap to assess whether financial markets are less integrated after the 2008 global financial crisis (GFC). The valuation gap for firms from developed markets increases by 31% after the GFC – a reversal in financial globalization – while the gap for firms from emerging markets (excluding China) stays stable. There is no evidence of greater segmentation for non-US firms cross-listed on major US exchanges and the typical valuation premium of such firms relative to domestic counterparts stays unchanged. However, the number of such firms shrinks sharply, so that the importance of US cross-listings as a mechanism for market integration diminishes. >more

SURVEY: MARKET RISK PREMIUM AND RISK-FREE RATE USED FOR 88 COUNTRIES IN 2021
Pablo Fernandez, Sofia Bañuls, and Pablo Fernandez Acin
2021
This paper contains the statistics of a survey about the Risk-Free Rate (RF) and the Market Risk Premium (MRP) used in 2021 for 88 countries. We got answers for 92 countries, but we only report the results for 88 countries with more than 6 answers. Many respondents use for European countries a RF higher than the yield of the 10-year Government bonds. The coefficient of variation (standard deviation / average) of RF is higher than the coefficient of variation of MRP for the Euro countries. The paper also contains the links to previous years surveys, from 2008 to 2020. >more

NORMALIZED RISK-FREE RATE: FICTION OR SCIENCE FICTION?
Pablo Fernandez
2020
As interest rates on Government Bonds have decreased, some analysts and consultants in Europe and in the US are using what they call “Normalized Risk-Free rate”. We show several inconsistencies and errors in the use of “Normalized Risk-Free rate”. Section 5 is a short case that may be used in class. It contains 26 interesting comments. >more

EMPIRICAL ASSET PRICING VIA MACHINE LEARNING
Shihao Gu, Bryan T. Kelly, and Dacheng Xiu
2019
We perform a comparative analysis of machine learning methods for the canonical problem of empirical asset pricing: measuring asset risk premia. We demonstrate large economic gains to investors using machine learning forecasts, in some cases doubling the performance of leading regression-based strategies from the literature. We identify the best performing methods (trees and neural networks) and trace their predictive gains to allowance of nonlinear predictor interactions that are missed by other methods. All methods agree on the same set of dominant predictive signals which includes variations on momentum, liquidity, and volatility. Improved risk premium measurement through machine learning simplifies the investigation into economic mechanisms of asset pricing and highlights the value of machine learning in financial innovation. >more