TIME-SERIES PROPERTIES OF THE EQUITY RISK PREMIUM

In this paper we use time-series models to investigate the presence of autoregression, random variation, and random walk movements of historic equity risk premiums. An autoregressive risk premium is found for 1926–58, but random variation around a much lower risk premium mean is found for 1959–90. This finding is not sensitive to holding-period length, the choice of the risk-free rate proxy, or January/July seasonal effects.     

Estimating the Equity Risk Premium and Expected Equity Rates of Return: The Case of Canada

It is common to use the average excess return of equities over bonds estimated over long time periods as an expected equity risk premium on the grounds that going back far enough covers most possible economic scenarios. But although this data is useful in guiding the exercise of judgment, it cannot substitute for judgment. Adding more years of data to the near century of Canadian stock and bond returns that inform today's estimate of the equity risk premium will not produce a “random walk” for a simple reason: the historic bond series is the result of a specific historic monetary policy. This is particularly true of and important for the case of Canada, where today's very low current bond yields reflect the emergence of the Canadian dollar as a reserve currency as well as the impact of unconventional monetary policy elsewhere. After analyzing the historic record of the Canadian equity risk premium and noting the need for adjustments when this premium is applied to the current anomalously low Canadian long‐term bond yields, the author reaches the following conclusions:

• The historic Canadian equity risk premium is approximately 5.0% (based on arithmetic returns), which is slightly lower than the roughly 6.0% value for the U.S.
• The historic equity risk premium has not been constant because of obvious changes in the Canadian bond market. To some extent, the huge cycle in which bond yields began their increase from the 4.0% level starting in 1957, when markets were liberalized, and then fell back to the 4.0% level in 2007‐2008 completed an adjustment to changes in fiscal versus monetary policy. However, in 2016, average long Canada bond yields dropped to an anomalously low 1.8%, which is below the long‐term inflation target of the Bank of Canada, and have barely recovered since. It is difficult to view this as an equilibrium rate determined by private investors.
• Of the drop in bond yields, about 0.50% is unique to Government of Canada bonds as they became attractive to sovereign investors as a rare AAA‐rated issuer.
• Using an indicator variable for the post‐2010 years, a simple regression analysis indicates that current long Canada bond yields should be about 2.75% higher but for the recent changes. And for 2018, this means that the 2.35% average long Canada bond yield should have been about 5.0%. Apart from the impact of higher government deficits, this is consistent with average yields before the 2008 financial crisis.
• Adding an adjusted 5.0% long Canada bond yield to the historic equity risk premium in Canada of 4.50% gives 9.50% for the cost of the overall equity market or, given the Bank of Canada's target inflation rate of 2.0%, a real equity return of 7.5%, both slightly higher than the long‐run averages.

In sum, the conventional practice of adding a historic market risk premium to the current low Canada long bond yields would impart a sharp downward bias to current equity cost estimates; use of this method would not be appropriate until long Canada bond yields increase to at least the 4.0% level.     

An introduction to security returns

The equity premium - the difference between the return achievable from investment in the equity market (R_M ) and the risk-free rate of return (R_F )- plays an important part in corporate finance. The expression equity premium (sometimes referred to as the equity risk premium) is used to denote the ex ante expectation of investors. The term excess return refers to the ex post achievement of stock returns over and above the risk-free return. If we compare US and UK returns, we find that total returns, real returns and the value of (R_M - R_F ) are all marginally higher for the UK. Summarized evidence appears in Table 1 and Table 6. Such greater returns may be due to an increased risk premium related to increasing unexpected inflation. Particularly important in estimating the equity risk premium is whether excess returns are measured using a geometric or an arithmetic mean return. To a significant extent, this question revolves around mean reversion in stock returns. Evidence of mean reversion is substantial, although it cannot be proved unequivocally. Given the weight of evidence of mean reversion, there may be a strong case for the use of a geometric mean with an equity premium of between 3% and 5% - or even less.     

AN ECONOMETRIC ANALYSIS OF EQUITY COSTS AND RISK PREMIUMS IN THE ELECTRIC UTILITY INDUSTRY: 1971–1985

This paper develops a varying parameter econometric model that estimates the cost of equity of individual utility firms from 1971 to 1985. The equity costs estimated in this framework can be analyzed in terms of their statistical precision. The paper also examines, theoretically and empirically, the relationship between the econometric estimates of the equity risk premiums and the risk-free interest rates. The data do not support the hypothesis that risk premiums are independent of interest rates. Also, the relationship appears to vary over time. These results invalidate the risk premium approach in which equity costs are estimated by adding a constant, historical average risk premium to the prevailing interest rates.     

