A very interesting paper:1 A large and relatively novel data set2 A new dynamic copula model, the largest to date3 Interesting contrasts between the dependence between CDS spreadsand dependence between corresponding equity returns
The cross-section of stock returns has substantial exposure to risk captured by higher moments in market returns. We estimate these moments from daily S&P 500 index option data. The resulting time series of factors are thus genuinely conditional and forward-looking. Stocks with high sensitivities to innovations in implied market volatility and skewness exhibit low returns on average, whereas those with high sensitivities to innovations in implied market kurtosis exhibit somewhat higher returns on average. The results on market skewness risk are robust to various permutations of the empirical setup. The estimated premium for bearing market skewness risk is between ?3.72% and ?5.76% annually. This market skewness risk premium is economically significant and cannot be explained by other common risk factors such as the market excess return or the size, book-to-market, momentum, and market volatility factors, or by firm characteristics. Using ICAPM intuition, the negative price of market skewness risk indicates that it is a state variable that negatively affects the future investment opportunity set.
Characterizing the dependence between companies' defaults is a central problem in the credit risk literature. This dependence structure is a first order determinant of the relative values of structured credit products such as collateralized debt obligations (CDO). We present a number of stylized facts useful in guiding the modeling of default dependence. We systematically com- pare correlation measures implied from three different markets: base correlations implied by CDO prices, correlations implied by equity returns, and correlations estimated from default in- tensities implied by CDS prices. We use flexible dynamic equicorrelation techniques introduced by Engle and Kelly (2007) to capture time variation in CDS-implied and equity return-implied correlations while base correlations are obtained using the Gaussian copula. We perform this analysis using North American data, the components of the CDX index, as well as European data, the components of the iTraxx index. For each index, there is substantial co-movement between the three correlation time-series. All correlations are highly time-varying and per- sistent. European and North American correlation series display considerable co-movement. Correlations across both markets increased significantly during the turbulent second half of 2007.
This paper investigates the importance of idiosyncratic consumption risk for the cross- sectional variation in asset returns. We find that besides the rate of aggregate con- sumption growth, the cross-sectional variance of consumption growth is also a priced factor. This suggests that consumers are not fully insured against idiosyncratic con- sumption risk, and that asset returns reflect their attempts to reduce their exposure to this risk. The resulting two-factor consumption-based asset pricing model signifi- cantly outperforms the CAPM, and its performance compares favorably with that of the Fama French three-factor model.
This paper investigates the importance of idiosyncratic consumption risk for the cross- sectional variation in asset returns. We find that besides the rate of aggregate con- sumption growth, the cross-sectional variance of consumption growth is also a priced factor. This suggests that consumers are not fully insured against idiosyncratic con- sumption risk, and that asset returns reflect their attempts to reduce their exposure to this risk. The resulting two-factor consumption-based asset pricing model signifi- cantly outperforms the CAPM, and its performance compares favorably with that of the Fama French three-factor model.
The paper investigates a two-factor affine model for the credit spreads on corporate bonds. The first factor can be interpreted as the level of the spread, and the second factor is the volatility of the spread. The riskless interest rate is modeled using a standard two-factor affine model, thus leading to a four- factor model for corporate yields. This approach allows us to model the volatility of corporate credit spreads as stochastic, and also allows us to capture higher moments of credit spreads. We use an extended Kalman filter approach to estimate our model on corporate bond prices for 108 firms. The model is found to be successful at fitting actual corporate bond credit spreads, resulting in a significantly lower root mean square error than a standard alternative model in both in-sample and out-of-sample analyses. In addition, key properties of actual credit spreads are better captured by the
This paper investigates the importance of idiosyncratic consumption risk for the cross-sectional variation in average returns on stocks and bonds. If idiosyncratic consumption risk is not priced, the only pricing factor in a multiperiod economy is the rate of aggregate consumption growth. We offer evidence that the cross-sectional variance of consumption growth is also a priced factor. This demonstrates that consumers are not fully insured against idiosyncratic consumption risk, and that asset returns reflect their attempts to reduce their exposure to this risk. We find that over the sample period the resulting two-factor consumption-based asset pricing model significantly outperforms the CAPM. The model s empirical performance also compares favorably with that of the Fama-French three-factor model. Moreover, in the presence of the market factor and the size and book-to-market factors, the two consumption based factors retain explanatory power. Together with the results of Lettau and Ludvigson (2000), these findings indicate that consumption-based asset pricing is relevant for explaining the cross-section of asset returns.
