Showing papers on "Stochastic discount factor published in 2012"
TL;DR: In this article, a representative agent model is proposed to generate the empirical patterns in the pricing kernel, albeit only for parameter constellations that are not typically observed in the real world.
Abstract: The pricing kernel puzzle of Jackwerth (2000) concerns the fact that the empirical pricing kernel implied in S&P 500 index options and index returns is not monotonically decreasing in wealth as standard economic theory would suggest. Thus, those options are currently priced in a way such that any risk-averse investor would increase his/her utility by trading in them. We provide a representative agent model where volatility is a function of a second momentum state variable. This model is capable of generating the empirical patterns in the pricing kernel, albeit only for parameter constellations that are not typically observed in the real world.
81 citations
TL;DR: In this paper, a growing empirical literature estimates models of long-term interest rates and uses them to forecast the declining discount rate schedule for public projects, focusing on models for the United States.
Abstract: Should governments, in discounting the future benefits and costs of public projects, use a discount rate that declines over time? The argument for a declining discount rate is a simple one: if the discount rates that will be applied in the future are persistent, and if the analyst can assign probabilities to these discount rates, this will result in a declining schedule of certainty-equivalent discount rates. A growing empirical literature estimates models of long-term interest rates and uses them to forecast the declining discount rate schedule. I briefly review this literature, focusing on models for the United States. This literature has, however, been criticized for a lack of connection to the theory of project evaluation. In cost-benefit analysis, the net benefits of a project in year t (in consumption units) are to be discounted to the present at the rate at which society would trade consumption in year t for consumption in the present. With simplifying assumptions, this leads to the Ramsey discounting formula. The Ramsey formula results in a declining certainty-equivalent discount rate if the rate of growth in consumption is uncertain and if shocks to consumption are correlated over time. Using the extended Ramsey formula to estimate a numerical schedule of certainty-equivalent discount rates is, however, challenging.
52 citations
TL;DR: In this article, the authors explain the economic principles that lead to an increasing part in the pricing kernel and compare the resulting pricing kernels with the empirical pricing kernel estimated in Jackwerth (2000).
Abstract: The pricing kernel is an important link between economics and finance. In standard models of financial economics it is proportional to the aggregate marginal utility in the economy. We first how that none of the three standard assumptions (completeness, risk aversion, and correct beliefs) is needed for the pricing kernel to be generally decreasing. If at least one of the three assumptions is violated, the pricing kernel can have increasing parts. We explain the economic principles that lead to an increasing part in the pricing kernel and compare the resulting pricing kernels with the empirical pricing kernel estimated in Jackwerth (2000).
51 citations
TL;DR: In this article, a critical look at these class of models and their inability to rationalize the statistics that have characterized US financial markets over the past century is explained, and the research efforts to enhance the model's ability to replicate the empirical data are summarized.
50 citations
TL;DR: In this paper, the authors show that volatility news affects the stochastic discount factor and carries a separate risk premium and that volatility risks are persistent and are strongly correlated with discount-rate news.
Abstract: We show that volatility movements have first-order implications for consumption dynamics and asset prices. Volatility news affects the stochastic discount factor and carries a separate risk premium. In the data, volatility risks are persistent and are strongly correlated with discount-rate news. This evidence has important implications for the return on aggregate wealth and the cross-sectional differences in risk premia. Estimation of our volatility risks based model yields an economically plausible positive correlation between the return to human capital and equity, while this correlation is implausibly negative when volatility risk is ignored. Our model setup implies a dynamics capital asset pricing model (DCAPM) which underscores the importance of volatility risk in addition to cash-flow and discount-rate risks. We show that our DCAPM accounts for the level and dispersion of risk premia across book-to-market and size sorted portfolios, and that equity portfolios carry positive volatility-risk premia.
50 citations
TL;DR: The compensation demanded by investors in equilibrium for incremental exposure to growth-rate risk is characterized and a term structure of risk prices is traced that shows how the valuation of risky cash flows depends on the investment horizon.
