Showing papers on "Stochastic discount factor published in 2021"
TL;DR: In this paper, the authors show that an equal-weighted portfolio has a higher total return than a value weighted portfolio, and that a considerable part of rebalancing to maintain constant weights.
Abstract: We show that an equal-weighted portfolio has a higher total return than a value-weighted portfolio. As one may expect, this is partly because the equal-weighted portfolio has higher exposure to value and size factors, but we show that a considerable part (42%) comes from rebalancing to maintain constant weights. We then demonstrate, through four applications, that inferences from asset-pricing tests are substantially different depending on whether one uses equal- or value-weighted portfolios. These four applications are tests of the: Capital Asset Pricing Model, spanning properties of the stochastic discount factor, relation between characteristics and returns, and pricing of idiosyncratic volatility.
79 citations
TL;DR: In this article, a supervised principal component analysis (SPCA) is proposed to estimate the risk premium of a factor of interest, as well as the entire stochastic discount factor, that explicitly accounts for weak factors and test assets with highly correlated risk exposures.
Abstract: Estimation and testing of factor models in asset pricing requires choosing a set of test assets. The choice of test assets determines how well different factor risk premia can be identified: if only few assets are exposed to a factor, that factor is weak, which makes standard estimation and inference incorrect. In other words, the strength of a factor is not an inherent property of the factor: it is a property of the cross-section used in the analysis. We propose a novel way to select assets from a universe of test assets and estimate the risk premium of a factor of interest, as well as the entire stochastic discount factor, that explicitly accounts for weak factors and test assets with highly correlated risk exposures. We refer to our methodology as supervised principal component analysis (SPCA), because it iterates an asset selection step and a principal-component estimation step. We provide the asymptotic properties of our estimator, and compare its limiting behavior with that of alternative estimators proposed in the recent literature, which rely on PCA, Ridge, Lasso, and Partial Least Squares (PLS). We find that the SPCA is superior in the presence of weak factors, both in theory and in finite samples. We illustrate the use of SPCA by applying it to estimate the risk premia of several tradable and nontradable factors, to evaluate asset managers’ performance, and to de-noise asset pricing factors.
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22 citations
TL;DR: The authors provided a theoretical characterization of international stochastic discount factors (SDFs) in incomplete markets under different degrees of market segmentation and found that large permanent SDF components help to reconcile the low exchange rate volatility, the exchange rate cyclicality, and the forward premium anomaly.
Abstract: We provide a theoretical characterization of international stochastic discount factors (SDFs) in incomplete markets under different degrees of market segmentation. Using 40 years of data on a cross-section of countries, we estimate model-free SDFs and factorize them into permanent and transitory components. We find that large permanent SDF components help to reconcile the low exchange rate volatility, the exchange rate cyclicality, and the forward premium anomaly. However, integrated markets entail highly volatile and almost perfectly comoving international SDFs. In contrast, segmented markets can generate less volatile and more dissimilar SDFs. In quest of relating the SDFs to economic fundamentals, we document strong links between proxies of financial intermediaries' risk-bearing capacity and model-free international SDFs. We interpret this evidence through the lens of an economy with two building blocks: limited participation by households and financiers who face an intermediation friction.
18 citations
TL;DR: In this article, the weak form of PPP is incorporated into a joint model of the stochastic discount factor, the nominal exchange rate, and domestic and foreign yield curves.
Abstract: Exposures of expected future nominal depreciation rates to the current interest rate differential violate the UIP hypothesis in a pattern that is a nonmonotonic function of horizon. Forward expected nominal depreciation rates are monotonic. We explain the two patterns by simultaneously incorporating the weak form of PPP into a joint model of the stochastic discount factor, the nominal exchange rate, and domestic and foreign yield curves. Departures from PPP generate the first pattern. The risk premiums for these departures generate the second pattern. Thus, the variance of the stochastic discount factor is related to the real exchange rate.
