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2391 | A generalized autoregressive conditional heteroskedasticity
- Bollerslev
- 1986
(Show Context)
Citation Context ...n financial econometrics on modeling and forecasting time-varying volatility. Since Engle’s (1982) seminal paper on ARCH, much of the literature has focused on variants of the univariate GARCH model (=-=Bollerslev 1986-=-), in which return volatility is modeled as a function of past shocks to returns and of its own lags (see Poon and Granger (2003) and Andersen et al. (2006) for recent surveys). More recently, realize... |

2231 | Common risk factors in the returns of stocks and bonds
- Fama, French
- 1993
(Show Context)
Citation Context ... univariate models, even those designed to fit long-run movements in volatility, and that our VAR method for calculating long-horizon forecasts preserves this information. 26 5 Test Assets and Beta Measurement 5.1 Test assets In addition to the six VAR state variables, our analysis requires excess returns on a cross section of test assets. We construct several sets of portfolios for this purpose, reporting details on the construction method in the online appendix. Our primary cross section consists of the excess returns over Treasury bills on the 25 ME- and BE/ME-sorted portfolios, studied in Fama and French (1993), extended in Davis, Fama, and French (2000), and made available by Professor Kenneth French on his website. We consider two main subsamples: early (1931:3-1963:3) and modern (1963:4-2011:4) due to the findings in CV (2004) of important differences in the risks of these portfolios between the early and modern period. To guard against the concerns of Daniel and Titman (1997, 2012) and Lewellen, Nagel, and Shanken (2010) that characteristic-sorted portfolios may have a low-order factor structure that is easily fit by spurious models, we construct a second set of six portfolios doublesorted on pa... |

1902 |
Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation
- Engle
- 1982
(Show Context)
Citation Context ...is more consistent with models of real options held by growth firms, such as McQuade (2012), and with the underperformance of value stocks during periods of elevated volatility including the Great Depression, the technology boom of the late 1990s, and the Great Recession of the late 2000s (CGP 2013). Stochastic volatility has been explored in other branches of the finance literature that we summarize in the online appendix. Most obviously, this is a prime concern of the field of financial econometrics. However, the focus has mostly been on univariate models, such as the GARCH class of models (Engle 1982, Bollerslev 1986), or univariate filtering methods that use realized high-frequency volatility (Barndorff-Nielsen and Shephard 2002, Andersen et al. 2003). A much smaller literature has, like us, looked directly at the information in other economic and financial variables concerning future volatility (Schwert 1989, Christiansen, Schmeling, and Schrimpf 2012, Paye 2012, Engle, Ghysels, and Sohn 2013). 3 An Intertemporal Model with Stochastic Volatility In this section, we derive an expression for the log stochastic discount factor (SDF) of the intertemporal CAPM model that allows for stochasti... |

1504 | A closed-form solution for options with stochastic volatility with applications to bond and currency options
- Heston
- 1993
(Show Context)
Citation Context ...ount rates, and volatility. An attractive feature of our model is that the prices of these three risk factors depend on only one free parameter, the long-horizon investor’s coeffi cient of risk aversion. This protects our empirical analysis from the critique of Daniel and Titman (1997, 2012) and Lewellen, Nagel, and Shanken (2010) that models with multiple free parameters can spuriously fit the returns to a set of test assets with a low-order factor structure. Our use of risk-sorted test assets further protects us from this critique. 2Affi ne stochastic volatility models date back at least to Heston (1993) in continuous time. Similar models have been applied in the long-run risk literature by Eraker (2008) and Hansen (2012), among others, but much of this literature uses volatility specifications that are not guaranteed to remain positive. 4 Our work is complementary to recent research on the “long-run risk model”of asset prices (Bansal and Yaron 2004) which can be traced back to insights in Kandel and Stambaugh (1991). Both the approximate closed-form ICAPM and the long-run risk model start with the first-order conditions of an infinitely-lived Epstein-Zin investor. As originally stated by Eps... |

