Aggregate Jump and Volatility Risk in the Cross‐Section of Stock Returns

We examine the pricing of both aggregate jump and volatility risk in the cross‐section of stock returns by constructing investable option trading strategies that load on one factor but are orthogonal to the other. Both aggregate jump and volatility risk help explain variation in expected returns. Consistent with theory, stocks with high sensitivities to jump and volatility risk have low expected returns. Both can be measured separately and are important economically, with a two‐standard‐deviation increase in jump (volatility) factor loadings associated with a 3.5% to 5.1% (2.7% to 2.9%) drop in expected annual stock returns.     

A Tale of Two Anomalies: Higher Returns of Low‐Risk Stocks and Return Seasonality

Prior studies have shown that low beta and low volatility stocks earn higher average returns than high beta and high volatility stocks, contradicting the prediction of the capital asset pricing model and the fundamental relationship between risk and return. In this paper, we demonstrate that this phenomenon is driven by the seasonality of stock returns. We show that the risk‐return tradeoff does hold in the nonsummer months, and that switching to a portfolio of low‐risk stocks in summer outperforms—both in terms of absolute and in risk‐adjusted returns—buy and hold strategies as well as the Sell in May strategy of switching to treasury bills in summer.     

The Cross-Section of Volatility and Expected Returns

We examine the pricing of aggregate volatility risk in the cross‐section of stock returns. Consistent with theory, we find that stocks with high sensitivities to innovations in aggregate volatility have low average returns. Stocks with high idiosyncratic volatility relative to the Fama and French (1993, Journal of Financial Economics 25, 2349) model have abysmally low average returns. This phenomenon cannot be explained by exposure to aggregate volatility risk. Size, book‐to‐market, momentum, and liquidity effects cannot account for either the low average returns earned by stocks with high exposure to systematic volatility risk or for the low average returns of stocks with high idiosyncratic volatility.     

Value versus Growth: Time‐Varying Expected Stock Returns

Is the value premium predictable? We study time variations of the expected value premium using a two‐state Markov switching model. We find that when conditional volatilities are high, the expected excess returns of value stocks are more sensitive to aggregate economic conditions than the expected excess returns of growth stocks. As a result, the expected value premium is time varying. It spikes upward in the high volatility state, only to decline more gradually in the subsequent periods. However, out‐of‐sample predictability of the value premium is close to nonexistent.     

Stock return volatility,operating performance and stock returns: International evidence on drivers of the ‘low volatility’ anomaly

This study highlights the link between stock return volatility, operating performance, and stock returns. Prior studies suggest that there is a ‘low volatility’ anomaly, where firms with a low stock return volatility out-perform firms with a high stock return volatility. This paper confirms that low volatility stocks earn higher returns than high volatility stocks in emerging markets and developed markets outside of North America. We also show that low volatility stocks have higher operating returns and this might explain why low volatility stocks earn higher stock returns. These results provide a partial explanation for the ‘low volatility effect’ that is independent from the existence of market anomalies or per se inefficiencies that might otherwise drive a low volatility effect. We emphasize the importance of controlling for stock return volatility when analyzing operating performance and stock performance.     

Idiosyncratic Volatility Covariance and Expected Stock Returns

Given that the idiosyncratic volatility (IDVOL) of individual stocks co‐varies, we develop a model to determine how aggregate idiosyncratic volatility (AIV) may affect the volatility of a portfolio with a finite number of stocks. In portfolio and cross‐sectional tests, we find that stocks whose returns are more correlated with AIV innovations have lower returns than those that are less correlated with AIV innovations. These results are robust to controlling for the stock's own IDVOL and market volatility. We conclude that risk‐averse investors pay a premium for stocks that pay well when AIV is high, consistent with our model.     

The Volatility of Bid‐Ask Spreads

This study tests whether the volatility of bid‐ask spreads is positively related to expected returns. After controlling for market‐risk factors, we find that the average risk‐adjusted excess return for stocks in the highest spread volatility quintile is around 50 basis points per month. In a variety of multivariate tests, we find robust evidence of a return premium associated with spread volatility that is both statistically significant and economically meaningful. Our results are robust to controls for a variety of stock characteristics, different tick‐size regimes, and other measures of liquidity volatility.     