14 citations
TL;DR: A class of conditional GARCH models that offers significantly added flexibility to accommodate empirically relevant features of financial asset returns while admitting closed-form recursive solutions for the moment generating function, a variance dependent pricing kernel and, therefore, efficient option pricing in a realistic setting is introduced.
13 citations
TL;DR: In this paper, the authors derive a frequency domain decomposition of the unconditional asset return premium in a general setting with a log-affine stochastic discount factor (SDF) and show that the cospectrum between returns and the SDF only displays frequency dependencies through the state vector and its dynamics and risk prices can be inferred from covariances between asset (portfolio) returns, that is, from the cross-section.
11 citations
TL;DR: The generalized aggregators relax the common perfect substitutability of the candidate models, implicit in linear averaging and pooling and illustrate the performance and economic significance of the aggregation approach in the context of stochastic discount factor models and inflation forecasting.
8 citations
8 citations
TL;DR: In this paper, the authors analyse the stand-alone performance of hedge fund strategies using a stochastic discount factor approach and then consider the diversification benefits of each hedge fund strategy when combined with a portfolio of US equities and bonds.
Abstract: For 5,500 North American hedge funds following 11 different strategies, we analyse the stand-alone performance of these strategies using a stochastic discount factor approach. Employing the same data, we then consider the diversification benefits of each hedge fund strategy when combined with a portfolio of US equities and bonds. We compute the out-of-sample Black-Litterman portfolios, with Bayes-Stein, higher moments, simulations, desmoothed data and allowance for regimes as robustness checks. All but two hedge fund strategies out-perform the market as stand-alone investments; and all but one provide significant diversification benefits. The higher is an investor’s risk aversion, the more beneficial is diversification into hedge funds.
7 citations
TL;DR: The authors showed that when the currencies are attractive, they tend to deviate from the uncovered interest rate parity and to comove with the global stochastic discount factor (SDF).
6 citations
04 Mar 2021
TL;DR: In this article, a model-free Bayesian extraction procedure for the stochastic discount factor under a yield curve prior was developed, where the external information about the historically very low levels of U.S. short and long-term interest rates was enforced.
Abstract: We developed a model-free Bayesian extraction procedure for the stochastic discount factor under a yield curve prior. Previous methods in the literature directly or indirectly use some particular parametric asset-pricing models such as with long-run risks or habits as the prior. Here, in contrast, we used no such model, but rather, we adopted a prior that enforces external information about the historically very low levels of U.S. short- and long-term interest rates. For clarity and simplicity, our data were annual time series. We used the extracted stochastic discount factor to determine the stripped cash flow risk premiums on a panel of industrial profits and consumption. Interestingly, the results align very closely with recent limited information (bounded rationality) models of the term structure of equity risk premiums, although nowhere did we use any theory on the discount factor other than its implied moment restrictions.
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TL;DR: In this article, the authors present a broad class of financial models in which the prices of assets are L\'evy-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 L\'evy-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 L\'evy 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.
TL;DR: In this article, the authors provide a theoretical exploration of cryptocurrency option pricing under the presence of regime-switching cryptocurrency prices with jumps and state-dependent interest rates, and the European-style cryptocurrency options are priced when the dynamics of the cryptocurrency price and the instantaneous forward interest rate are, respectively, driven by a two-factor, statedependent stochastic volatility model with jumps.
TL;DR: In this article, the authors analyse the stand-alone performance of hedge fund strategies using a stochastic discount factor approach and then consider the diversification benefits of each hedge fund strategy when combined with a portfolio of US equities and bonds.
Abstract: For 5,500 North American hedge funds following 11 different strategies, we analyse the stand-alone performance of these strategies using a stochastic discount factor approach. Employing the same data, we then consider the diversification benefits of each hedge fund strategy when combined with a portfolio of US equities and bonds. We compute the out-of-sample Black-Litterman portfolios, with Bayes-Stein, higher moments, simulations, desmoothed data and allowance for regimes as robustness checks. All but two hedge fund strategies out-perform the market as stand-alone investments; and all but one provide significant diversification benefits. The higher is an investor’s risk aversion, the more beneficial is diversification into hedge funds.
