Showing papers on "Stochastic discount factor published in 2019"
TL;DR: In this article, the authors formally proved that the stationary wealth distribution in a simple Huggett model with random discounting has power law tails and characterised the Pareto exponents analytically.
38 citations
TL;DR: In this paper, the authors demonstrate in an intermediary-based asset pricing model that violations of no-arbitrage such as CIP violations, along with intermediary wealth returns, can be used to price assets.
Abstract: Violations of no-arbitrage conditions measure the shadow cost of constraints on intermediaries, and the risk that these constraints tighten is priced. We demonstrate in an intermediary-based asset pricing model that violations of no-arbitrage such as covered interest rate parity (CIP) violations, along with intermediary wealth returns, can be used to price assets. We describe a “forward CIP trading strategy†that bets on CIP violations becoming smaller, and show that its returns help identify the price of the risk that the shadow cost of intermediary constraints increases. This risk contributes substantially to the volatility of the stochastic discount factor, and appears to be priced consistently in U.S. treasury, emerging market sovereign bond, and foreign exchange portfolios.
28 citations
TL;DR: It is shown that cryptocurrency prices are cointegrated with computing power and network and that the two aggregate blockchain characteristics are procyclical asset pricing factors with positive risk premia and explain a significant portion of the cross-sectional variation in expected cryptocurrency returns.
Abstract: We show that cryptocurrency returns relate to asset pricing factors derived from two blockchain characteristics, growth in aggregate computing power and network size. Consistent with theoretical models, cryptocurrency returns have positive risk exposures to these blockchain-based factors, which carry positive risk prices. A stochastic discount factor with computing power and network explains a significantly larger portion of the cross-sectional variation in expected cryptocurrency returns than a model with Bitcoin and cryptocurrency momentum. The explanatory power of the blockchain factors increases over time as the cryptocurrency market matures. Overall, economically motivated factors are important sources of risk for cryptocurrency expected returns.
18 citations
TL;DR: This article developed a conditional capital asset pricing model in continuous-time that allows for stochastic beta exposure, which predicts that low-beta stocks earn high returns because their beta co-moves positively with market variance and the SDF.
Abstract: We develop a conditional capital asset pricing model in continuous-time that allows for stochastic beta exposure. When beta co-moves with market variance and the stochastic discount factor (SDF), beta risk is priced, and the expected return on a stock deviates from the security market line. The model predicts that low-beta stocks earn high returns because their beta co-moves positively with market variance and the SDF. The opposite is true for high-beta stocks. Estimating the model on equity and option data, we find that beta risk explains expected returns on low- and high-beta stocks, resolving the "betting against beta" anomaly.
14 citations
TL;DR: In this article, a frictionless neoclassical model of financial markets is presented, in which firm sizes, stock returns, and the pricing kernel are all endogenously determined, parsimoniously specifying the supply and demand of financial capital allocated to each firm and providing general equilibrium sizes and returns in closed form.
Abstract: This paper presents a frictionless neoclassical model of financial markets in which firm sizes, stock returns, and the pricing kernel are all endogenously determined. The model parsimoniously specifies the supply and demand of financial capital allocated to each firm and provides general equilibrium sizes and returns in closed form. We show that the interaction of supply and demand can coherently explain a large number of asset pricing facts. The equilibrium security market line is flatter than the CAPM predicts and can be nonlinear or downward-sloping. The model also generates the size, profitability, investment growth, value, asymmetric volatility, betting-against-beta, and betting-against-correlation anomalies, while also fitting the cross-section of firm characteristics.
10 citations
TL;DR: In this paper, the authors derive the correct identity linking current mispricing to subsequent returns, generating a price-level analogue to the fundamental asset pricing equation, E[MR^e]=0, used to study returns.
Abstract: We propose a novel way to study asset prices based on price distortions rather than abnormal returns. We derive the correct identity linking current mispricing to subsequent returns, generating a price-level analogue to the fundamental asset pricing equation, E[MR^e]=0, used to study returns. Our empirical test reveals that the CAPM describes the cross-section of prices better than it describes expected short-horizon returns. Despite the improvement, significant mispricing remains. An interaction of book-to-market and quality provides a parsimonious model of CAPM mispricing that both long-term buy-and-hold investors and researchers disciplining models from the price perspective should prioritize.
