A tale of two regimes: Theory and empirical evidence for a Markov-modulated jump diffusion model of equity returns and derivative pricing implications

We provide closed-form solutions for a continuous time, Markov-modulated jump diffusion model in a general equilibrium framework for options prices under a variety of jump diffusion specifications. We further demonstrate that the two-state model provides the leptokurtic return features, volatility smile, and volatility clustering observed empirically for the Dow Jones Industrial Average (DJIA) and its component stocks. Using 10 years of stock return data, we confirm the existence of jump intensity switching and clustering, illustrate transition probabilities, and verify superior empirical fit over competing Poisson-style models.     

Executive stock options,differential risk-taking incentives,and firm value

The sensitivity of stock options' payoff to return volatility, or vega, provides risk-averse CEOs with an incentive to increase their firms' risk more by increasing systematic rather than idiosyncratic risk. This effect manifests because any increase in the firm's systematic risk can be hedged by a CEO who can trade the market portfolio. Consistent with this prediction, we find that vega gives CEOs incentives to increase their firms' total risk by increasing systematic risk but not idiosyncratic risk. Collectively, our results suggest that stock options might not always encourage managers to pursue projects that are primarily characterized by idiosyncratic risk when projects with systematic risk are available as an alternative.     

Fundamentals or Managerial Discretion? The Relationship between Accrual Variability and Future Stock Return Volatility

This study extends the theoretical framework of Callen and Segal (2004) and Vuolteenaho (2002) to investigate the association between accrual variability and firm‐level stock return volatility. The empirical evidence supports our prediction that increased uncertainty in current‐period accounting accruals is associated with significantly higher volatility of future stock returns, and the results are valid for measures of both systematic and idiosyncratic volatility. When accrual variability is decomposed into fundamental and discretionary portions, we find that the positive relationship between accrual variability and future stock return volatility is dominated by the fundamental component of accrual variability. Overall, our results suggest that uncertainty reflected in accrual information is subsequently reflected in the fluctuation of future stock returns, and that the predictive content in accruals primarily reflects firms' fundamental uncertainty, rather than any effects of managerial choices and interventions in the accounting process.     

Idiosyncratic risk,costly arbitrage,and the cross-section of stock returns

We test a new cross-sectional relation between expected stock return and idiosyncratic risk implied by the theory of costly arbitrage. If arbitrageurs find it more difficult to correct the mispricing of stocks with high idiosyncratic risk, there should be a positive (negative) relation between expected return and idiosyncratic risk for undervalued (overvalued) stocks. We combine several well-known anomalies to measure stock mispricing and proxy stock idiosyncratic risk using an exponential GARCH model for stock returns. We confirm that average stock returns monotonically increase (decrease) with idiosyncratic risk for undervalued (overvalued) stocks. Overall, our results support the importance of idiosyncratic risk as an arbitrage cost.     

The cross-sectional relation between conditional heteroskedasticity,the implied volatility smile,and the variance risk premium

This paper estimates how the shape of the implied volatility smile and the size of the variance risk premium relate to parameters of GARCH-type time-series models measuring how conditional volatility responds to return shocks. Markets in which return shocks lead to large increases in conditional volatility tend to have larger variance risk premia than markets in which the impact on conditional volatility is slight. Markets in which negative (positive) return shocks lead to larger increases in future volatility than positive (negative) return shocks tend to have downward (upward) sloping implied volatility smiles. Also, differences in how volatility responds to return shocks as measured by GARCH-type models explain much, but not all, of the variations in excess kurtosis and multi-period skewness across different markets.     

Can tail risk explain size,book‐to‐market,momentum, and idiosyncratic volatility anomalies?

We examine the impact of tail risk on the return dynamics of size, book‐to‐market ratio, momentum and idiosyncratic volatility sorted portfolios. Our time‐series analyses document significant portfolio return exposures to aggregate tail risk. In particular, portfolios that contain small, value, high idiosyncratic volatility and low momentum stocks exhibit negative and statistically significant tail risk betas. Our cross‐sectional analyses at the individual stock level suggest that tail risk helps in explaining the four pricing anomalies, particularly size and idiosyncratic volatility anomalies.     

New evidence on the implied-realized volatility relation

We consider the relation between the volatility implied in an option's price and the subsequently realized volatility. Earlier studies on stock index options have found biases and inefficiencies in implied volatility as a forecast of future volatility. More recently, Christensen and Prabhala find that implied volatility in at-the-money one-month OEX call options on the S&P 100 index in fact is an unbiased and efficient forecast of ex-post realized index volatility after the 1987 stock market crash. In this paper, the robustness of the unbiasedness and efficiency result is extended to a more recent period covering April 1993 to February 1997. As a new contribution, implied volatility is constructed as a trade weighted average of implied volatilities from both in-the-money and out-of-the-money options and both puts and calls. We run a horse race between implied call, implied put, and historical return volatility. Several robustness checks, including a new simultaneous equation approach, underscore our conclusion, that implied volatility is an efficient forecast of realized return volatility.     