TL;DR: This paper discusses the pricing performances of a large collection of GARCH models by questioning the global synergy between the choice of the affine/non-affine GARCH specification, the use of competing alternatives to the Gaussian distribution, the selection of an appropriate pricing kernel and the choiceof different estimation strategies based on several sets of financial information.
Abstract: In this paper, we discuss the pricing performances of a large collection of GARCH models by questioning the global synergy between the choice of the affine/non-affine GARCH specification, the use of competing alternatives to the Gaussian distribution, the selection of an appropriate pricing kernel and the choice of different estimation strategies based on several sets of financial information. Furthermore, the study answers an important question in relation to the correlation between the performance of a pricing scheme and its ability to forecast VIX dynamics. VIX analysis clearly appears as a parsimonious first-stage filter to discard the worst GARCH option pricing models.
TL;DR: This paper designs two novel tail risk options (TROs) for hedging and evaluating short-term tail risks, and defines two ad hoc underlying “assets”, which are analogous to the Black-Scholes implied volatility and the TRO-implied tail index.
Abstract: Tail risk is an important financial issue today, but directly hedging tail risks with an ad hoc option is still an unresolved problem since it is not easy to specify a suitable and asymmetric pricing kernel. By defining two ad hoc underlying “assets”, this paper designs two novel tail risk options (TROs) for hedging and evaluating short-term tail risks. Under the Frechet distribution assumption for maximum losses, the closed-form TRO pricing formulas are obtained. Simulation examples demonstrate the accuracy of the pricing formulas. Furthermore, they show that, no matter whether at scale level (symmetric “normal” risk, with greater volatility) or shape level (asymmetric tail risk, with a smaller value in tail index), the greater the risk, the more expensive the TRO calls, and the cheaper the TRO puts. Using calibration, one can obtain the TRO-implied volatility and the TRO-implied tail index. The former is analogous to the Black-Scholes implied volatility, which can measure the overall symmetric market volatility. The latter measures the asymmetry in underlying losses, mirrors market sentiment, and provides financial crisis warnings. Regarding the newly proposed TRO and its implied tail index, economic implications can be offered to investors, portfolio managers, and policy-makers.
TL;DR: In this article, the authors investigated the valuation of foreign exchange (FX) options by identifying a two-factor Markov-modulated stochastic volatility model with double exponential jumps to capture long and short-term volatility and asymmetrical jumps in the underlying spot FX rate.
TL;DR: In this article, a non-parametric approach (stochastic discount factor) is applied to improve the forecasts of the usual factorial models in emerging markets and the information portfolio built from the stochastic discount factors shows better goodness of fit of emerging market and only the factor that accounts value stocks versus growth stocks is relevant to emerging equity markets, specifically, it is a sensitivity measure at risk.
TL;DR: In this article, the authors argue that the unit market discount factor creates a theoretical trade-off within a two-country general equilibrium model, but it counterfactually implies perfect consumption risk sharing and flat money demand.
Abstract: Engel and West (2005) show that the observed near random‐walk behavior of nominal exchange rates is an equilibrium outcome of a partial equilibrium asset approach when economic fundamentals follow exogenous first‐order integrated processes and the discount factor approaches one. In this paper, I argue that the unit market discount factor creates a theoretical trade‐off within a two‐country general equilibrium model. The unit discount factor generates near random‐walk nominal exchange rates, but it counterfactually implies perfect consumption risk sharing and flat money demand. Bayesian posterior simulation exercises, based on post‐Bretton Woods data from Canada and the United States, reveal difficulties in reconciling the equilibrium random‐walk proposition within the canonical model; in particular, the market discount factor is identified as being much smaller than one. A relative money demand shock is identified as the main driver of nominal exchange rates.
TL;DR: In this paper, the authors investigate and demonstrate the capital asset pricing model (CAPM) based on distribution uncertainty (or ambiguity, defined as uncertainty about unknown probability) and obtain the valuation of the market portfolio return under the condition of uncertain distributions of returns.
