We find support for a negative relation between conditional expected monthly return and conditional variance of monthly return, using a GARCH-M model modified by allowing (1) seasonal patterns in volatility, (2) positive and negative innovations to returns having different impacts on conditional volatility, and (3) nominal interest rates to predict conditional variance. Using the modified GARCH-M model, we also show that monthly conditional volatility may not be as persistent as was thought. Positive unanticipated returns appear to result in a downward revision of the conditional volatility whereas negative unanticipated returns result in an upward revision of conditional volatility. THE TRADEOFF BETWEEN RISK and return has long been an important topic in asset valuation research. Most of this research has examined the tradeoff between risk and return among different securities within a given time period. The intertemporal relation between risk and return has been examined by several authors-Fama and Schwert (1977), French, Schwert, and Stambaugh (1987), Harvey (1989), Campbell and Hentschel (1992), Nelson (1991), and Chan, Karolyi, and Stulz (1992), to name a few. This paper extends that research.

https://faculty.washington.edu/ezivot/econ589/GJRJOF1993.pdf

On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks

ARCH modeling in finance: A review of the theory and empirical evidence

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. In addition, we find that stocks with high idiosyncratic volatility relative to the Fama and French (1993) 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.

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. IT IS WELL KNOWN THAT THE VOLATILITY OF STOCK RETURNS varies over time. While considerable research has examined the time-series relation between the volatility of the market and the expected return on the market (see, among others, Campbell and Hentschel (1992) and Glosten, Jagannathan, and Runkle (1993)), the question of how aggregate volatility affects the cross-section of expected stock returns has received less attention. Time-varying market volatility induces changes in the investment opportunity set by changing the expectation of future market returns, or by changing the risk-return trade-off. If the volatility of the market return is a systematic risk factor, the arbitrage pricing theory or a factor model predicts that aggregate volatility should also be priced in the cross-section of stocks. Hence, stocks with different sensitivities to innovations in aggregate volatility should have different expected returns. The first goal of this paper is to provide a systematic investigation of how the stochastic volatility of the market is priced in the cross-section of expected stock returns. We want to both determine whether the volatility of the market

https://www0.gsb.columbia.edu/faculty/rhodrick/crosssection.pdf

We model dividend and consumption growth rates as containing a small long-run predictable component and economic uncertainty (i.e., growth rate volatility) as being time-varying. The magnitudes of the predictable variation and changing volatility in growth rates, as in the data, are quite small. These growth rate dynamics, for which we provide empirical support, in conjunction with plausible parameter configurations of the Epstein and Zin (1989) preferences can explain key observed asset markets phenomena. In particular, we show that the model can justify the observed equity premium, the low risk free rate, and the ex-post volatilities of the market return, real risk free rate, and the price-dividend ratio. As in the data, the model also implies that dividend yields predict returns and that market return volatility is stochastic. The main economic insight we capture is that news about growth rates significantly alter agent's perceptions regarding long run expected growth rates and growth rate uncertainty--in equilibrium, this leads to a large equity risk premium, low risk free interest rate, and large market volatility.

Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles

It is sometimes argued that an increase in stock market volatility raises required stock returns, and thus lowers stock prices. This paper modifies the generalized autoregressive conditionally heteroskedastic (GARCH) model of returns to allow for this volatility feedback effect. The resulting model is asymmetric, because volatility feedback amplifies large negative stock returns and dampens large positive returns, making stock returns negatively skewed and increasing the potential for large crashes. The model also implies that volatility feedback is more important when volatility is high. In U.S. monthly and daily data in the period 1926-88, the asymmetric model fits the data better than the standard GARCH model, accounting for almost half the skewness and excess kurtosis of standard monthly GARCH residuals. Estimated volatility discounts on the stock market range from 1% in normal times to 13% after the stock market crash of October 1987 and 25% in the early 1930's. However volatility feedback has little effect on the unconditional variance of stock returns.

No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns

https://www.nber.org/system/files/working_papers/w3742/w3742.pdf

No news is good news: An asymmetric model of changing volatility in stock returns

All in the family Nesting symmetric and asymmetric GARCH models

Public discussion about corporate use of derivatives focuses on whether firms use derivatives to reduce or increase firm risk. In contrast, em- pirical, academic studies of corporate derivatives-use take it for granted that firms hedge with derivatives. Using data from financial statements of 425 large u.s. corporations, we investigate whether firms systematically reduce or increase their riskiness with derivatives. We find that many firms manage their exposures with large derivatives positions. Nonetheless, compared to firms that do not use financial derivatives, firms that use derivatives display few, if any, measurable differences in risk that are associated with the use of derivatives.

/pdf/are-corporations-reducing-or-taking-risks-with-derivatives-2g1m9pqrb1.pdf

Are Corporations Reducing or Taking Risks with Derivatives

Estimating implied volatility by inverting the Black-Scholes formula is subject to considerable error when option characteristics are observed with plausible errors. Especially for options away from the money, large changes in volatility produce small changes in option prices. Conversely, small errors in option prices and other option characteristics produce large errors in implied volatilities. In the presence of small measurement errors, unobserved truncation of option prices that violate lower bounds for absence of arbitrage can also lead to systematic volatility smiles. The paper proposes feasible GLS estimators that reduce the noise and bias in implied volatility estimates.

/pdf/errors-in-implied-volatility-estimation-4makjsg9iv.pdf

Ludger Hentschel

Papers

No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns

No news is good news: An asymmetric model of changing volatility in stock returns

All in the family Nesting symmetric and asymmetric GARCH models

Are Corporations Reducing or Taking Risks with Derivatives

Errors in Implied Volatility Estimation