1413 |
Substitution Risk Aversion and the Temporal Behaviour of Consumption and Asset Returns: An Empirical Analysis
- Epstein, Zin
- 1991
(Show Context)
Citation Context ...93) in continuous time. Similar models have been applied in the long-run risk literature by Eraker (2008) and Hansen (2012), among others, but much of this literature uses volatility specifications that are not guaranteed to remain positive. 4 Our work is complementary to recent research on the “long-run risk model”of asset prices (Bansal and Yaron 2004) which can be traced back to insights in Kandel and Stambaugh (1991). Both the approximate closed-form ICAPM and the long-run risk model start with the first-order conditions of an infinitely-lived Epstein-Zin investor. As originally stated by Epstein and Zin (1989), these first-order conditions involve both aggregate consumption growth and the return on the market portfolio of aggregate wealth. Campbell (1993) pointed out that the intertemporal budget constraint could be used to substitute out consumption growth, turning the model into a Merton-style ICAPM. Restoy and Weil (1998, 2011) used the same logic to substitute out the market portfolio return, turning the model into a generalized consumption CAPM in the style of Breeden (1979). Bansal and Yaron (2004) added stochastic volatility to the Restoy-Weil model, and subsequent theoretical and empirical ... |

1111 | An intertemporal capital asset pricing model - Merton - 1973 |

713 | Expected Stock Returns and Volatility - French, Schwert, et al. - 1987 |

637 |
Studies of Stock Price Volatility Changes
- Black
- 1976
(Show Context)
Citation Context ...news about future variance is more volatile than discount-rate news. Second, it is negatively correlated (-0.22) with cash-flow news: as one might expect from the literature on the “leverage effect” (=-=Black 1976-=-, Christie 1982), news about low cash flows is associated with news about higher future volatility. Third, NV correlates negatively (-0.09) with discountrate news, indicating that news of high volatil... |

618 |
An intertemporal asset pricing model with stochastic consumption and investment opportunities
- Breeden
- 1979
(Show Context)
Citation Context ...model start with the first-order conditions of an infinitely-lived Epstein-Zin investor. As originally stated by Epstein and Zin (1989), these first-order conditions involve both aggregate consumption growth and the return on the market portfolio of aggregate wealth. Campbell (1993) pointed out that the intertemporal budget constraint could be used to substitute out consumption growth, turning the model into a Merton-style ICAPM. Restoy and Weil (1998, 2011) used the same logic to substitute out the market portfolio return, turning the model into a generalized consumption CAPM in the style of Breeden (1979). Bansal and Yaron (2004) added stochastic volatility to the Restoy-Weil model, and subsequent theoretical and empirical research in the long-run risk framework has increasingly emphasized the importance of stochastic volatility (Bansal, Kiku, and Yaron 2012, Beeler and Campbell 2012, Hansen 2012). In this paper, we give the approximate closed-form ICAPM the same ability to handle stochastic volatility that its cousin, the long-run risk model, already possesses.3 Bansal, Kiku, Shaliastovich and Yaron (BKSY 2014), a paper written contemporaneously with the first version of this paper, explores ... |

564 | Stock Returns and the Term Structure
- Campbell
- 1987
(Show Context)
Citation Context ...empirically this restriction fails to hold when standard empirical proxies for Rf,t+1 are used.10 Consistent with this, we find that our empirical measure of σ2t , EVAR, does not significantly forecast returns in our unrestricted VAR. However, in our empirical analysis we do test conditional asset pricing implications of the model by performing our GMM estimation using as instruments conditioning variables implied by the model (specifically σ2t ). The only restriction we do not impose on the dynamics of returns in the VAR is the counterfactual tight link between NDR and NV . 10See for example Campbell (1987), Harvey (1989, 1991), or the review in Lettau and Ludvigson (2010). 15 3.2.4 Estimation Estimation via GMM is straightforward in this model given the moment representation of the asset pricing equation (14). Conditional on the news terms, the model is a linear factor model (with the caveat that both level and log returns appear), which is easy to estimate via GMM even though it imposes nonlinear restrictions on the factor risk prices. The model has only one free parameter, γ, that determines the risk prices as γ for NCF , 1 for −NDR, and −ω(γ)/2 for NV , where ω(γ) is the solution of the quad... |