This paper estimates the rate of relative risk aversion using Euler equations based on household- level consumption data. These Euler equations are implications of market structures that do not necessarily allow agents to perfectly insure themselves. The paper focuses on tests of the unconditional Euler equation. In representative-agent frameworks, this type of test leads to the most intuitively convincing rejections of asset-pricing models, such as the equity premium puzzle and the riskfree rate puzzle. When measurement error in consumption is ignored, Euler equation errors are not statistically different from zero for values of the rate of relative risk aversion between 1 and 3. When allowing for the presence of measurement error, conservative estimates of the rate of risk aversion for asset market participants indicate a value between 2 and 8. These findings suggest that the rate of risk aversion may be much lower than commonly thought. Consequently, market incompleteness is likely to be part of a resolution of asset pricing puzzles.
This paper investigates the importance of market incompleteness by comparing the rates of risk aversion estimated from complete and incomplete markets environments. For the incomplete-markets case, we use consumption data for 50 U.S. states. While the use of state-level data is conceptually inferior to the use of data on individual consumption, it may be preferable because state-level data are less susceptible to measurement errors. We find that the rate of risk aversion under the incomplete- markets setup is much lower. Furthermore, including the second and third moments of the cross- sectional distribution of consumption growth in the pricing kernel lowers the estimate of risk aversion. These findings suggest that market incompleteness ought to be seen as an important component of solutions to the equity premium puzzle.
Peter Christoffersen
Kris Jacobs
Chayawat Ornthanalai
We present a new discrete-time GARCH jump framework that allows for rich dynamics in higher moments by combining heteroskedastic processes with fat-tailed innovations in returns and volatility. We provide a tractable risk neutralization framework allowing for option valuation with separate modeling of risk premia for the jump and normal innovations. Our models can be estimated with ease on returns using standard maximum likelihood techniques, and joint estimation on returns and a large sample of options is also feasible. We... nd very strong empirical support for time-varying jump intensities, when estimating on S&P500 returns and on returns and options jointly.
This paper estimates the rate of relative risk aversion using Euler equations based on household-level consumption data. These Euler equations are implications of market structures that do not necessarily allow agents to perfectly insure themselves. The paper focuses on tests of the unconditional Euler equation. In representative-agent frameworks, this type of test leads to the most intuitively convincing rejections of asset-pricing models, such as the equity premium puzzle and the riskfree rate puzzle. When measurement error in consumption is ignored, Euler equation errors are not statistically dierent from zero for values of the rate of relative risk aversion between 1 and 3. When allowing for the presence of measurement error, conservative estimates of the rate of risk aversion for asset market participants indicate a value between 2 and 8. These ndings suggest that the rate of risk aversion may be much lower than commonly thought. Consequently, market incompleteness is likely to be part of a resolution of asset pricing puzzles.
We study the ability of three-factor affine term-structure models to extract conditional volatility using interest rate swap yields for 1991–2005 and Treasury yields for 1970–2003. For the Treasury sample, the correlation between model-implied and EGARCH volatility is between 60%and 75%. For the swap sample, this correlation is rather low or negative. We find that these differences in model performance are primarily due to the timing of the swap sample, and not to institutional differences between swap and Treasury markets. We conclude that the ability of multifactor affine models to extract conditional volatility depends on the sample period, but that overall these models perform better than has been argued in the literature.
We study the ability of three-factor affine term-structure models to extract conditional volatility using interest rate swap yields for 1991–2005 and Treasury yields for 1970–2003. For the Treasury sample, the correlation between model-implied and EGARCH volatility is between 60%and 75%. For the swap sample, this correlation is rather low or negative. We find that these differences in model performance are primarily due to the timing of the swap sample, and not to institutional differences between swap and Treasury markets. We conclude that the ability of multifactor affine models to extract conditional volatility depends on the sample period, but that overall these models perform better than has been argued in the literature.