The Conditional Performance of REIT Stock Repurchases

This paper uses a conditional performance measure to test whether real estate investment trust (REIT) managers announcing stock repurchases have private information about their firms' prospects. We use stock price to condition for public information and measure the managers' implied private information by the covariance between repurchase size and subsequent stock payoffs (or operating performance). Results show that managers have private information but mostly with respect to long-term as opposed to near-term payoffs. We also find that repurchase size is positively related to a stock's idiosyncratic return volatility, perhaps because noisy stocks deviate farther from fundamental value, offering informed managers larger profit potential. JEL Classification G12 G14 G35     

Short-term asymptotics for the implied volatility skew under a stochastic volatility model with Lévy jumps

The implied volatility skew has received relatively little attention in the literature on short-term asymptotics for financial models with jumps, despite its importance in model selection and calibration. We rectify this by providing high order asymptotic expansions for the at-the-money implied volatility skew, under a rich class of stochastic volatility models with independent stable-like jumps of infinite variation. The case of a pure-jump stable-like Lévy model is also considered under the minimal possible conditions for the resulting expansion to be well defined. Unlike recent results for “near-the-money” option prices and implied volatility, the results herein aid in understanding how the implied volatility smile near expiry is affected by important features of the continuous component, such as the leverage and vol-of-vol parameters. As intermediary results, we obtain high order expansions for at-the-money digital call option prices, which furthermore allow us to infer analogous results for the delta of at-the-money options. Simulation results indicate that our asymptotic expansions give good fits for options with maturities up to one month, underpinning their relevance in practical applications, and an analysis of the implied volatility skew in recent S&P 500 options data shows it to be consistent with the infinite variation jump component of our models.     

Does more information in stock price lead to greater or smaller idiosyncratic return volatility?

We investigate the relation between price informativeness and idiosyncratic return volatility in a multi-asset, multi-period noisy rational expectations equilibrium. We show that the relation between price informativeness and idiosyncratic return volatility is either U-shaped or negative. Using several price informativeness measures, we empirically document a U-shaped relation between price informativeness and idiosyncratic return volatility. Our study therefore reconciles the opposing views in the following two strands of literature: (1) the growing body of research showing that firms with more informative stock prices have greater idiosyncratic return volatility, and (2) the studies arguing that more information in price reduces idiosyncratic return volatility.     

Cross section of option returns and idiosyncratic stock volatility

This paper presents a robust new finding that delta-hedged equity option return decreases monotonically with an increase in the idiosyncratic volatility of the underlying stock. This result cannot be explained by standard risk factors. It is distinct from existing anomalies in the stock market or volatility-related option mispricing. It is consistent with market imperfections and constrained financial intermediaries. Dealers charge a higher premium for options on high idiosyncratic volatility stocks due to their higher arbitrage costs. Controlling for limits to arbitrage proxies reduces the strength of the negative relation between delta-hedged option return and idiosyncratic volatility by about 40%.     

The pricing of idiosyncratic risk: evidence from the implied volatility distribution

A recent strand in the literature has investigated the relationship between idiosyncratic risk and future stock returns. Although several authors have found significant predictive power of idiosyncratic volatility, the magnitude and direction of the dependence is still being debated. Using a sample of all S&P 100 constituents, we identify positive risk premia for option-implied idiosyncratic risk. Depending on the model used to identify unsystematic risk, we observe a statistically and economically significant average annual premium of 1.72 percent. To investigate whether this impact is driven by the definition of idiosyncratic risk, we extend the pricing kernel by implied skewness. Using a double-sorting procedure, we show that the compensation of unsystematic risk is mainly driven by firms with high positive implied skewness.     

Idiosyncratic return volatility and the role of firm fundamentals: A cross-country analysis

We investigate the relation between fundamental idiosyncratic volatility and stock returns idiosyncratic volatility using data from 56 countries. We find a strong positive relation between fundamental idiosyncratic volatility and idiosyncratic volatility of returns. This association, however, seems to be entirely concentrated in the developed economies, and we find no effect in the emerging markets. Specifically, fundamental idiosyncratic volatility does not lead to more idiosyncratic return volatility in countries with poor legal institutions and weak shareholder protection laws.     