542 |
The conditional CAPM and the cross-section of expected returns
- Jagannathan, Wang
- 1996
(Show Context)
Citation Context ...we consider in this paper as a representative investor who trades freely in all asset markets. There are however two obstacles to this interpretation. First, as already mentioned, our model does not explain why such an agent would not vary equity exposure with the level of the equity premium. Borrowing constraints can fix equity exposure at 100% when they bind, but we estimate that they will not bind at all times in our historical sample. Second, the aggregate stock index we consider here may not be an adequate proxy for all wealth, a point emphasized by many papers including Campbell (1996), Jagannathan and Wang (1996), Lettau and Ludvigson (2001), and Lustig, Van Nieuwerburgh, and Verdelhan (2013). For both these reasons, we interpret our results in microeconomic terms, as a description of the intertemporal considerations that limit the desire of conservative long-term equity investors (including institutions such as pension funds and endowments) to follow value strategies and other equity strategies with high average returns. These considerations may contribute to the explanation of cross-sectional patterns in stock returns in a general equilibrium setting with heterogeneous investors, even if they do not... |

456 |
Understanding risk and return
- Campbell
- 1996
(Show Context)
Citation Context ...ed-form solutions for the ICAPM’s risk prices (Campbell 1993). These solutions can be implemented empirically if they are combined with vector autoregressive (VAR) estimates of asset return dynamics (=-=Campbell 1996-=-). Campbell and Vuolteenaho (2004), Campbell, Polk, and Vuolteenaho (2010), and Campbell, Giglio, and Polk (2012) use this approach to argue that value stocks outperform growth stocks on average becau... |

433 | Fractionally integrated generalized autoregressive conditional heteroskedasticity - Baillie, Bollerslev, et al. - 1996 |

417 |
Capital market equilibrium with restricted borrowing,
- Black
- 1972
(Show Context)
Citation Context ...ated by equation (10), with ρ = 0.95 per year; 4) a partially-constrained three-beta model that restricts the price of discount-rate risk to equal the variance of the market return but freely estimates the other two risk prices (effectively decoupling γ and ω); and 5) an unrestricted three-beta model that allows free risk prices for cash-flow, discount-rate, and volatility betas. Each model is estimated in two different forms: one with a restricted zero-beta rate equal to the Treasury-bill rate as in the Sharpe-Lintner version of the CAPM, and one with an unrestricted zero-beta rate following Black (1972). Allowing for an unrestricted zerobeta rate may be particularly important given the extensive evidence in Krishnamurthy and Vissing-Jørgensen (2012) that Treasury Bills provide convenience benefits in terms of 33 liquidity and safety.18 We present our main pricing results in the next two subsections. The online appendix examines the robustness of our results to a wide variety of methodological changes. This analysis includes using various subsets of variables in our baseline VAR, estimating the VAR in different ways, using different estimates of realized variance, altering the set of variable... |

383 |
No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns
- Campbell, Hentschel
- 1992
(Show Context)
Citation Context ...e volatility. However, several of the other state variables also drive news about volatility. Specifically, we find that innovations in PE, DEF , and V S are associated with news of higher future volatility. This panel also indicates that all state variables with the exception of RTbill are statistically significant in terms of their contribution to at least one of the three news terms. We choose to leave RTbill in the VAR, though its presence in 15Though the point estimate of this correlation is negative, the large standard error implies that we cannot reject the “volatility feedback effect”(Campbell and Hentschel 1992, Calvet and Fisher 2007), which generates a positive correlation. For related research see French, Schwert, and Stambaugh (1987). 23 the system makes little difference to our conclusions. Figure 2 plots the smoothed series for NCF , −NDR and NV using an exponentiallyweighted moving average with a quarterly decay parameter of 0.08. This decay parameter implies a half-life of approximately two years. The pattern of NCF and −NDR we find is consistent with previous research. As a consequence, we focus on the smoothed series for market variance news. There is considerable time variation in NV , an... |

355 | Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models - Tauchen, Hussey - 1991 |

