Isolating the disaster risk premium with equity options

The US equity risk premium is approximated with a mean unhedged equity return. I utilize out-of-the-money put options to obtain a hedged equity return, which allows me to quantify the disaster risk premium as the difference between the means of unhedged and hedged equity returns. I demonstrate that a substantial fraction of the U.S. equity risk premium over the period from 1996 to 2016 is attributed to disasters defined as stock price depreciations below a pre-specified strike price. Employing alternative hedging schemes increases the contribution of disasters to the equity risk premium.     

Estimating the equity premium

Accurate estimation of the equity premium (the expected difference between the returns to a well-diversified stock market portfolio and a riskfree asset) is of central importance in many applications of finance theory including project appraisal and portfolio selection. The standard approach is to take the average observed excess returns to the market over some recent time period (sometimes referred to as the ex post equity premium) and apply this as an unbiased estimate of the ex ante equity premium. The paper reviews the problems associated with such an approach and contrasts it with alternative theoretical techniques.     

货币政策公告、政策不确定性及股票市场的预公告溢价效应——来自中国市场的证据

中国人民银行周期性发布的货币政策相关公告为市场判断货币政策走向提供重要信息。较于实体经济反馈政策信息具有滞后性,股票市场是否在货币政策公告期内及时对政策消息做出反应,即存在公告效应？股票价格是否体现预期货币政策调整带来的不确定性？本文基于2011-2017年A股市场数据,研究我国股票市场在我国货币政策相关公告发布前后几日这一较短窗口区间内的市场反应。结果表明,股市指数在发布货币供应量指标的公告前几天内会出现显著为正的风险溢价,而在指标发布后溢价并不显著,这一现象我们称之为货币政策相关公告的“预公告溢价效应”。本文发现,预公告溢价的产生并非由于市场提前预期到货币政策的走向,而是来源于投资者预先获得了对政策不确定性的溢价补偿。本文进一步就防范系统性风险、从数量型货币政策工具向价格型转变等问题提出了相关政策建议。     

MACROECONOMIC VARIABLES AND SEASONAL MEAN REVERSION IN STOCK RETURNS

In this paper I investigate whether seasonal mean reversion in stock portfolio returns is related to common macroeconomic risk factors. I decompose excess returns into explained and unexplained returns using a multifactor pricing model. The explained excess returns exhibit January mean reversion; the unexplained excess returns do not. The mean reversion can be attributed to the components of return related to unexpected inflation, bond default premium, and market risk. The results do not depend on the time-series properties of the portfolio betas. Bond default premia and excess market returns are mean reverting in January.     

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.     

ESTIMATING THE EQUITY RISK PREMIUM AND EQUITY COSTS: NEW WAYS OF LOOKING AT OLD DATA

This article examines three alternative ways of estimating the expected return on the equity market in using the CAPM or some other risk premium model. The three techniques are (1) direct estimation of the average nominal equity return for use as a forecast nominal equity return; (2) estimation of the average real equity return, which can then be added to a forecast inflation rate; and (3) estimation of an average equity risk premium, which is then added to a current risk-free rate. Ibbotson and Sinquefeld's data on annual holding period returns are used to test the validity of their assumption that the equity risk premium follows a random walk and that the third of these approaches is thus the best method.
The paper reaches three major conclusions. First, each of these three techniques involves a "bias" of some kind. The use of average equity returns as a forecast is subject to "risk-free rate" and "inflation rate" biases, while the use of an average equity risk premium is subject to a "term premium" bias. As a result, only the data can tell us which approach is best. Second, from analyzing equity and bond return data and the trend in interest rates, the author concludes that the term premium bias when using average historic equity risk premium is by far the largest of the three sources of bias. Indeed, the popular practice of adding an historic average equity risk premium to the 30-year Treasury bond rate significantly overstates equity costs. Third, after examining equity rates of return back to 1871, the author concludes that the real equity return seems to follow a process that is close to a random walk and is thus the "best" of the three techniques to use as a "naive" forecast.     