GLOBAL EVIDENCE ON THE EQUITY RISK PREMIUM

The size of the equity risk premium—the incremental return that shareholders require to hold risky equities rather than risk-free securities—is a key issue in corporate finance. Financial economists generally measure the equity premium over long periods of time in order to obtain reliable estimates. These estimates are widely used by investors, finance professionals, corporate executives, regulators, lawyers, and consultants. But because the 20th century proved to be a period of such remarkable growth in the U.S. economy, estimates of the risk premium that rely on past market performance may be too high to serve as a reliable guide to the future.
The authors analyze a 103-year history of risk premiums in 16 countries and conclude that the U.S. risk premium relative to Treasury bills was 5.3% for that period—lower than previous studies suggest—as compared to 4.2% for the U.K. and 4.5% for a world index. But the article goes on to observe that the historical record may still overstate expectations of the future risk premium, partly because market volatility in the future may be lower than in the past, and partly because of a general decline in risk resulting from new technological advances and increased diversification opportunities for investors. After adjusting for the expected impact of these factors, the authors calculate forward-looking equity risk premiums of 4.3% for the U.S., 3.9% for the U.K., and 3.5% for the world index. At the same time, however, they caution that the risk premium can fluctuate over time and that managers should make appropriate adjustments when there are compelling economic reasons to think that expected premiums are unusually high or low.     

Returns after personal tax on UK equity and gilts, 1919–1998

This paper investigates whether personal tax could help explain the size of the historic equity premium in the UK measured before personal tax. If there has been a higher tax burden on equity, some of the premium could be viewed as compensation for tax. It is estimated here that personal tax reduces the arithmetic mean nominal return on equity from 13.3% to 11.1% pa during the period 1919–1998, and the mean return on gilts from 7.1% to 5.6% pa. Thus, personal tax accounts for a slightly higher proportion of the before-tax return on gilts than on equity, implying that the equity premium is not a compensation for a higher tax burden on equity.     

我国企业财务决策分析框架的构建

本文提出建立适应我国资本市场化条件下的企业财务决策分析框架问题,主要包括价值极大化目标问题、无风险利率的形成机制及测算、市场风险的定价、权益资本风险溢价、试算财务报表的编制、自由现金流量测算以及股权资本价值测算等.     

The pricing of capital assets in a multiperiod world

This paper proposes a general framework for the pricing of capital assets in a multiperiod world. Under quite general conditions, the analysis shows that the equilibrium expected nominal return on any asset can always be expressed as the sum of the risk-free rate and various risk premiums. The first risk premium is identical to the usual risk premium in the Sharpe-Lintner-Mossin capital asset pricing model. The mathematical forms of all the remaining risk premiums are identical even though each individual risk premium may be present for a different reason.     

Market Illiquidity and Conditional Equity Premium

We examine the time‐series relation between aggregate bid‐ask spreads and conditional equity premium. We document that average marketwide relative effective bid‐ask spreads forecast aggregate market returns only when controlling for average idiosyncratic variance. This control allows us to document the otherwise elusive relation between illiquidity and returns. The reason is that idiosyncratic variance correlates positively with spreads but has a negative effect on conditional equity premium, causing an omitted variable bias. Our results are robust to standard return predictors, alternative illiquidity measures, and out‐of‐sample tests. These findings are important because they provide strong support for the literature's conjecture that marketwide liquidity is an important asset pricing risk factor.     

Monetary rules and the nominal rate of interest under uncertainty

The expected real rate of return on a nominal bond is shown to be equal to the real rate of interest plus a premium for systematic purchasing power risk. The particular monetary rule employed by the central monetary authority affects the entire joint distribution of inflation and aggregate real wealth. Thus, the monetary authority is able to influence the relationship between the real and nominal interest rate not only by affecting the expected rate of inflation but also by affecting the systematic purchasing power risk of fixed nominal claims.     

Robust general equilibrium under stochastic volatility model

This paper studies the implications of model uncertainty under stochastic volatility model for equilibrium asset pricing. We derive the equilibrium equity premium and risk-free rate in a pure-exchange economy with one representative agent who is averse not only to risk but also to model uncertainty. The results show that robustness increases the equilibrium equity premium while lowers the risk-free rate.     

Asset pricing in production economies with extrapolative expectations

Introducing extrapolative bias into a standard production-based model with recursive preferences reconciles salient stylized facts about business cycles (low consumption volatility, high investment volatility relative to output) and financial markets (high equity premium, volatile stock returns, low and smooth risk-free rate) with plausible levels of risk aversion and intertemporal elasticity of substitution. Furthermore, the model captures return predictability based upon dividend yield, Q, and investment. Intuitively, extrapolative bias increases the variation in the wealth–consumption ratio, which is heavily priced under recursive preferences; adjustment costs decrease the covariance between marginal utility and asset returns. Empirical support for key implications of the model is also provided.     

Equity Risk Premium

Abstract

The equity risk premium (ERP) is an essential building block of the market value of risk. In theory, the collective action of all investors results in an equilibrium expectation for the return on the market portfolio excess of the risk-free return, the ERP. The ability of the valuation actuary to choose a sensible value for the ERP, whether as a required input to capital asset pricing model valuation, or any of its descendants, is as important as choosing risk-free rates and risk relatives (betas) to the ERP for the asset at hand.

The historical realized ERP for the stock market appears to be at odds with pricing theory parameters for risk aversion. Since 1985, there has been a constant stream of research, each of which reviews theories of estimating market returns, examines historical data periods, or both. Those ERP value estimates vary widely from about ?1% to about 9%, based on a geometric or arithmetic averaging, short or long horizons, short- or long-run expectations, unconditional or conditional distributions, domestic or international data, data periods, and real or nominal returns.