352 | 2002a): “Econometric Analysis of Realized Volatility and its use in Estimating Stochastic Volatility Models
- Barndorff-Nielsen, Shephard
(Show Context)
Citation Context ...nderperformance of value stocks during periods of elevated volatility including the Great Depression, the technology boom of the late 1990s, and the Great Recession of the late 2000s (CGP 2013). Stochastic volatility has been explored in other branches of the finance literature that we summarize in the online appendix. Most obviously, this is a prime concern of the field of financial econometrics. However, the focus has mostly been on univariate models, such as the GARCH class of models (Engle 1982, Bollerslev 1986), or univariate filtering methods that use realized high-frequency volatility (Barndorff-Nielsen and Shephard 2002, Andersen et al. 2003). A much smaller literature has, like us, looked directly at the information in other economic and financial variables concerning future volatility (Schwert 1989, Christiansen, Schmeling, and Schrimpf 2012, Paye 2012, Engle, Ghysels, and Sohn 2013). 3 An Intertemporal Model with Stochastic Volatility In this section, we derive an expression for the log stochastic discount factor (SDF) of the intertemporal CAPM model that allows for stochastic volatility. We then discuss the properties of the model, including the requirements for a solution to exist, the implications for ... |

319 | Aggregate Wealth, and Expected Stock Returns
- Lettau, Ludvison, et al.
(Show Context)
Citation Context ...a representative investor who trades freely in all asset markets. There are however two obstacles to this interpretation. First, as already mentioned, our model does not explain why such an agent would not vary equity exposure with the level of the equity premium. Borrowing constraints can fix equity exposure at 100% when they bind, but we estimate that they will not bind at all times in our historical sample. Second, the aggregate stock index we consider here may not be an adequate proxy for all wealth, a point emphasized by many papers including Campbell (1996), Jagannathan and Wang (1996), Lettau and Ludvigson (2001), and Lustig, Van Nieuwerburgh, and Verdelhan (2013). For both these reasons, we interpret our results in microeconomic terms, as a description of the intertemporal considerations that limit the desire of conservative long-term equity investors (including institutions such as pension funds and endowments) to follow value strategies and other equity strategies with high average returns. These considerations may contribute to the explanation of cross-sectional patterns in stock returns in a general equilibrium setting with heterogeneous investors, even if they do not provide a complete explanati... |

297 | The world price of covariance risk, - Harvey - 1991 |

276 |
Intertemporal asset pricing without consumption data
- Campbell
- 1993
(Show Context)
Citation Context ... Campbell and Shiller (1988a) and the assumption that a representative investor has Epstein-Zin utility (Epstein and Zin 1989) to obtain approximate closed-form solutions for the ICAPM’s risk prices (=-=Campbell 1993-=-). These solutions can be implemented empirically if they are combined with vector autoregressive (VAR) estimates of asset return dynamics (Campbell 1996). Campbell and Vuolteenaho (2004), Campbell, P... |

264 | The cross-section of volatility and expected returns - Ang, Hodrick, et al. - 2006 |

256 |
Time-Varying Conditional Covariances in Tests of Asset Pricing Models
- Harvey
- 1989
(Show Context)
Citation Context ...restriction fails to hold when standard empirical proxies for Rf,t+1 are used.10 Consistent with this, we find that our empirical measure of σ2t , EVAR, does not significantly forecast returns in our unrestricted VAR. However, in our empirical analysis we do test conditional asset pricing implications of the model by performing our GMM estimation using as instruments conditioning variables implied by the model (specifically σ2t ). The only restriction we do not impose on the dynamics of returns in the VAR is the counterfactual tight link between NDR and NV . 10See for example Campbell (1987), Harvey (1989, 1991), or the review in Lettau and Ludvigson (2010). 15 3.2.4 Estimation Estimation via GMM is straightforward in this model given the moment representation of the asset pricing equation (14). Conditional on the news terms, the model is a linear factor model (with the caveat that both level and log returns appear), which is easy to estimate via GMM even though it imposes nonlinear restrictions on the factor risk prices. The model has only one free parameter, γ, that determines the risk prices as γ for NCF , 1 for −NDR, and −ω(γ)/2 for NV , where ω(γ) is the solution of the quadratic equation... |