9 citations
TL;DR: This paper analyzes the valuation and pricing of physical electricity delivery contracts from the viewpoint of a producer with given capacities for production and fuel-storage, and takes the perspective of an electricity producer, who serves contractual deliveries but avoids unacceptable losses.
Abstract: This paper analyzes the valuation and pricing of physical electricity delivery contracts from the viewpoint of a producer with given capacities for production and fuel-storage. Using stochastic optimization problems in discrete time with general state space, the dual problems of production problems are used to derive no-arbitrage conditions for fuel and electricity prices as well as superhedging values and prices of bilaterally traded electricity delivery contracts. In particular we take the perspective of an electricity producer, who serves contractual deliveries but avoids unacceptable losses. The resulting no-arbitrage conditions, stochastic discount factors and superhedging prices account for typical frictions like limitation of storage and production capacity and for the fact that it is possible to produce electricity from fuel, but not to produce fuel from electricity. Similarities, but also substantial differences to purely financial results can be demonstrated in this way. Furthermore, using acceptability measures, we analyze capital requirements and acceptability prices for delivery contracts, when the producer accepts some risk.
8 citations
TL;DR: This article showed that currencies with a steeper yield curve tend to depreciate at business cycle horizons, in violation of uncovered interest parity (UIP), but the yield curve adds no explanatory power over and above interest differentials in explaining the exchange rate at longer horizons.
Abstract: We show that currencies with a steeper yield curve tend to depreciate at business cycle horizons, in violation of uncovered interest parity (UIP), but the yield curve adds no explanatory power over and above interest differentials in explaining the exchange rate at longer horizons. We argue that exchange rate risk premia reallocate returns intertemporally to investors who value them relatively highly, reflecting transitory innovations to their stochastic discount factor consistent with business cycle risk. Using holding period returns, we identify a tent-shape relationship, across horizons, between dollar-bond excess returns for long maturity bonds and the relative slope. In addition, we find that short-horizon UIP deviations switch sign following yield curve inversions, consistent with the interpretation of inversions as indicators of changes in growth and inflation expectations. We show that accounting for liquidity yields does not alter our results, but rather contributes to explaining cross-sectional differences across currencies, consistent with permanent innovations to agents' stochastic discount factor.
7 citations
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TL;DR: In this article, the authors present an overview of the broad class of financial models in which the prices of assets are Levy-Ito processes driven by an $n$-dimensional Brownian motion and an independent Poisson random measure.
Abstract: We present an overview of the broad class of financial models in which the prices of assets are Levy-Ito processes driven by an $n$-dimensional Brownian motion and an independent Poisson random measure. The Poisson random measure is associated with an $n$-dimensional Levy process. Each model consists of a pricing kernel, a money market account, and one or more risky assets. We show how the excess rate of return above the interest rate can be calculated for risky assets in such models, thus showing the relationship between risk and return when asset prices have jumps. The framework is applied to a variety of asset classes, allowing one to construct new models as well as interesting generalizations of familiar models.
6 citations
TL;DR: In this article, the authors studied how ambiguity aversion affects the pricing of mortgage insurance and found that ambiguity aversion increases MI premium rate by 77% (46bps) and explains about 60-90% of pricing errors.
Abstract: This paper studies how ambiguity aversion affects the pricing of mortgage insurance (MI). We consider pricing-kernel ambiguity arising from market incompleteness. This ambiguity model is applied to a standard framework of MI-ML (mortgage loan) structural pricing. Our quantitative results show that insurers’ ambiguity aversion generates substantial positive effects on MI premium. Ambiguity impacts are highly sensitive to loan-to-value ratio, ambiguity magnitude, and the tightness of information constraints. By using the U.S. city-level housing and mortgage data, we estimate that, on average, ambiguity aversion increases MI premium rate by 77 % (46 bps), and explains about 60–90 % of pricing errors.