Equity returns,bond returns,and the equity premium in the German capital market

This article reviews the empirical evidence for equity returns, bond returns, and the equity premium in the German capital market for the period from 1870 to 1995. Taken together, the studies reviewed provide convincing evidence that over longer investment periods, average equity returns have been higher than average bond returns. These excess returns, however, have been highly volatile and negative in many years, illustrating the higher risk of equity investments. Moreover, market timing had a major positive or negative impact on overall returns. Despite the historical evidence of a substantial equity premium there is still little equity investment by German households.     

Habit formation and the equity–premium puzzle: a skeptical view

We argue that, ceteris paribus, introducing a habit that resolves the equity–premium puzzle is equivalent to increasing the Arrow-Pratt coefficient of relative risk aversion, AP-RRA. If we constrain the AP-RRA to a constant ‘acceptable’ level, the effect on the equity premium is quantitatively insignificant. In a dynamic setting, the fluctuations of the habit increase the equity premium, slightly, though generates unrealistic fluctuations in the risk-free interest rate. We conclude a habit is observationally equivalent, up to a first-order approximation, to a higher AP-RRA and to a preference shock. These effects cannot resolve the equity–premium puzzle.      

Monetary policy and the cyclicality of risk

A dynamic general equilibrium model to study the relationship between monetary policy and movements in risk is developed. Variation in risk arises because households face fixed costs of transferring cash across financial accounts, implying that some households rebalance their portfolios infrequently. Accordingly, prices for risky assets respond sharply to aggregate shocks because only a relatively small subset of consumers are available to absorb these shocks. The model can account for both the mean and the volatility of returns on equity and the risk-free rate and generates a decline in the equity premium following an unanticipated easing of monetary policy.     

Estimating the Equity Risk Premium Using Accounting Fundamentals

This study uses recent developments in the theoretical modelling of the links between unrecorded accounting goodwill, accounting profitability and the cost of equity, together with Capital Asset Pricing Model (CAPM) betas, to estimate the ex-ante equity risk premium in the UK. The results suggest that, over our sample period from 1968 to 1995, the premium has been in the region of 5%. Our estimate lends support to the view that the ex-ante equity risk premium is substantially less than the historical average of the excess of equity returns over the risk-free rate, and is similar to the rates applied recently by UK competition regulators.     

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.     

Time-varying risk aversion and asset prices

This paper uses a variant of the consumption-based representative agent model in Campbell and Cochrane [Campbell, J.Y., Cochrane, J.H., 1999. By force of habit: Consumption-based explanation of aggregate stock market behavior. Journal of Political Economy 107, 205–251] to study how investors’ time-varying risk aversion affects asset prices. First, we show that a countercyclical variation of risk aversion drives a procyclical conditional risk premium. Second, we show that with a small value for the volatility of the log surplus consumption ratio, a large value of risk aversion may not determine whether the equity premium and the risk-free rate puzzles can be resolved or not. Third, we show that countercyclical risk aversion may not help explain the predictability of long-horizon stock returns, the univariate mean-reversion of stock prices and the “leverage effect” in return volatility.     

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.     

Do Beta Pricing Models Explain January Mean Reversion in Stock Returns?

Jegadeesh (1991) finds evidence of January mean reversion in stock returns. In this paper we attempt to distinguish between two competing economic explanations of January mean reversion in returns: (1) mispricing in irrational markets versus (2) predictable time variation in security risk premia. Excess portfolio returns are decomposed into “explained” and “unexplained” components using the Fama-French (1993) pricing model. The explained excess returns exhibit January mean reversion. The unexplained excess returns are not mean reverting. Mean reversion is therefore consistent with rational pricing in the framework of the Fama-French model. Mean reversion can be attributed to the component of return related to a relative distress factor (SMB). A comparison with the Chen, Roll, and Ross (1986) macroeconomic factors reveals that mean reversion is due to the components related to SMB and bond default premium.     