246 | Consumption strikes back? Measuring long-run risk. - Hansen, Heaton, et al. - 2008 |

210 | Characteristics, covariances, and average returns - Davis, Eugene, et al. - 2000 |

184 | The relationship between credit default swap spreads, bond yields, and credit rating announcements - Hull, Predescu, et al. - 2004 |

167 | The Dog That Did Not Bark: A Defense of Return Predictability, - Cochrane - 2005 |

165 | Portfolio selection in stochastic environments, - Liu - 2007 |

148 |
Asset returns and intertemporal preferences
- Kandel, Stambaugh
- 1991
(Show Context)
Citation Context ...o a set of test assets with a low-order factor structure. Our use of risk-sorted test assets further protects us from this critique. 2Affi ne stochastic volatility models date back at least to Heston (1993) in continuous time. Similar models have been applied in the long-run risk literature by Eraker (2008) and Hansen (2012), among others, but much of this literature uses volatility specifications that are not guaranteed to remain positive. 4 Our work is complementary to recent research on the “long-run risk model”of asset prices (Bansal and Yaron 2004) which can be traced back to insights in Kandel and Stambaugh (1991). Both the approximate closed-form ICAPM and the long-run risk model start with the first-order conditions of an infinitely-lived Epstein-Zin investor. As originally stated by Epstein and Zin (1989), these first-order conditions involve both aggregate consumption growth and the return on the market portfolio of aggregate wealth. Campbell (1993) pointed out that the intertemporal budget constraint could be used to substitute out consumption growth, turning the model into a Merton-style ICAPM. Restoy and Weil (1998, 2011) used the same logic to substitute out the market portfolio return, turning... |

145 | Expected option returns. - Coval, Shumway - 2001 |

134 | Dynamic consumption and portfolio choice with stochastic volatility in incomplete markets, - Chacko - 2005 |

107 | The aggregate demand for treasury debt.
- Vissing-Jorgensen
- 2012
(Show Context)
Citation Context ...discount-rate risk to equal the variance of the market return but freely estimates the other two risk prices (effectively decoupling γ and ω); and 5) an unrestricted three-beta model that allows free risk prices for cash-flow, discount-rate, and volatility betas. Each model is estimated in two different forms: one with a restricted zero-beta rate equal to the Treasury-bill rate as in the Sharpe-Lintner version of the CAPM, and one with an unrestricted zero-beta rate following Black (1972). Allowing for an unrestricted zerobeta rate may be particularly important given the extensive evidence in Krishnamurthy and Vissing-Jørgensen (2012) that Treasury Bills provide convenience benefits in terms of 33 liquidity and safety.18 We present our main pricing results in the next two subsections. The online appendix examines the robustness of our results to a wide variety of methodological changes. This analysis includes using various subsets of variables in our baseline VAR, estimating the VAR in different ways, using different estimates of realized variance, altering the set of variables in the VAR, exploring the VAR’s out-of-sample properties, using different proxies for the wealth portfolio including delevered equity portfolios, a... |

102 |
Idiosyncratic risk and the cross-section of expected stock returns,
- Fu
- 2009
(Show Context)
Citation Context ...s effect is stronger in the modern sample where growing firms with flexible investment opportunities are more prevalent. These results have the potential to explain the puzzling finding that high idiosyncraticvolatility stocks have lower average returns than low idiosyncratic-volatility stocks (Ang, Hodrick, Xing, and Zhang 2006 AHXZ), as well as the fact that the unconditional ivol effect is non-monotonic (AHXZ Table VI).17 They may also explain why the ivol effect appears to be less robust in some samples using different methodologies (Bali and Cakici 2008) and even switches sign in others (Fu 2009), because different samples and weighting schemes may alter the value characteristic and hence the volatility beta of stocks with high idiosyncratic volatility. Taken together, the findings from the characteristic- and risk-sorted test assets suggest that volatility betas vary with multiple stock characteristics, and that techniques that take this into account may be more effective in generating a spread in post-formation volatility beta. 17Barinov (2013) and Chen and Petkova (2014) also argue that the idiosyncratic volatility effect can be explained by aggregate volatility risk, but they do n... |

