The Portuguese Equity Risk Premium

Equity risk premiums are a central component of every risk and return model in finance and are a key input into estimating costs of equity and capital in both corporate finance and valuation. Given their 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 equity risk premiums, historical returns are used, with the difference in annual returns on stocks versus bonds over a long time 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 ar 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. We also 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 generated 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. (In an addendum, we also look at equity risk premiums during the market crisis, starting on September 12, 2008 through December 31, 2008, and then track the shift the changes through September 30, 2009.)

The U.S. equity risk premium using historical estimates of stocks and bonds is 6 to 8 percent. However, research has suggested that the risk premium should be much lower. An important stream of literature in this respect is using analysts’ earnings forecasts and reverse engineering the residual income valuation model to impute risk premium. The use of analysts’ earnings forecasts leads to an upward bias of the estimated risk premium. In this study, we implement methodology to measure equity risk premium without using analysts’ earnings forecasts. Our results provide evidence supporting a close to zero risk premium.

We model and estimate equity premium in a general equilibrium setting. It is done by reframing the Merton's model (1974) in the context of general equilibrium models such as Ahn and Thompson (1988) and Bates (1991). Our approach is novel in its attempt to derive equity premium by evaluating the equity returns dynamics in equilibrium and to thereby estimate non‐risk convexity premium for equity as well as its risk premium. While risk premium is generally due to systematic risk, convexity premium is due to the option‐like feature of equity, and exists under returns discontinuity and risk neutrality. We model equity premium such that the convexity premium pays for the liquidity and information costs of equity. We calibrate our equity premium model and report that the convexity premium counts for about one third of our predicted equity premium. We find relevance for our non‐risk convexity premium in relation to the premium puzzle and anomalies in the stock market.

Risk premiums and macroeconomic dynamics in a heterogeneous agent model

Continuous trading in an exchange economy under discontinuous dynamics: A resolution of the equity premium puzzle

I. INTRODUCTION The consumption-based capital asset pricing model (CCAPM) has become the dominant paradigm in asset pricing theory because of its intuitive characterization of asset risk. That is, unlike expectations-based asset pricing theories (e.g. the present value model of stock prices) which inherently assume risk neutrality, the CCAPM is predicated upon risk-averse agents attempting to achieve a smooth consumption profile through the trading of assets. From this perspective, the risk of an asset is captured by the covariance of the asset's return with agents' marginal utility of consumption, or, more broadly, agents' intertemporal marginal rate of substitution of wealth. With this characterization, the CCAPM extends the results of the standard CAPM, i.e. the risk of an asset is reflected in the covariance of the asset's return with the market portfolio, to a general equilibrium setting. However, this intuitively appealing theory has not found much empirical support. Perhaps the most famous demonstration of inconsistency between the theory and data was Rajnish Mehra and Edward Prescott's [1985] analysis of the equity premium, i.e. the difference between the average return on equity and that on government bonds. Using calibration methods rather than a formal statistical approach, they showed that a standard CCAPM severely underpredicts the size of the risk premium on equity. The important implication of this finding is that the basic CCAPM incorrectly models the covariance structure between the return on equity and asset holders' intertemporal marginal rate of substitution. Economists' response to this empirical rejection has been to either identify new sources of risk (e.g., that implied by a particular monetary environment as in Labadie [1989]) or define alternative preferences toward risk (e.g., the use of non-expected utility theory as presented in Weil [1989] and Epstein and Zin [1989]). The potential for this research was illustrated recently by George Constantinides's [1990] resolution of the equity premium puzzle in a model that included habit formation in consumption. By relaxing the standard CCAPM's assumption of time-separable preferences, Constantinides demonstrated that a relatively smooth consumption profile and large risk premium on equity are consistent with equilibrium in a complete markets, rational-expectations framework.(1) I use this insight to study another risk premium puzzle; specifically the behavior of the nominal term premium. The existence of a nominal term premium puzzle was demonstrated in papers by Backus, Gregory, and Zin [1989] and Salyer [1990] in which the term structure implications within a Lucas [1982] type cash-in-advance (CIA) economy were studied. While some equilibrium characteristics of this model were consistent with the data, both papers demonstrated that the model predicts the wrong sign of the term premium: the theory implies the term premium should be negative while, based on quarterly data for yields of three- and six-month U.S. Treasury Bills over the period 1959.1-1989.4, the observed term premium is positive. Similar to the equity premium puzzle as posed by Mehra and Prescott [1985], the prediction of a negative average term premium signals a critical discrepancy between the risk associated with nominal bonds as perceived by market participants and as captured by the models. Moreover, this term premium puzzle is in some sense a stronger rejection of the underlying asset pricing model than that embodied by the equity premium puzzle. To see this, recall that within the consumption-based asset pricing model, the sign of the risk premium on any asset depends on the sign of the covariance between the marginal utility of consumption and that asset's return. Applying this reasoning to the case of the equity premium suggests that, while the discrepancy in size between the observed equity premium and that generated within the model is troubling, the model's prediction of a positive equity premium implies that the basic payout structure of equity within the model is consistent with that in the data (e. …