Equity premium estimates from economic fundamentals under structural breaks

This article compares three estimates of the conditional equity premium using dividend and earnings growth rates to measure the expected rate of capital gain. The premia are estimated using a theory-informed Bayesian model that admits structural breaks. The equity premium fell from 8.16% in 1951 to 1.15% in 1985. Approximately half of this decline was reversion of a high conditional premium to the long run mean and the remainder resulted from a decline in the expected stock return. The decline in the expected stock return was largely driven by the Fed Accord (1951) and the Fed's ‘monetarist policy experiment’ (1979–1982).     

Rejoinder

This paper provides a formula for a commonly used measure of the economic value of asset return predictability. In doing this, we find that there is a strong connection between this measure and a traditional statistical measure of predictive quality. In particular, we demonstrate that the maximum amount an investor is willing to pay for predictability knowledge (the performance fee) is a simple transformation of the R ² statistic associated with the predictor equation. We illustrate the use of these results with an application to the Ibbotson US bond and equity data (and a set of pertinent predictors), and via application to the results published in Fama and French [1988. Dividend yields and expected stock returns. Journal of Financial Economics 22: 3–25], Balvers, Cosimano, and McDonald [1990. Predicting stock returns in an efficient market. Journal of Finance 45: 1109–28], Lettau and Ludvigson [2001. Consumption, aggregate wealth and expected stock returns. Journal of Finance 56: 815–49], and Santa-Clara and Yan [2010. Crashes, volatility, and the equity premium: Lessons from S&;P 500 options. Review of Economics and Statistics 92: 435–51].     

The Comovement of US and UK Stock Markets

US and UK stock returns are highly positively correlated over the period 1918–99. Using VAR‐based variance decompositions, we investigate the nature of this comovement. Excess return innovations are decomposed into news about future dividends, real interest rates, and excess returns. We find that the latter news component is the most important in explaining stock return volatility in both the USA and the UK and that stock return news is highly correlated across countries. This is evidence against Beltratti and Shiller's (1993) finding that the comovement of US and UK stock markets can be explained in terms of a simple present value model. We interpret the comovement as indicating that equity premia in the two countries are hit by common real shocks.     

Explaining the equity premium in Hong Kong with C-CAPM: The use of emigration growth as an instrument

We test the C-CAPM with CRRA utility using Hong Kong data. In 2SLS regressions, we obtain rather high estimates of the coefficient of relative risk aversion, which could explain the high equity premium in Hong Kong. Because we use lagged emigration growth as an instrument in the first-stage regression, which has significant negative impact on future stock market return in Hong Kong, the first-stage R² and F-statistics are rather high and the weak instrument critique of the validity of 2SLS regressions is potentially resolved. Weak-instrument-robust tests also confirm that the degree of risk aversion is indeed high for Hong Kong.     

Stock selection using a multi-factor model - empirical evidence from the French stock market

Using a Barra-type factor model, we have attempted to determine whether it is possible to beat the benchmark by taking advantage of anomalies established in the financial empirical literature. More specifically we have built an equity premium model based on three sets of factors (accounting variables, stock market characteristics and sector indicators) using a Bayesian method corrected for heteroscedasticity to estimate risk premiums, a technique that takes agents' learning into account. The results are encouraging: first, the factors that carried most weight on the equity premiums corroborated the results of empirical studies described in the financial literature, secondly, the portfolios constructed from our methodology and simulated outside our sample, returned higher performance than the benchmark and rewarded the supplement of volatility.     

Conditional Equity Premium and Aggregate Corporate Investment

We document a strong negative relation between aggregate corporate investment and conditional equity premium estimated from direct stock market risk measures. Consistent with the investment-based asset pricing model, the comovement with conditional equity premium fully accounts for aggregate investment's market return predictive power. Similarly, conditional equity premium is a significant determinant of classic Tobin's q measure, although q has much weaker explanatory power for aggregate investment possibly because of its measurement errors. Moreover, the positive relation between aggregate investment and investor sentiment documented in previous studies reflects the fact that both variables correlate closely with conditional equity premium.