74 | The Long-Run Risks Model and Aggregate Asset Prices: An Empirical Assessment,” Critical Finance Review,
- Beeler, Campbell
- 2012
(Show Context)
Citation Context ...esearch on the long-run risk model has increasingly emphasized the importance of stochastic volatility for generating empirically plausible implications from this model (Bansal, Kiku, and Yaron 2012, =-=Beeler and Campbell 2012-=-). In this paper we give the approximate closed-form ICAPM the same capability to handle stochastic volatility that its cousin, the long-run risk model, already possesses. One might ask whether there ... |

67 |
Modeling and Forecasting Realized Volatility”, Econometrica 71:579—625.
- Andersen, Bollerslev, et al.
- 2003
(Show Context)
Citation Context ...Andersen et al. (2006) for recent surveys). More recently, realized volatility from high-frequency data has been used to estimate stochastic volatility processes (Barndorff-Nielsen and Shephard 2002, =-=Andersen et al. 2003-=-). The use of realized volatility 5has improved the modeling and forecasting of volatility, including its long-run component; however, this literature has primarily focused on the information content... |

58 | Yuhang Xing, and Xiaoyan Zhang, 2006, The cross-section of volatility and expected returns - Ang, Hodrick |

57 | An Empirical Evaluation of the Long-Run Risks Model for Asset Prices.” critical Finance review - Bansal, Kiku, et al. - 2012 |

53 | Stock returns and volatility: Pricing the short-run and long-run components of market risk.
- Adrian, Rosenberg
- 2008
(Show Context)
Citation Context ...LHRV ARh = 4Σhj=1ρ j−1RV ARt+j Σhj=1ρ j−1 , on the variables included in our VAR system, the VAR long-horizon forecast, and some alternative forecasts of long-run variance. We focus on a 10-year horizon (h = 40) as longer horizons come at the cost of fewer independent observations; however, the online appendix confirms that our results are robust to horizons ranging from one to 15 years. As alternatives to the VAR approach, we estimate two standard GARCH-type models, specifically designed to capture the long-run component of volatility: the two-component exponential (EGARCH) model proposed by Adrian and Rosenberg (2008), and the fractionally integrated (FIGARCH) model of Baillie, Bollerslev, and Mikkelsen (1996). We first estimate both GARCH models using the full sample of daily returns and then generate the appropriate forecast of LHRV AR40. To these two models, we add the set of variables from our VAR, and compare the forecasting ability of these different models. We find that while the EGARCH and FIGARCH forecasts do forecast long-run volatility, our VAR variables provide as good or better explanatory power, and RV AR, PE and DEF are strongly statistically significant. Our long-run VAR forecast has a coef... |

38 | Testing Factor-Model Explanations of Market Anomalies - Daniel, Titman - 2005 |

23 | Multifrequency news and stock returns,
- Calvet, Fisher
- 2007
(Show Context)
Citation Context ...r with news about lower future volatility. 9 Though the point estimate is negative, the large standard errors imply that we cannot reject the “volatility feedback effect”(Campbell and Hentschel 1992, =-=Calvet and Fisher 2007-=-). 194.4 Predicting long-run volatility The predictability of volatility, and especially of its long-run component, is central to this paper. In the previous sections, we have shown that volatility i... |

23 | An Econometric Model of the Term Structure of Interest Rate Swap Yields”, - Duffi, Darrell, et al. - 1997 |

21 | Intertemporal substitution and risk aversion. - Hansen, Heaton, et al. - 2006 |

11 |
Idiosyncratic Volatility, Growth Options, and the Cross-Section of Returns, working paper,
- Barinov
- 2011
(Show Context)
Citation Context ...y the ivol effect appears to be less robust in some samples using different methodologies (Bali and Cakici 2008) and even switches sign in others (Fu 2009), because different samples and weighting schemes may alter the value characteristic and hence the volatility beta of stocks with high idiosyncratic volatility. Taken together, the findings from the characteristic- and risk-sorted test assets suggest that volatility betas vary with multiple stock characteristics, and that techniques that take this into account may be more effective in generating a spread in post-formation volatility beta. 17Barinov (2013) and Chen and Petkova (2014) also argue that the idiosyncratic volatility effect can be explained by aggregate volatility risk, but they do not use a theoretically-motivated volatility risk factor. 32 6 Pricing the Cross-Section of Stock Returns We now turn to pricing the cross section of excess returns on our test assets. We estimate our model’s single parameter via GMM, using the moment condition (14). For ease of exposition, we report our results in terms of the expected return-beta representation from equation (15), rescaled by the variance of market return innovations as in section 5.2: R... |