6 citations
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TL;DR: In this article, the role of factor strength and pricing errors in asset pricing models, and their implications for identification and estimation of risk premia are discussed, and the authors establish an explicit relationship between the pricing errors and the presence of weak factors that are correlated with stochastic discount factors.
Abstract: In this paper we are concerned with the role of factor strength and pricing errors in asset pricing models, and their implications for identification and estimation of risk premia. We establish an explicit relationship between the pricing errors and the presence of weak factors that are correlated with stochastic discount factor. We introduce a measure of factor strength, and distinguish between observed factors and unobserved factors. We show that unobserved factors matter for pricing if they are correlated with the discount factor, and relate the strength of the weak factors to the strength (pervasiveness) of non-zero pricing errors. We then show, that even when the factor loadings are known, the risk premia of a factor can be consistently estimated only if it is strong and if the pricing errors are weak. Similar results hold when factor loadings are estimated, irrespective of whether individual returns or portfolio returns are used. We derive distributional results for two pass estimators of risk premia, allowing for non-zero pricing errors. We show that for inference on risk premia the pricing errors must be sufficiently weak. We consider both when n (the number of securities) is large and T (the number of time periods) is short, and the case of large n and T. Large n is required for consistent estimation of risk premia, whereas the choice of short T is intended to reduce the possibility of time variations in the factor loadings. We provide monthly rolling estimates of the factor strengths for the three Fama-French factors over the period 1989-2018.
TL;DR: In this paper, a non-monotonic decreasing pricing kernel implies the existence of a trading strategy in contingent claims that stochastically converges to the market efficiency and the pricing kernel.
Abstract: Market efficiency and the pricing kernel are closely related. A non-monotonic decreasing pricing kernel implies the existence of a trading strategy in contingent claims that stochastically ...
TL;DR: In this paper, the authors developed a GARCH option pricing model with jump variance dynamics and a nonmonotonic pricing kernel featuring jump variance risk premium, which yields a closed-form option pricing formula and improves in fitting index options from 1996 to 2015.
Abstract: We study jump variance risk by jointly examining both stock and option markets. We develop a GARCH option pricing model with jump variance dynamics and a nonmonotonic pricing kernel featuring jump variance risk premium. The model yields a closed‐form option pricing formula and improves in fitting index options from 1996 to 2015. The model‐implied jump variance risk premium has predictive power for future market returns. In the cross‐section, heterogeneity in exposures to jump variance risk leads to a 6% difference in risk‐adjusted returns annually.
TL;DR: This work presents a Bayesian hierarchical framework for both cross-sectional and time-series return prediction that builds on a market-timing predictive system that jointly allows for time-varying coefficients driven by fundamental characteristics.
Abstract: This paper investigates the asset allocation problem when returns are predictable. We introduce a market-timing Bayesian hierarchical (BH) approach that adopts heterogeneous time-varying coefficients driven by lagged fundamental characteristics. Our approach estimates the conditional expected returns and residual covariance matrix jointly enables evaluating the estimation risk in the portfolio analysis. The hierarchical prior allows the modeling of different assets separately while sharing information across assets. We demonstrate the performance of the U.S. equity market, and our BH approach outperforms most alternative methods in terms of point prediction and interval coverage. In addition, the BH efficient portfolio achieves monthly returns of 0.92% and a significant Jensen's alpha of 0.32% in sector investment over the past twenty years. We detect that technology, energy, and manufacturing are the most critical sectors in the past decade, and size, investment, and short-term reversal factors are heavily weighted in our portfolio. Furthermore, the stochastic discount factor constructed by our BH approach can explain many risk anomalies.
21 Mar 2019
TL;DR: In this paper, the authors extend the realized volatility option pricing model by adding a jump component, which provides a rapidly moving volatility factor and improves on the fitting properties under the physical measure.