Additional evidence on transparency and bank financial performance

This paper examines the relationship between volatility and the probability of occurrence of expected extreme returns in the Canadian market. Four measures of volatility are examined: implied volatility from firm option prices, conditional volatility calculated using an EGARCH model, idiosyncratic volatility, and expected shortfall. A significantly positive relationship is observed between a firm's idiosyncratic volatility and the probability of occurrence of an extreme return in the subsequent month for firms. A 10% increase in idiosyncratic volatility in a given month is associated with the probability of an extreme shock in the subsequent month (top or bottom 1.5% of the returns distribution) of 26.4%. Other firm characteristics, including firm age, price, volume and book‐to‐market ratio, are also shown to be significantly related to subsequent firm extreme returns. The effects of conditional and implied volatility are mixed. The E‐GARCH and expected shortfall measures of conditional volatility are consistent with mean reversion: high short term realizations of conditional volatility foreshadow a lower probability of extreme returns.     

The information content of implied skewness and kurtosis changes prior to earnings announcements for stock and option returns

We use option prices to examine whether changes in stock return skewness and kurtosis preceding earnings announcements provide information about subsequent stock and option returns. We demonstrate that changes in jump risk premiums can lead to changes in implied skewness and kurtosis and are also associated with the mean and variability of the stock price response to the earnings announcement. We find that changes in both moments have strong predictive power for future stock returns, even after controlling for implied volatility. Additionally, changes in both moments predict call returns, while put return predictability is primarily linked to changes in skewness.     

Return dispersion and expected returns

This paper proposes a two-factor asset-pricing model that incorporates market return and return dispersion. Consistent with this model, we find that stocks with higher sensitivities to return dispersion have higher average returns, and that return dispersion carries a significant positive price of risk. In particular, the return dispersion factor dominates the book-to-market factor in explaining cross-sectional expected returns. The return dispersion model outperforms the CAPM, MVM, IVM, and FF-3M when using a set of 5×5 test portfolios constructed from NYSE and AMEX stock returns from August 1963 to December 2005. Return dispersion continues to play an important role in explaining the cross-sectional variation of expected returns, even when market volatility, idiosyncratic volatility, size, book-to-market factors, and a momentum factor are included. This study sheds some light on the ability of return dispersion to explain expected returns beyond the standard asset-pricing factors. Our finding suggests that return dispersion captures two dimensions of systematic risk: the business cycle and fundamental economic restructuring.     

Idiosyncratic risk does not matter: A re-examination of the relationship between average returns and average volatilities

A recent study by Goyal and Santa-Clara [J. Finance 58 (2003) 975] finds a significantly positive relationship between average stock returns and pre-determined average return volatility measures, while finding no relationship between the average return and its own volatility. The result is interpreted as evidence that idiosyncratic risk matters in asset pricing. We re-examine the issue in extended sample periods and find the proclaimed positive relationship is not substantiated. Our analysis indicates that the above-mentioned positive relationship is mainly driven by the data in the 1990s. The trading strategy suggested by Goyal and Santa-Clara to exploit the return predictability by pre-determined volatility does not yield sustained economic gains.     

Analysts’ estimates of the cost of equity capital

We explore a large sample of analysts' estimates of the cost of equity capital (CoE) to evaluate their usefulness as expected return proxies (ERP). We find that the CoE estimates are significantly related to a firm's beta, size, book-to-market ratio, leverage, and idiosyncratic volatility but not other risk proxies. Even after controlling for the popular return predictors, the CoE estimates incrementally predict future stock returns. This predictive ability is better explained as the CoE estimates containing ERP information rather than reflecting stock mispricing. When evaluated against traditional ERPs, including the implied costs of capital, the CoE estimates are found to be the least noisy. Finally, we document CoE responses around earnings announcements, demonstrating their usefulness to study discount-rate reactions of market participants. We conclude that analysts' CoE estimates are meaningful ERPs that can be fruitfully employed in a variety of asset pricing contexts.     

Credible reforms and stock return volatility: Evidence from privatization

In this paper we investigate how privatization affects stock return volatility. A credible privatization builds investors’ confidence through a reduction in political risk. In particular, a privatization program that is maintained over time signals credibility, which reduces political risk and in turn volatility. We further show that privatization is associated with lower idiosyncratic volatility mainly among developed markets, while it is associated with lower systematic volatility in developing markets. Additional tests suggest that the reduction in volatility is greater when privatization sales are carried out through the stock market than through asset sales.     

Do idiosyncratic jumps matter?

We show that idiosyncratic jumps are a key determinant of mean stock returns from both an ex post and ex ante perspective. Ex post, the entire annual average return of a typical stock accrues on the four days on which its price jumps. Ex ante, idiosyncratic jump risk earns a premium: a value-weighted weekly long-short portfolio that buys (sells) stocks with high (low) predicted jump probabilities earns annualized mean returns of 9.4% and four-factor alphas of 8.1%. This strategy’s returns are larger when there are greater limits to arbitrage. These results are consistent with investor aversion to idiosyncratic jump risk.