10 | Time-Variation in the Covariance Between Stock Returns and Consumption Growth”, - Duffee - 2005 |

9 | Idiosyncratic Volatility and the Cross Section of Expected Returns, - Bali, Cakici - 2008 |

9 | Does Idiosyncratic Volatility Proxy for Risk Exposure? Review of Financial Studies,
- Chen, Petkova
- 2012
(Show Context)
Citation Context ...ppears to be less robust in some samples using different methodologies (Bali and Cakici 2008) and even switches sign in others (Fu 2009), because different samples and weighting schemes may alter the value characteristic and hence the volatility beta of stocks with high idiosyncratic volatility. Taken together, the findings from the characteristic- and risk-sorted test assets suggest that volatility betas vary with multiple stock characteristics, and that techniques that take this into account may be more effective in generating a spread in post-formation volatility beta. 17Barinov (2013) and Chen and Petkova (2014) also argue that the idiosyncratic volatility effect can be explained by aggregate volatility risk, but they do not use a theoretically-motivated volatility risk factor. 32 6 Pricing the Cross-Section of Stock Returns We now turn to pricing the cross section of excess returns on our test assets. We estimate our model’s single parameter via GMM, using the moment condition (14). For ease of exposition, we report our results in terms of the expected return-beta representation from equation (15), rescaled by the variance of market return innovations as in section 5.2: Ri −RTbill = g0 + g1βi,CFM +... |

9 | Disentangling Risk Aversion and Intertemporal Substitution through a Reference Level”, forthcoming Finance Research Letters. - Garcia, Renault, et al. - 2006 |

8 |
Risks for the Long Run”,
- Bansal, Yaron
- 2004
(Show Context)
Citation Context ... for the market portfolio and for value stocks versus growth stocks. Section 6 concludes. 2 Literature Review Our work is complementary to recent research on the “long-run risk model”of asset prices (=-=Bansal and Yaron 2004-=-) which can be traced back to insights in Kandel and Stambaugh (1991). Both the approximate closed-form ICAPM and the long-run risk model start with the first-order conditions of an infinitely lived E... |

8 | Volatility, the macroeconomy, and asset prices. - Bansal, Kiku, et al. - 2014 |

6 | Approximate equilibrium asset prices. - Restoy, Weil - 1998 |

6 | A Comprehensive Look at Financial Volatility Prediction by Economic Variables”, - Christiansen, Schmeling, et al. - 2012 |

5 | Amir Yaron (2012) “An empirical evaluation of the long-run risks model for asset prices - Bansal, Kiku |

5 | An lntertrmporal asset pricing model with stochastic consumption and investment opportunltles - Douglas - 1979 |

4 | 2007, “Stock Returns and Volatility - Adrian, Rosenberg |

4 | Pitfalls in VAR Based Return Decompositions: A Clarification”, - Engsted, Pedersen, et al. - 2012 |

4 | How Much Would You Pay to Resolve Long-Run Risk,”American Economic Review, - Epstein, Farhi, et al. - 2014 |

2 |
Intertemporal CAPM and the Cross Section of Stock Returns”, unpublished paper,
- Chen
- 2003
(Show Context)
Citation Context ...retical analysis, we discuss some conditions that are required for their model solution to be valid and argue that these conditions are not satisfied empirically. The different modeling assumptions and some differences in empirical implementation account for our contrasting empirical results; we show that volatility risk is very important in explaining the cross-section of stock returns while they find it has little impact on cross-sectional differences in risk premia. Indeed, BKSY find that a value-minus-growth bet has a positive beta with volatility news, while we 3Two unpublished papers by Chen (2003) and Sohn (2010) also attempt to do this. As we discuss in detail in the online appendix, these papers make strong assumptions about the covariance structure of various news terms when deriving their pricing equations. 5 find it always has a negative volatility beta. Our negative volatility beta estimate is more consistent with models of real options held by growth firms, such as McQuade (2012), and with the underperformance of value stocks during periods of elevated volatility including the Great Depression, the technology boom of the late 1990s, and the Great Recession of the late 2000s (CGP... |