Abstract: We characterize the compensation demanded by investors in equilibrium for incremental exposure to growth-rate risk. Given an underlying Markov diusion that governs the state variables in the economy, the economic model implies a stochastic discount factor process S and a reference stochastic growth process G for the macroeconomy. Both are modeled conveniently as multiplicative functionals of a multidimensional Brownian motion. To study pricing we consider the pricing implications of parameterized family of growth processes G , with G 0 = G, as is made small. This parameterization denes a direction of growth-rate risk exposure that is priced using the stochastic discount factor S. By changing the investment horizon we trace a term structure of risk prices that shows how the valuation of risky cash ows depends on the investment horizon. Using methods of Hansen and Scheinkman (2009), we characterize the limiting behavior of the risk prices as the investment horizon is made arbitrarily
47 citations
08 Oct 2012
43 citations
01 Oct 2012
TL;DR: In this paper, the Cressie-Read family of discrepancies is considered and a family of convex functions that take into account higher moments of asset returns is proposed to solve the minimum discrepancy problem.
Abstract: Hansen and Jagannathan (1997) compare misspecified asset pricing models based on least-square projections on a family of admissible stochastic discount factors. We extend their fundamental contribution by considering Minimum Discrepancy projections where misspecification is measured by a family of convex functions that take into account higher moments of asset returns. The Minimum Discrepancy problems are solved on dual spaces producing a family of estimators that captures the least-square problem as a particular case. We derive the asymptotic distributions of the estimators for the Cressie–Read family of discrepancies, and illustrate their use with an assessment of the Consumption Asset Pricing Model.
42 citations
TL;DR: In this article, the authors use a standard neoclassical model supplemented by some frictions to understand large price swings in the housing market and construct a two good general equilibrium model in which housing is a composite good produced using structures and land.
Abstract: In this paper we use a standard neoclassical model supplemented by some frictions to understand large price swings in the housing market. We construct a two good general equilibrium model in which housing is a composite good produced using structures and land. We revisit the connection between changes in interest rates, credit conditions as measured by maximum loan-to-value ratios and expectations in influencing housing prices in a setting in which the stock of housing can be used as collateral for borrowing and credit markets are segmented. We find that changes in interest rates and credit conditions can generate significant price swings. Under rational expectations (perfect foresight) our model is able to explain 50% of the recent movements in U.S. house prices. When we allow shocks to expectations, the model’s ability to match the evidence increases significantly. Contrary to conventional wisdom, we show that standard asset pricing formulas seem to correctly describe the behavior of house prices if the appropriate pricing kernel is used.
38 citations
TL;DR: In this article, the authors provide a new dynamic asset pricing model for plain vanilla options and discuss its ability to produce minimum mispricing errors on equity option books, and compare this approach to natural competitors in order to test its efficiency.
Abstract: In this paper, we provide a new dynamic asset pricing model for plain vanilla options and we discuss its ability to produce minimum mispricing errors on equity option books. Given the historical measure, the dynamics of assets are modeled by Garch-type models with generalized hyperbolic innovations and the pricing kernel is an exponential affine function of the state variables, we show that the risk neutral distribution is unique and implies again a generalized hyperbolic dynamics with changed parameters. We provide an empirical test for our pricing methodology on two data sets of options respectively written on the French CAC 40 and the American SP 500. Then, using our theoretical result associated with Monte Carlo simulations, we compare this approach to natural competitors in order to test its efficiency. More generally, our empirical investigations analyze the ability of specific parametric innovations to reproduce market prices in the context of an exponential affine specification of the stochastic discount factor.
34 citations
TL;DR: This paper showed that financial markets cannot be Pareto efficient, except by chance, and that individuals in the model are rational; markets are not rational; therefore, these two minor and realistic changes to the Arrow-Debreu paradigm are sufficient to invalidate the implication that competitive financial markets efficiently allocate risk.
Abstract: Existing literature continues to be unable to offer a convincing explanation for the volatility of the stochastic discount factor in real world data. Our work provides such an explanation. We do not rely on frictions, market incompleteness or transactions costs of any kind. Instead, we modify a simple stochastic representative agent model by allowing for birth and death and by allowing for heterogeneity in agents' discount factors. We show that these two minor and realistic changes to the timeless Arrow-Debreu paradigm are sufficient to invalidate the implication that competitive financial markets efficiently allocate risk. Our work demonstrates that financial markets, by their very nature, cannot be Pareto efficient, except by chance. Although individuals in our model are rational; markets are not.
TL;DR: In this article, a risk premium is incorporated into the discount rate schedule for a real investment project with uncertain payoffs, and the model of this paper suggests that what should be combined in a weighted average are not the two discount rates, but rather the corresponding two discount factors.