We test a model to estimate the equity risk premium based on a stock valuation model suggested by former Federal Reserve Chairman, Alan Greenspan. The model suggests that the stock market is fairly priced when the price of the market portfolio is equal to the ratio between market earnings and the yield on the 10-year Treasury bond. From this stock valuation model and extensions to it, we derive an equation for the expected market risk premium. Ex post we find that a model which accounts for corporate bond yields and the inherent differences between common stocks and Treasury bonds (most notably risk) provides a good estimate of the equity risk premium. <b>TOPICS:</b>Analysis of individual factors/risk premia, factor-based models, statistical methods

Empirical Tests of Asset Pricing Models with Individual Assets: Resolving the Errors-in-Variables Bias in Risk Premium Estimation

The purpose of the work is to examine the relationship between market risk premium and default. The research hypothesis assumes that the amount of the market risk premium significantly affects the level of the estimated probability of default of the company. The analysis was carried out using the example of the largest capital markets in the European Union and GFCI within the period from 1 January 2012 to 31 December 2018. Time series of the 20 most important stock market indices of non-financial companies representing all continents were applied in the empirical study. The largest non-financial companies, with regard to assets held as of 1 January 2012, listed on particular capital markets and included in the analyzed stock indices, one for each index, were included in the study. The following research methods were applied: the CAPM equilibrium model, Sharpe’s market asset value ratio and the market value of the corporate equity. The empirical study used time series of the 20 most important stock market indices of non-financial companies representing the analyzed markets. As a result of the analysis, the following research conclusion was established: the final value of companies from the GFCI area does not prove any significant difference with regard to their value before considering the risk premium. In the case of the EU market, this difference is significant. This means that capital markets with weaker capital and poorer, less stable economic conditions are less able to face market risk

This paper investigates the relation between the conditional expected equity risk premium and the slope of the term structure of interest rates. Theoretically, these variables are linked, the relation may be nonlinear, and negative risk premiums are consistent with equilibrium. Given these implications, we employ a nonparametric estimation technique to document the empirical relation between the risk premium and the slope of the term structure using almost two hundred years of data. Of particular interest, the risk premium is increasing in the term structure slope; however, for either small or negative slopes, the risk premium is much more sensitive to changes in interest rates. In addition, the empirical results imply negative expected equity risk premiums for some inverted term structures. Finally, variations in the risk premium do not appear to be related to variations in the variance of equity returns. We illustrate these features in a stylized consumption-based model, and provide the economic intuition behind the results.

This study examines the relationship between interest rates and utility equity risk premiums. We found that an inverse relationship exists, with an equity risk premium changing by 37 basis points for each 100 basis-point change in the 30-year Treasury bond yield. The inverse relationship is stable; however, changes in the relative risk of debt and equity securities produce shifts in the level of risk premiums, regardless of the behavior of Treasury bond yields. We also found that the equity risk premiums were consistently positive over the study period, which conforms to the basic risk/return tenet of finance.

Exchange rate predictability, risk premiums, and predictive system

We examine the link between equity risk premiums and demographic changes using a very long sample over the whole twentieth century for the US, Japan, UK, Germany and France, and a shorter sample covering the last third of the twentieth century for fifteen countries. We find that demographic variables significantly predict excess returns internationally. However, the demographic predictability found in the US by past studies for the average age of the population does not extend to other countries. Pooling international data, we find that, on average, faster growth in the fraction of retired persons significantly decreases risk premiums. This demographic predictability of risk premiums is stronger for countries with well-developed social security systems and lesser-developed financial markets. JEL Classification: G12, G15, J10, P46

We examine the link between equity risk premiums and demographic changes using a very long sample over the twentieth century for the US, Japan, UK, Germany and France, and a shorter sample covering the last third of the twentieth century for fifteen countries. We find that demographic variables significantly predict excess returns internationally. However, the demographic predictability found in the US by past studies for the average age of the population does not extend to other countries. Pooling international data, we find that, on average, faster growth in the fraction of retired persons significantly decreases risk premiums. This demographic predictability of risk premiums is strongest in countries with well-developed social security systems and lesser-developed financial markets.

The Equity Risk Premium in 2008: Evidence from the Global CFO Outlook Survey