2 | Return Decomposition”, Review of Financial Studies 22:5213—5249. Christie, Andrew, “The Stochastic Behavior of Common Stock Variances —Value, Leverage, and Interest Rates Effects”, - Chen, Zhao - 2009 |

2 | An Equilibrium Guide to Designing Affi ne Pricing Models”, Mathematical Finance 18:519—543. - Eraker, Shaliastovich - 2008 |

2 | Eric Ghysels and Bumjean Sohn, - Engle - 2013 |

2 |
Dynamic Valuation DecompositionWithin Stochastic Economies”,
- Hansen
- 2012
(Show Context)
Citation Context ...only one free parameter, the long-horizon investor’s coeffi cient of risk aversion. This protects our empirical analysis from the critique of Daniel and Titman (1997, 2012) and Lewellen, Nagel, and Shanken (2010) that models with multiple free parameters can spuriously fit the returns to a set of test assets with a low-order factor structure. Our use of risk-sorted test assets further protects us from this critique. 2Affi ne stochastic volatility models date back at least to Heston (1993) in continuous time. Similar models have been applied in the long-run risk literature by Eraker (2008) and Hansen (2012), among others, but much of this literature uses volatility specifications that are not guaranteed to remain positive. 4 Our work is complementary to recent research on the “long-run risk model”of asset prices (Bansal and Yaron 2004) which can be traced back to insights in Kandel and Stambaugh (1991). Both the approximate closed-form ICAPM and the long-run risk model start with the first-order conditions of an infinitely-lived Epstein-Zin investor. As originally stated by Epstein and Zin (1989), these first-order conditions involve both aggregate consumption growth and the return on the market... |

1 | Shaliastovich and Amir Yaron - Bansal, Kiku, et al. |

1 | Volatility, the Macroeconomy and Asset Prices”, upublished paper, - Bansal, Kiku, et al. - 2011 |

1 | Econometric Analysis of Realized Campbell, - Barndorff-Nielsen, Shephard - 2002 |

1 | Internet Appendix to An Intertemporal CAPM with Stochastic Volatility”, available online at http://kuznets.fas.harvard.edu/~campbell/papers.html. - Campbell, Giglio, et al. - 2012 |

1 | Discount Rates”, NBERWorking Paper No. 16972, forthcoming - Cochrane - 2011 |

1 |
Affi ne General Equilibrium Models”,
- Eraker
- 2008
(Show Context)
Citation Context ...factors depend on only one free parameter, the long-horizon investor’s coeffi cient of risk aversion. This protects our empirical analysis from the critique of Daniel and Titman (1997, 2012) and Lewellen, Nagel, and Shanken (2010) that models with multiple free parameters can spuriously fit the returns to a set of test assets with a low-order factor structure. Our use of risk-sorted test assets further protects us from this critique. 2Affi ne stochastic volatility models date back at least to Heston (1993) in continuous time. Similar models have been applied in the long-run risk literature by Eraker (2008) and Hansen (2012), among others, but much of this literature uses volatility specifications that are not guaranteed to remain positive. 4 Our work is complementary to recent research on the “long-run risk model”of asset prices (Bansal and Yaron 2004) which can be traced back to insights in Kandel and Stambaugh (1991). Both the approximate closed-form ICAPM and the long-run risk model start with the first-order conditions of an infinitely-lived Epstein-Zin investor. As originally stated by Epstein and Zin (1989), these first-order conditions involve both aggregate consumption growth and the re... |

1 | Dynamic Present Values and the Intertemporal CAPM”, - Eraker, Wang - 2011 |

1 | Stock Market Volatility and Trading Strategy Based Factors”, unpublished paper, - Sohn - 2010 |