Abstract: What is the best way to incorporate a risk premium into the discount rate schedule for a real investment project with uncertain payoffs? The standard CAPM formula suggests a beta-weighted average of the return on a safe investment and the mean return on an economy-wide representative risky investment. Suppose, though, that the project constitutes a tail-hedged investment, meaning that it is expected to yield positive payoffs in catastrophic states of nature. Then the model of this paper suggests that what should be combined in a weighted average are not the two discount rates, but rather the corresponding two discount factors. This implies an effective discount rate schedule that declines over time from the standard CAPM formula down to the riskfree rate alone. Some simple numerical examples are given. Implications are noted for discounting long-term public investments and calculating the social cost of carbon in climate change.
TL;DR: In this article, the authors present three different approaches which do not require parametric functional assumptions on the underlying asset price dynamics nor on the distributional form of the risk neutral density, and compare them using European call option prices.
Abstract: This chapter deals with nonparametric estimation of the risk neutral density. We present three different approaches which do not require parametric functional assumptions on the underlying asset price dynamics nor on the distributional form of the risk neutral density. The first estimator is a kernel smoother of the second derivative of call prices, while the second procedure applies kernel type smoothing in the implied volatility domain. In the conceptually different third approach we assume the existence of a stochastic discount factor (pricing kernel) which establishes the risk neutral density conditional on the physical measure of the underlying asset. Via direct series type estimation of the pricing kernel we can derive an estimate of the risk neutral density by solving a constrained optimization problem. The methods are compared using European call option prices. The focus of the presentation is on practical aspects such as appropriate choice of smoothing parameters in order to facilitate the application of the techniques.
TL;DR: In this paper, the authors propose new spanning tests that assess if the initial and additional assets share the economically meaningful cost and mean representing portfolios, and prove their asymptotic equivalence to existing tests under local alternatives.
TL;DR: In this paper, the Second-Order Esscher Transform (SDF) is introduced to bridge the historical and the risk-neutral state vector dynamics, which is wider than the one implied by a classical exponential-affine stochastic discount factor.
Abstract: The purpose of the paper is to introduce, in a discrete-time no-arbitrage pricing context, a bridge between the historical and the risk-neutral state vector dynamics which is wider than the one implied by a classical exponential-affine stochastic discount factor (SDF) and to preserve, at the same time, the tractability and flexibility of the associated asset pricing model. This goal is achieved by introducing the notion of exponential-quadratic SDF or, equivalently, the notion of Second-Order Esscher Transform. The log-pricing kernel is specified as a quadratic function of the factor and the associated sources of risk are priced by means of possibly non-linear stochastic first-order and second-order risk-correction coefficients. Focusing on security market models, this approach is developed in the multivariate conditionally Gaussian framework and its usefulness is testified by the specification and calibration of what we name the Second-Order GARCH Option Pricing Model. The associated European Call option pricing formula generates a rich family of implied volatility smiles and skews able to match the typically observed ones.
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TL;DR: In this paper, the authors use a standard neoclassical model supplemented by some frictions to understand large price swings in the housing market and construct a two good general equilibrium model in which housing is a composite good produced using structures and land.
Abstract: In this paper we use a standard neoclassical model supplemented by some frictions to understand large price swings in the housing market. We construct a two good general equilibrium model in which housing is a composite good produced using structures and land. We revisit the connection between changes in interest rates, credit conditions as measured by maximum loan-to-value ratios and expectations in influencing housing prices in a setting in which the stock of housing can be used as collateral for borrowing and credit markets are segmented. We find that changes in interest rates and credit conditions can generate significant price swings. Under rational expectations (perfect foresight) our model is able to explain 50% of the recent movements in U.S. house prices. When we allow shocks to expectations, the model’s ability to match the evidence increases significantly. Contrary to conventional wisdom, we show that standard asset pricing formulas seem to correctly describe the behavior of house prices if the appropriate pricing kernel is used.
TL;DR: In this paper, the authors introduce a class of information-based models for the pricing of fixed-income securities and derive explicit expressions for the prices of nominal discount bonds and deduce the associated dynamics of the short rate of interest and the market price of risk.
Abstract: The purpose of this article is to introduce a class of information-based models for the pricing of fixed-income securities. We consider a set of continuous-time processes that describe the flow of information concerning market factors in a monetary economy. The nominal pricing kernel is assumed to be given at any specified time by a function of the values of information processes at that time. Using a change-of-measure technique, we derive explicit expressions for the prices of nominal discount bonds and deduce the associated dynamics of the short rate of interest and the market price of risk. The interest rate positivity condition is expressed as a differential inequality. An example that shows how the model can be calibrated to an arbitrary initial yield curve is presented. We proceed to model the price level, which is also taken at any specified time to be given by a function of the values of the information processes at that time. A simple model for a stochastic monetary economy is introduced...