This paper examines the principal strains of the recent research on the ERP and catalogues the empirical values of the ERP implied by that research. In addition, the paper supplies several time series analyses of the standard Ibbotson Associates 1926–2002 ERP data using short Treasuries for the risk-free rate. Recommendations for ERP values to use in common actuarial valuation problems also are offered.     

Resolving the Puzzling Intertemporal Relation between the Market Risk Premium and Conditional Market Variance: A Two-Factor Approach

The existing empirical literature fails to agree on the nature of the intertemporal relation between risk and return. This paper attempts to resolve the issue by estimating a conditional two-factor model motivated by Merton's intertemporal capital asset pricing model. When long-term government bond returns are included as a second factor, the partial relation between the market risk premium and conditional market variance is found to be positive and significant. The paper also helps explain the convoluted empirical relation between the market risk premium, conditional market variance, and the nominal risk-free rate previously reported in the literature.     

The ex ante real rate and inflation premium under a habit consumption model

This paper analyzes and quantifies ex ante components of bond yields – real rate of returns and risk premiums – from observed prices of nominal and indexed bonds in the United Kingdom from 1983 to 2000. The estimation uses an asset pricing framework based on a habit consumption model together with a joint formulation of consumption growth and inflation. Nominal yields carry a time-varying inflation premium that is significant throughout the period, increasing in the bond's maturity and contributing up to 25 basis points to yearly nominal yields. The analysis allows the extraction of the ex ante real rate from indexed bonds by properly taking into account both the incomplete indexation on these instruments and the inflation premium embedded in the nominal bonds.     

The equity premium implied by production

This paper studies the determinants of the equity premium as implied by producers’ first-order conditions. A simple closed form expression is presented for the Sharpe ratio as a function of investment volatility and technology parameters. Calibrated to the US postwar economy, the model can match the historical first and second moments of the market return and the risk-free interest rate. The model also generates a very volatile Sharpe ratio and market price of risk.     

Home bias in equity portfolios, inflation hedging, and international capital market equilibrium

We test whether the home bias in equity portfolios is causedby investors trying to hedge inflation risk. The empirical evidenceis consistent with this motive only if investors have very highlevels of risk tolerance and equity returns are negatively correlatedwith domestic inflation. We then develop a model of internationalportfolio choice and equity market equilibrium that integratesinflation risk and deadweight costs. Using this model we estimatethe levels of costs required to generate the observed home biasin portfolios consistent with different levels of risk aversion.For a level of risk aversion consistent with standard estimatesof the domestic equity market risk premium these costs are abouta few percent per annum greater than observable costs such aswithholding taxes. Thus, the home bias cannot be explained byeither inflation hedging or direct observable costs of internationalinvestment unless investors have very low levels of risk aversion.     

The Term Structure of Real Rates and Expected Inflation

Changes in nominal interest rates must be due to either movements in real interest rates, expected inflation, or the inflation risk premium. We develop a term structure model with regime switches, time‐varying prices of risk, and inflation to identify these components of the nominal yield curve. We find that the unconditional real rate curve in the United States is fairly flat around 1.3%. In one real rate regime, the real term structure is steeply downward sloping. An inflation risk premium that increases with maturity fully accounts for the generally upward sloping nominal term structure.     

Non-addictive Habit Formation and the Equity Premium Puzzle

I analyse a model in a simple representative-agent economy with one risky and one riskless asset, populated by habit forming consumer-investors. These consumer-investors exhibit non-addictive habit formation in the sense that the current consumption rate of the consumer-investors can fall below their past habit-forming consumption rate. I endogenise the real riskless rate of return in this representative-agent economy and find that the equity premium puzzle is resolved for plausible values of the coefficient of relative risk aversion, the discount rate, and the intensity of non-addictive habit formation. These values have been validated in previous empirical or survey-based studies. Non-addictive habit-formation studied here complements and extends current research on habit-forming preferences. Given a constant investment opportunity set, the real riskless rate in the economy increases with relative risk aversion of the consumer and decreases as the habit-formation intensity increases. Extensions with time-varying investment opportunity sets could explain the low risk-free rate and the relatively large variability of the market return over the variability of the risk-free rate through time.     

Do subjective expectations explain asset pricing puzzles?

The structural uncertainty model with Bayesian learning, advanced by Weitzman (AER 2007), provides a framework for gauging the effect of structural uncertainty on asset prices and risk premiums. This paper provides an operational version of this approach that incorporates realistic priors about consumption growth volatility, while guaranteeing finite asset pricing quantities. In contrast to the extant literature, the resulting asset pricing model with subjective expectations yields well-defined expected utility, finite moment generating function of the predictive distribution of consumption growth, and tractable expressions for equity premium and risk-free return. Our quantitative analysis reveals that explaining the historical equity premium and risk-free return, in the context of subjective expectations, requires implausible levels of structural uncertainty. Furthermore, these implausible prior beliefs result in consumption disaster probabilities that virtually coincide with those implied by more realistic priors. At the same time, the two sets of prior beliefs have diametrically opposite asset pricing implications.