Abstract: In this paper, we investigate and demonstrate the capital asset pricing model (CAPM) based on distribution uncertainty (or ambiguity, defined as uncertainty about unknown probability). We first achieve directly capital asset pricing model based on spectral risk measures (abbreviated as SCAPM) in the case of normal distributions; Then we can characterize SCAPM under the condition of uncertain distributions of returns by solving a robust optimal portfolio model based on spectral measures. Specifically, we do it in the following two folds: 1) Completing first the corresponding effective frontier fitting; 2) Getting the valuation of the market portfolio return \begin{document}$ r_m $\end{document} and the risk parameters of \begin{document}$ \beta_\phi $\end{document} in use of the kernel density estimation under the distribution uncertainty of returns. Finally, by selecting 10 stocks from the constituent stocks of the HS300 Index, and comparing the valuation results from the SCAPM formula with the actual yield in the market, we verify the model proposed in the present paper is reasonable and effective.
TL;DR: In this article, a tradeable stochastic discount factor (SDF) is used to model the long-run dynamics of the US stock market, and a top-down method is proposed to capture its long run dynamics in a generalized setting.
Abstract: This paper bases long-term investing on a tradeable stochastic discount factor (SDF), relates it to the growth optimal portfolio and argues for a top-down method, where modeling efforts are directed at capturing its long-run dynamics in a generalized setting. This differs from the common, cumbersome bottom-up method of modeling many risky securities in the marketplace. Various optimal portfolio strategies can be implemented efficiently using fractional expectations of the SDF. This paper illustrates empirically for the US stock market that the proposed method leads to higher wealth, higher returns on investment and higher long-term utility levels.
TL;DR: In this article, Liu et al. studied the pricing kernel monotonicity by adapting the recently proposed conditional density integration approach of Linn-Shive-Shumway (LSS).
Abstract: Using all the data of options on the China 50 ETF, we study the pricing kernel monotonicity by adapting the recently proposed conditional density integration approach of Linn-Shive-Shumway (LSS). Methodologically, we improve LSS on several useful aspects and make its procedures applicable universally. Empirically, we provide new supporting evidence for the monotonicity of pricing kernel from a Chinese portfolio. Equally important, we are the first to obtain monotonic pricing kernels over the whole range of returns. Finally, we initialize the study of the term structure of pricing kernel and report the results with one-, two-, four- and eight-week terms. Pricing kernels show little variation for less than one-month terms, but exhibit a higher curvature for eight weeks, implying higher aggregate risk for longer-term positive returns.
TL;DR: This paper developed a methodology to decompose the conditional market risk premium and risk premia on higher moments of excess market returns into components related to contingent claims on down, up, and normal market returns.
Abstract: We develop a methodology to decompose the conditional market risk premium and risk premia on higher moments of excess market returns into components related to contingent claims on down, up, and normal market returns We call these components the downside, upside, and central risk premia The decompositions do not depend on assumptions about investor preferences nor do they depend on assumptions about the market return distribution They can be computed in real time using a cross-section of option prices The components' contributions to total risk premia vary over time and across investment horizon, as do the total risk premia themselves Our risk premium decompositions offer powerful tools for evaluating representative agent models in a conditional setting We develop a related methodology to estimate analogous conditional decompositions implied by prominent representative agent models and compare these to the data-implied decompositions Although many representative agent models are able to match the unconditional market risk premium thus “explaining” the risk premium puzzle, they generally do a poor job matching conditional risk premia and their components Our results provide a host of new empirical facts regarding sources of conditional risk premia and identify a set of new challenges for representative agent models
TL;DR: In this paper, a market-timing Bayesian hierarchical (BH) approach is proposed to estimate the conditional expected returns and residual covariance matrix jointly enabling evaluating the estimation risk in the portfolio analysis.
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TL;DR: A novel way to select assets from a universe of test assets and estimate the risk premium of a factor of interest, as well as the entire stochastic discount factor, that explicitly accounts for weak factors and test assets with highly correlated risk exposures is proposed.