TL;DR: In this paper, the authors use a novel clustering approach to study the role of heterogeneity in asset pricing and find that nine clusters are sufficient to explain the equity premium with relative risk aversion coefficient equal to six.
Abstract: In this article we use a novel clustering approach to study the role of heterogeneity in asset pricing. We present evidence that the equity premium is consistent with a stochastic discount factor (SDF) calculated as the average of the household clusters’ intertemporal marginal rates of substitution in the 1984–2002 period. The result is driven by the skewness of the cluster-based cross-sectional distribution of consumption growth, but cannot be explained by the cross-sectional variance and mean alone. We find that nine clusters are sufficient to explain the equity premium with relative risk aversion coefficient equal to six. The result is robust to various averaging schemes of cluster-based consumption growth used to construct the SDF. Lastly, the analysis reveals that standard approximation schemes of the SDF using individual household data produce unreliable results, implying a negative SDF.
TL;DR: In this paper, the authors derived a liquidity-adjusted conditional two-moment capital asset pricing model (CAPM) and a liquidity adjusted conditional threemoment CAPM respectively based on theory of stochastic discount factor.
TL;DR: In this article, a strategy of identifying discount rates is proposed based on imputing the utility/profits using decisions made in a context where the future is inconsequential, the objective function is concave, and the decision space is continuous; and then using these utilities/profits to identify discount rates in contexts where dynamics become material.
Abstract: Because utility/profits, state transitions and discount rates are confounded in dynamic models, discount rates are typically fixed for the purpose of identification. We propose a strategy of identifying discount rates. The identification rests upon imputing the utility/profits using decisions made in a context where the future is inconsequential, the objective function is concave, and the decision space is continuous; and then using these utilities/profits to identify discount rates in contexts where dynamics become material. We exemplify this strategy using a field study wherein cellphone users transitioned from a linear to three-part-tariff pricing plan.We find that the estimated discount rate corresponds to a weekly discount factor (0.90), lower than the value typically assumed in empirical research (0.995). When using a standard 0.995 discount factor, we find the price coefficient is underestimated by 16%. Moreover, the predicted inter-temporal substitution pattern and demand elasticities are biased, leading to a 29% deterioration in model fit; and suboptimal pricing recommendations that would lower potential revenue gains by 76%.
TL;DR: In this article, the authors consider a family of SKUs for which the supplier will offer a quantity discount, according to the aggregate purchases of the product group, and illustrate the impact of price-sensitivity and joint decision-making on the supplier's discount policy.
TL;DR: In this paper, a theoretical analysis using tail-sensitive risk preferences suggests that active value and growth funds may serve to reduce downside risk and capture upside potential, respectively, and that tail-sensitivity measures estimated from the empirical pricing kernel have significant explanatory power for active fund flows.
Abstract: Actively managed mutual funds have distinct return distributions from their passive benchmarks and our theoretical analysis using tail-sensitive risk preferences suggests that active value and growth funds may serve to reduce downside risk and capture upside potential, respectively. Furthermore, tail-sensitivity measures estimated from the empirical pricing kernel have significant explanatory power for active fund flows, even after controlling for business cycles and market-wide sentiment. Finally, active funds, unlike their passive counterparts, have exposures to option strategies hedging downside risk or capturing upside potential.
TL;DR: In this paper, the authors study the cross-sectional pricing of market volatility and find that the value effect is mainly related to the persistent diffusion volatility factor, whereas the size effect is associated with both the diffusion volatility and the jump volatility factor.
Abstract: The main goal of this paper is to study the cross-sectional pricing of market volatility. The paper proposes that the market return, diffusion volatility, and jump volatility are fundamental factors that change the investors’ investment opportunity set. Based on estimates of diffusion and jump volatility factors using an enriched dataset including S&P 500 index returns, index options, and VIX, the paper finds negative market prices for volatility factors in the cross-section of stock returns. The findings are consistent with risk-based interpretations of value and size premia and indicate that the value effect is mainly related to the persistent diffusion volatility factor, whereas the size effect is associated with both the diffusion volatility factor and the jump volatility factor. The paper also finds that the use of market index data alone may yield counter-intuitive results.