Abstract: Stochastic and time-varying volatility models typically fail to correctly price out-of-the-money put options at short maturity. We extend realized volatility option pricing models by adding a jump component which provides a rapidly moving volatility factor and improves on the fitting properties under the physical measure. The change of measure is performed by means of an exponentially affine pricing kernel which depends on an equity and two variance risk premia, associated with the continuous and jump components of realized volatility. Our choice preserves analytical tractability and offers a new way of estimating variance risk premia by combining high-frequency returns and option data in a multicomponent pricing model.
TL;DR: In this article, a simple three-factor consumption-based asset pricing model that includes wage growth as a risk factor was developed, and evaluated whether the model explains six major CAPM anomalies: book-to-market, investment, operating profitability, long-term return reversal, net share issues, and residual variance.
Abstract: We develop a simple three-factor consumption-based asset pricing model that includes wage growth as a risk factor, and evaluate whether the model explains six major CAPM anomalies: book-to-market, investment, operating profitability, long-term return reversal, net share issues, and residual variance. Wage growth arises in the pricing kernel by using a non-separable utility over consumption and leisure, and represents the growth in the opportunity cost of enjoying leisure hours. In the model, wage growth earns a negative price of risk, that is, higher wage growth leads to a decline in leisure demand, which increases the marginal utility of consumption for an investor with risk aversion above one. The empirical cross-sectional tests show that the model explains around 50% of the cross-sectional dispersion in average returns of the joint six CAPM anomalies (160 equity portfolios). Further, the proposed model compares favorably with alternative return-based multifactor models widely used in the literature. The risk price estimates for wage growth are significantly negative, while the implied preference parameter (share of leisure) estimates are economically plausible in most cases. Overall, our results suggest that aggregate wage growth can help explaining cross-sectional equity risk premia.
TL;DR: In this paper, the authors use option prices to infer real-time moments of stochastic discount factors (SDFs) from daily SP 500 index option data, without relying on past observations.
Abstract: I use option prices to infer real-time moments of stochastic discount factors (SDFs). The moments are estimated, from daily SP 500 index option data, in real time, without relying on past observations. These moments are forward-looking and significantly predict the market excess return. The theory suggests that the SDF variance (kurtosis) is positively priced while the SDF skewness is negatively priced in the cross section of returns. A cross-sectional analysis shows that the price of risks associated with the moments of the SDF are economically and statistically significant after controlling for a comprehensible set of economic variables.
TL;DR: In this article, a Green's function solution for a generic multi-factor short rate model based on correlated state variables of Ornstein-Uhlenbeck type, whose drift is assumed to be an affine function of the state variables (and of time), is presented.
Abstract: We present a Green's function solution (aka pricing kernel) for a generic multi-factor short rate model based on correlated state variables of Ornstein-Uhlenbeck type, whose drift is assumed to be an affine function of the state variables (and of time). The solution is obtained in general as a perturbation expansion valid in the limit of low rates (an assumption almost invariably satisfied). We exhibit explicit solutions in the case where the interest rate model is of Hull-White and of Black-Karasinski type. We observe that the theory is equally applicable to the modelling of stochastic credit default intensity governed by a Black-Karasinski model as it is to interest rate modelling. It is not difficult either to extend it to multi-asset pricing problems.
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TL;DR: A market-timing Bayesian hierarchical (BH) approach that adopts heterogeneous time-varying coefficients driven by lagged fundamental characteristics is introduced that outperforms most alternative methods in terms of point prediction and interval coverage and the stochastic discount factor constructed by the approach can explain many risk anomalies.
Abstract: This paper investigates asset allocation problems when returns are predictable. We introduce a market-timing Bayesian hierarchical (BH) approach that adopts heterogeneous time-varying coefficients driven by lagged fundamental characteristics. Our approach includes a joint estimation of conditional expected returns and covariance matrix and considers estimation risk for portfolio analysis. The hierarchical prior allows modeling different assets separately while sharing information across assets. We demonstrate the performance of the U.S. equity market. Though the Bayesian forecast is slightly biased, our BH approach outperforms most alternative methods in point and interval prediction. Our BH approach in sector investment for the recent twenty years delivers a 0.92\% average monthly returns and a 0.32\% significant Jensen`s alpha. We also find technology, energy, and manufacturing are important sectors in the past decade, and size, investment, and short-term reversal factors are heavily weighted. Finally, the stochastic discount factor constructed by our BH approach explains most anomalies.