Abstract: Estimation and testing of factor models in asset pricing requires choosing a set of test assets. The choice of test assets determines how well different factor risk premia can be identified: if only few assets are exposed to a factor, that factor is weak, which makes standard estimation and inference incorrect. In other words, the strength of a factor is not an inherent property of the factor: it is a property of the cross-section used in the analysis. We propose a novel way to select assets from a universe of test assets and estimate the risk premium of a factor of interest, as well as the entire stochastic discount factor, that explicitly accounts for weak factors and test assets with highly correlated risk exposures. We refer to our methodology as supervised principal component analysis (SPCA), because it iterates an asset selection step and a principal-component estimation step. We provide the asymptotic properties of our estimator, and compare its limiting behavior with that of alternative estimators proposed in the recent literature, which rely on PCA, Ridge, Lasso, and Partial Least Squares (PLS). We find that the SPCA is superior in the presence of weak factors, both in theory and in finite samples. We illustrate the use of SPCA by applying it to estimate the risk premia of several tradable and nontradable factors, to evaluate asset managers' performance, and to de-noise asset pricing factors.
TL;DR: In this article, the existence and uniqueness of equilibrium asset prices in infinite horizon, discrete-time, arbitrage free environments were studied. And they were obtained using local spectral radius methods, and a globally convergent method for computing prices whenever they exist.
TL;DR: The authors investigate the predictive power of several innovative tradable risk factors that have proved to be competent factors in recent asset pricing studies and show that all these risk factors can predict the future state of the economy to some significant extent.
Abstract: We investigate the predictive power of several innovative tradable risk factors that have proved to be competent factors in recent asset pricing studies. Our evidence indicates that all these risk factors can predict the future state of the economy to some significant extent, and they appear to perform better in short‐horizon than in long‐horizon forecasting. Using a bootstrap simulation, our estimations of bootstrapped critical values robustly reject the criticism that our significance of statistics is overstated or understated. Such results lend support to Cochrane's argument: that a competent pricing risk factor in a plausible pricing kernel may predict the future state of economy.
TL;DR: In this paper, the no-arbitrage valuation of options on two assets whereby one asset is exchanged for another is investigated, and a correlated bivariate jump-diffusion model with capturing both individual jumps and systematic cojumps is proposed.
TL;DR: This article developed Residual MisPricing (RMP), an index capturing mispricing relative to a linear benchmark asset pricing model, from the structure imposed by no-arbitrage.
Abstract: We develop Residual MisPricing (RMP), an index capturing mispricing relative to a linear benchmark asset pricing model, from the structure imposed by no-arbitrage. RMP is fully conditional and depends only on the returns of basic assets. Return data for several economies reveal that RMP is countercyclical and related to financial uncertainty. RMP further shows a strong positive relation to conditional international equity and currency risk premia, as well as a close link to market-wide funding liquidity shocks. The relations we document hold in particular out-of-sample. Our evidence points to new record highs for RMP during the COVID-19 era, similar to its behavior in the 2008 financial crisis.
TL;DR: The authors examined carry-trade returns from a risk-pricing perspective and examined if these returns can be connected to cross-country differences in risk pricing in the interest-rate market compared to the stock market.
Abstract: The returns to carry trades are controversially discussed. There seems to be no unifying risk-based explanation of currency returns and stock returns, while the countries’ interest rate differential plays a leading part in the carry-trade performance. Therefore, this paper addresses carry-trade returns from a risk-pricing perspective and examines if these returns can be connected to cross-country differences in risk pricing in the interest-rate market compared to the stock market. Data from Thomson Reuters Datastream and Federal Reserve Economic Data covering Australia, Japan, New Zealand, Switzerland and the United States were analyzed based on GMM estimation. The results indicate significant and persistent cross-country differences in risk aversion in the interest-rate market compared to the implied risk aversion in the stock market. This may offer opportunities for risk arbitrage and, therefore, a risk pricing-related explanation of carry-trade returns.