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TL;DR: In this article, the Arrow-Debreu paradigm is used to explain the volatility of the stochastic discount factor in real world data, and it is shown that financial markets cannot be Pareto efficient except by chance.
Abstract: Existing literature continues to be unable to offer a convincing explanation for the volatility of the stochastic discount factor in real world data. Our work provides such an explanation. We do not rely on frictions, market in completeness or transactions costs of any kind. Instead, we modify a simple stochastic representative agent model by allowing for birth and death and by allowing for heterogeneity in agents' discount factors. We show that these two minor and realistic changes to the timeless Arrow-Debreu paradigm are sufficient to invalidate the implication that competitive financial markets efficiently allocate risk. Our work demonstrates that financial markets, by their very nature, cannot be Pareto efficient except by chance. Although individuals in our model are rational; markets are not.
TL;DR: In this paper, the authors explore methods that characterize model-based valuation of stochastically growing cash flows and explore dynamic value decomposition (DVD) methods that capture concurrent compounding of a stochastic growth and discount factors in determining risk-adjusted values.
Abstract: I explore methods that characterize model-based valuation of stochastically growing cash flows. Following previous research, I use stochastic discount factors as a convenient device to depict asset values. I extend that literature by focusing on the impact of compounding these discount factors over alternative investment horizons. In modeling cash flows, I also incorporate stochastic growth factors. I explore dynamic value decomposition (DVD) methods that capture concurrent compounding of a stochastic growth and discount factors in determining risk-adjusted values. These methods are supported by factorizations that extract martingale components of stochastic growth and discount factors. These components reveal which ingredients of a model have long-term implications for valuation. The resulting martingales imply convenient changes in measure that are distinct from those used in mathematical finance, and they provide the foundations for analyzing model-based implications for the term structure of risk prices. As an illustration of the methods, I re-examine some recent preference based models. I also use the martingale extraction to revisit the value implications of some benchmark models with market restrictions and heterogenous consumers.
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TL;DR: In this article, the authors show that volatility news affects the stochastic discount factor and carries a separate risk premium and that volatility risks are persistent and are strongly correlated with discount-rate news.
Abstract: We show that volatility movements have first-order implications for consumption dynamics and asset prices. Volatility news affects the stochastic discount factor and carries a separate risk premium. In the data, volatility risks are persistent and are strongly correlated with discount-rate news. This evidence has important implications for the return on aggregate wealth and the cross-sectional differences in risk premia. Estimation of our volatility risks based model yields an economically plausible positive correlation between the return to human capital and equity, while this correlation is implausibly negative when volatility risk is ignored. Our model setup implies a dynamics capital asset pricing model (DCAPM) which underscores the importance of volatility risk in addition to cash-flow and discount-rate risks. We show that our DCAPM accounts for the level and dispersion of risk premia across book-to-market and size sorted portfolios, and that equity portfolios carry positive volatility-risk premia.
Abstract: Generalizing a result by Cox and Leland, 2000 , Vanduffel et al., 2009 , this note shows that risk-averse investors with fixed planning horizon prefer path-independent payoffs in any financial market if the pricing kernel is a function of the underlying’s price at the end of the planning horizon. Generally, for every payoff which is not a function of the pricing kernel, there is a more attractive alternative that depends solely on the pricing kernel at the end of the planning horizon.
TL;DR: In this paper, the authors identify positive risk premia for option-implied idiosyncratic risk and show that the compensation of unsystematic risk is mainly driven by firms with high positive implied skewness.
Abstract: 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.
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TL;DR: In this paper, a time-varying risk premium for the whole market is estimated within a restriction in the form of the Lucas-Breeden consumption-based capital asset pricing model, which is derived as a restriction of a general stochastic discount factor model.
Abstract: Time-varying risk premiums and CAPM betas for several assets traded on the Prague Stock Exchange are estimated within a model which is derived as a restriction of a general stochastic discount factor model. The restriction takes the form of the Sharpe-Lintner capital asset pricing model. A time-varying risk premium for the whole market is then estimated within a restriction in the form of the Lucas-Breeden consumption-based capital asset pricing model. A multivariate GARCH-in-mean model is used to estimate the two restrictions. The estimation of the CAPM restriction seems to be favorable to the theoretical model, while the CCAPM seems to be less in accordance with the data. Models with dummies and tests of structural changes are used to show that the market experienced a significant shock in 2008–2009, but on the whole the tests do not give indisputable evidence that the shock had a lasting impact on the market.