Investor Sentiment and the Cross-Section of Stock Returns

We study how investor sentiment affects the cross‐section of stock returns. We predict that a wave of investor sentiment has larger effects on securities whose valuations are highly subjective and difficult to arbitrage. Consistent with this prediction, we find that when beginning‐of‐period proxies for sentiment are low, subsequent returns are relatively high for small stocks, young stocks, high volatility stocks, unprofitable stocks, non‐dividend‐paying stocks, extreme growth stocks, and distressed stocks. When sentiment is high, on the other hand, these categories of stock earn relatively low subsequent returns.     

Leverage and the Cross‐Section of Equity Returns

Building on theoretical asset pricing literature, we examine the role of market risk and the size, book‐to‐market (BTM), and volatility anomalies in the cross‐section of unlevered equity returns. Compared with levered (stock) returns, unlevered market beta plays a more important role in explaining the cross‐section of unlevered equity returns, even after controlling for size and BTM. The size effect is weakened, while the value premium and the volatility puzzle virtually disappear for unlevered returns. We show that leverage induces heteroskedasticity in returns. Unlevering returns removes this pattern, which is otherwise difficult to address by controlling for leverage in regressions.     

The return impact of realized and expected idiosyncratic volatility

We show that the negative relation between realized idiosyncratic volatility, measured over the prior month, and returns is robust in non-January months. Controlling for realized idiosyncratic volatility, we show that the relation between returns and expected idiosyncratic volatility is positive and robust. Realized and expected idiosyncratic volatility are separate and important effects describing the cross-section of returns. We find the negative return on a zero-investment portfolio that is long high realized idiosyncratic volatility stocks and short low realized idiosyncratic volatility stocks is dependent on aggregate investor sentiment. In cross-sectional tests, we find the negative relation is weaker for stocks with a large analyst following and stronger for stocks with high dispersion of analyst forecasts. The positive relation between expected idiosyncratic volatility and returns is not due to mispricing.     

ESTIMATING EXPECTED EXCESS RETURNS USING HISTORICAL AND OPTION‐IMPLIED VOLATILITY

We test the relation between expected and realized excess returns for the S&P 500 index from January 1994 through December 2003 using the proportional reward‐to‐risk measure to estimate expected returns. When risk is measured by historical volatility, we find no relation between expected and realized excess returns. In contrast, when risk is measured by option‐implied volatility, we find a positive and significant relation between expected and realized excess returns in the 1994–1998 subperiod. In the 1999–2003 subperiod, the option‐implied volatility risk measure yields a positive, but statistically insignificant, risk‐return relation. We attribute this performance difference to the fact that, in the 1994–1998 subperiod, return volatility was lower and the average return was much higher than in the 1999–2003 subperiod, thereby increasing the signal‐to‐noise ratio in the latter subperiod.     

Does Idiosyncratic Risk Really Matter?

Goyal and Santa‐Clara (2003) find a significantly positive relation between the equal‐weighted average stock volatility and the value‐weighted portfolio returns on the NYSE/AMEX/Nasdaq stocks for the period of 1963:08 to 1999:12. We show that this result is driven by small stocks traded on the Nasdaq, and is in part due to a liquidity premium. In addition, their result does not hold for the extended sample of 1963:08 to 2001:12 and for the NYSE/AMEX and NYSE stocks. More importantly, we find no evidence of a significant link between the value‐weighted portfolio returns and the median and value‐weighted average stock volatility.     

High Idiosyncratic Volatility and Low Returns: A Prospect Theory Explanation

The well‐documented negative relationship between idiosyncratic volatility and stock returns is puzzling if investors are risk‐averse. However, under prospect theory, while investors are risk‐averse in the domain of gains, they exhibit risk‐seeking behavior in the domain of losses. Consistent with risk‐seeking investors’ preference for high‐volatility stocks in the loss domain, we find that the negative relationship between idiosyncratic volatility and stock returns is concentrated in stocks with unrealized capital losses, but is nonexistent in stocks with unrealized capital gains. This finding is robust to control for short‐term return reversals and maximum daily return, among other variables.     