TL;DR: This article examined similarities between the low-beta premium, the value premium, small-size premium and the equity premium in a special case of a static consumption-based asset pricing model with constant relative risk aversion and lognormal dividends that can be solved in closed form.
Abstract: The stochastic discount factor is a crucial determinant of the equity premium as well as the cross-sectional distribution of stock returns. This gives rise to the idea that there is a tight link between the equity premium puzzle and cross-sectional asset pricing puzzles. This paper examines similarities between the low-beta premium, the value premium, the small-size premium and the equity premium in a special case of a static consumption-based asset pricing model with constant relative risk aversion and lognormal dividends that can be solved in closed form. The results show that cross-sectional asset pricing puzzles are quantitative puzzles just like the equity premium puzzle: The model generates a premium for stocks with a low beta, a high dividend-price ratio and a small market capitalization but the size of the premium is too small. Furthermore, the size of the premium rises together with the equity premium as the risk aversion coefficient or consumption risk is increased.
TL;DR: By assuming that the stochastic discount factor (SDF) M is a proper but unspecified function of state variables X, the authors showed that this function M(X) must solve a simple second-order linear differenti...
Abstract: By assuming that the stochastic discount factor (SDF) M is a proper but unspecified function of state variables X, we show that this function M(X) must solve a simple second-order linear differenti...
TL;DR: In this paper, the authors incorporate household debt and delinquency decisions into a standard model of lifecycle consumption-saving-investment and impose a punishment to the delinquent behavior by assuming that the percentage of endowment available is a linear function of the default decision.
Abstract: I incorporate household debt and delinquency decisions into a standard model of lifecycle consumption-saving-investment. I also impose a punishment to the delinquent behavior by assuming that the percentage of endowment available is a linear function of the default decision. Theoretically such additional investor decisions are playing a relevant role in terms of completing markets. In practice, it enables me to derive an extended system of Euler equations which does not alter consumption-based fundamental asset pricing equation. It imposes the pricing kernel to account jointly for two additional first-order conditions. I perform empirical exercises aiming to price equity premium in United States from 1987:1 to 2018:1. I find significant elasticity of intertemporal substitution in consumption of the representative agent ranging from 0.24 to 0.55 and risk aversion from 1.82 to 3.51. This approach is also useful to account for the cross-section behavior of domestic assets. I can also use this framework to draw bounds for the household decisions on loan and delinquency and to propose a new rule of thumb relating preferences parameters and credit variables.
TL;DR: This paper developed a methodology for inference on asset pricing models linear in latent risk factors, valid when the number of assets diverges but the time series dimension is fixed, possibly very small.
Abstract: This paper develops a methodology for inference on asset pricing models linear in latent risk factors, valid when the number of assets diverges but the time series dimension is fixed, possibly very small. We cast the factor model within the Arbitrage Pricing Theory of Ross (1976) and show that the no-arbitrage condition permits to identify the risk premia as the expectation of the latent risk factors. This result paves the way to an inferential procedure for the factors’ risk premia and for the stochastic discount factor, spanned by the latent risk factors. The strength of our set up is that it naturally handles time-varying factor models, where every feature is allowed to be time-varying including loadings, idiosyncratic risk and the number of risk factors. Several Monte Carlo experiments corroborate our theoretical findings. An empirical application based on individual asset returns data demonstrates the power of the methodology, allowing to tease out the empirical content of the time-variation stemming from asset pricing theory.
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TL;DR: The condition is obtained, and hence the problem of existence and uniqueness of asset prices, with the recent literature on stochastic discount factor decompositions, providing a Monte Carlo method that is naturally parallelizable.
Abstract: We obtain an exact necessary and sufficient condition for the existence and uniqueness of equilibrium asset prices in infinite horizon, discrete-time, arbitrage free environments. Through several applications we show how the condition sharpens and improves on previous results. We connect the condition, and hence the problem of existence and uniqueness of asset prices, with the recent literature on stochastic discount factor decompositions. Finally, we discuss computation of the test value associated with our condition, providing a Monte Carlo method that is naturally parallelizable.
TL;DR: In this article, the authors use a minimum discrepancy objective function to construct a stochastic discount factor from asset returns using only the economic assumption of no arbitrage, and show that the estimated risk-premia can be used as an extra moment condition to discipline the creation of factor mimicking portfolios.
Abstract: This paper shows that factor risk premia can be consistently estimated using a semi-parametric estimate of the stochastic discount factor without requiring a correctly specified linear factor model. We use a minimum discrepancy objective function to construct a stochastic discount factor from asset returns using only the economic assumption of no arbitrage. The stochastic discount factor and factor risk-premia are estimated using only data on portfolio returns and factor realizations: The same data used when evaluating linear models. The econometrics are applications of standard extremum estimator arguments and the Delta Method, making inference simple. In simulations, the estimated risk-premia have low root mean squared errors and are comparable to classic two-pass estimates even when the model is correctly specified. Empirical estimates of popular traded factors are close to their mean excess returns. For non-traded factors, we find that intermediary leverage and consumption growth carry risk-premia, while employment growth does not. A final application shows that the estimated risk-premia can be used as an extra moment condition to discipline the creation of factor mimicking portfolios.
TL;DR: In this paper, the authors proposed a representation of suboptimal investment behavior based on the stochastic discount factor (SDF) paradigm, and developed a novel Monte Carlo simulation approach to compute the welfare costs for this sub-optimal behavior.
TL;DR: In this paper, the authors apply a nonparametric estimator to US and Brazilian data to identify how the yield of a long-term zero-coupon bond responds to the initial state of the economy.
Abstract: We use the framework developed by Christensen (2017) and Hansen and Scheinkman (2009) to study the long-term interest rates in the US and Brazil. We apply a nonparametric estimator to US and Brazilian data to identify how the yield of a long-term zero-coupon bond responds to the initial state of the economy. Using a flexible specification for the state process leads to an interesting non-linear response of the yield to changes in the initial state. As a by-product of our work, we assess the performance of Christensen's estimator using Monte Carlo simulations based on two widely adopted asset pricing models (rare disasters and habit formation).
TL;DR: This paper developed a dynamic stochastic general equilibrium framework that can account for important macroeconomic and financial moments, given Epstein-Zin preferences, heterogeneous banking and third-order approximation methods that yield a timevarying term premium that feeds back to the real economy.
Abstract: We develop a dynamic stochastic general equilibrium framework that can account for important macroeconomic and financial moments, given Epstein-Zin preferences, heterogeneous banking and third-order approximation methods that yield a time-varying term premium that feeds back to the real economy. A risk perception shock increases term premia, lowers output, and reduces short-term credit in the private sector in response to higher loan rates and constrained borrowers, as banks rebalance their portfolios. A ‘bad’ credit boom, driven by investors mispricing risk, leads to a more severe recession and is less supportive of economic growth than a ‘good’ credit boom based on fundamentals.
TL;DR: In this article, the authors estimate the pricing kernel from options on the S&P 500 index for different horizons and over time, and compare short-term and long-term pricing kernels and analyze their time-series variation.
Abstract: We estimate the pricing kernel from options on the S&P 500 index for different horizons and over time. This allows us to compare short-term and long-term pricing kernels and analyze their time-series variation. We show that the well documented pricing kernel puzzle–the non-monotonicity of the pricing kernel–only exists for short horizons. For longer horizons the puzzle disappears and the level, shape and time-series variation of the pricing kernel are in line with standard rational asset-pricing models. In contrast, we show that the empirical features of the short-term kernel can be explained by a behavioral asset-pricing model.
TL;DR: The authors applied the Bilinear GARCH (BGARCH) in the consumption-based asset pricing framework to estimate the predicted equity risk premium using monthly data between January 1998 and June 2016.