Learning and predictability via technical analysis: Evidence from bitcoin and stocks with hard‐to‐value fundamentals

What predicts returns on assets with “hard‐to‐value” fundamentals such as Bitcoin and stocks in new industries? We are the first to propose an equilibrium model that shows how technical analysis can arise endogenously via rational learning, providing a theoretical foundation for using technical analysis in practice. We document that ratios of prices to their moving averages forecast daily Bitcoin returns in and out of sample. Trading strategies based on these ratios generate an economically significant alpha and Sharpe ratio gains relative to a buy‐and‐hold position. Similar results hold for small‐cap, young‐firm, and low analyst‐coverage stocks as well as NASDAQ stocks during the dotcom era.     

The Timing of Opening Trades and Pricing Errors

After demonstrating that a zero investment trading strategy that buys stocks with overnight returns below the market average and sells stocks with overnight returns above the market average earns more than 1% monthly profit, I demonstrate that this profit is greater for stocks that start trading more quickly than for other stocks. These results control for trading costs. The resulting pricing errors are a material portion of stock price volatility and suggest that a quick response to overnight information adds non‐information‐based stock volatility to stock prices.     

Volatility and market structure

This study examines volatility within three related intra-day series – transaction returns, quote midpoint returns, and limit order book midpoint returns – for a set of NYSE-listed stocks. We document statistically significant GARCH effects both overall and surrounding earnings announcements in all three series for the majority of stocks in the sample. We then compare the extent of volatility clustering among the series. In addition, the relation between volatility and market structure is examined via a set of cross-sectional regressions, and relations among the series over time are studied in a vector autoregressive framework.     

Idiosyncratic Volatility and Firm‐Specific News: Beyond Limited Arbitrage

We examine the relation between idiosyncratic volatility and returns around news announcements. Mispricing is most likely to occur during news announcements. If idiosyncratic volatility generates a limit to arbitrage, then the negative relation between returns and news volatility should be stronger than the relation to nonnews volatility. Instead, we find nonnews volatility has a robust negative relation to returns and lacks key features expected if volatility were a reflection of limits to arbitrage. Pricing of nonnews volatility is related to lottery‐like features of a stock's return. Our results suggest that volatility has a price effect beyond a limit to arbitrage.     

State‐preference pricing and volatility indices

This study uses a state‐preference pricing approach to develop a state‐price volatility index (SVX), as a forecast for market future realised volatility. We show that SVX is a more efficient forecaster than CBOE VIX for 30‐day realised volatility of SPX returns, using both in‐the‐sample and out‐of‐the‐sample tests. This result is robust to different measures of realised market volatilities. We also show that SVX provides a better volatility forecast than other alternative measures, including the at‐the‐money implied volatilities and GARCH (1, 1) volatility. Our results provide a foundation for forecasting higher risk‐neutral moments using the same state prices.     

Price Momentum and Idiosyncratic Volatility

We find that returns to momentum investing are higher among high idiosyncratic volatility ( IVol) stocks, especially high IVol losers. Higher IVol stocks also experience quicker and larger reversals. The findings are consistent with momentum profits being attributable to underreaction to firm‐specific information and with IVol limiting arbitrage of the momentum effect. We also find a positive time‐series relation between momentum returns and aggregate IVol. Given the long‐term rise in IVol, this result helps explain the persistence of momentum profits since Jegadeesh and Titman's (1993) study.     

Noise and the Trading Mechanism: the Case of SETS

On 20 October 1997 the London Stock Exchange introduced a new trading system called SETS. This system was to replace the dealer system SEAQ, which had been in operation since 1986. Using the iterative sum of squares test introduced by Inclan and Tiao (1994) , we investigate whether there was a change in the unconditional variance of opening and closing returns, at the time SETS was introduced. We show that for the FTSE‐100 stocks traded on SETS, on the days following its introduction, there was a widespread increase in the volatility of both opening and closing returns. However, no synchronous volatility changes were found to be associated with the FTSE‐100 index or FTSE‐250 stocks. We conclude therefore that the introduction of the SETS trading mechanism caused an increase in noise at the time the system was introduced.