scholarly journals Relative Entropy and Minimum-Variance Pricing Kernel in Asset Pricing Model Evaluation

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 721
Author(s):  
Javier Rojo-Suárez ◽  
Ana Belén Alonso-Conde
Keyword(s):  
Asset Pricing ◽  
Relative Entropy ◽  
Explanatory Power ◽  
Minimum Variance ◽  
Pricing Models ◽  
Pricing Kernel ◽  
Cross Sectional ◽  
Testing Procedures ◽  
Asset Pricing Models ◽  
Leibler Divergence

Recent literature shows that many testing procedures used to evaluate asset pricing models result in spurious rejection probabilities. Model misspecification, the strong factor structure of test assets, or skewed test statistics largely explain this. In this paper we use the relative entropy of pricing kernels to provide an alternative framework for testing asset pricing models. Building on the fact that the law of one price guarantees the existence of a valid pricing kernel, we study the relationship between the mean-variance efficiency of a model’s factor-mimicking portfolio, as measured by the cross-sectional generalized least squares (GLS) R 2 statistic, and the relative entropy of the pricing kernel, as determined by the Kullback–Leibler divergence. In this regard, we suggest an entropy-based decomposition that accurately captures the divergence between the factor-mimicking portfolio and the minimum-variance pricing kernel resulting from the Hansen-Jagannathan bound. Our results show that, although GLS R 2 statistics and relative entropy are strongly correlated, the relative entropy approach allows us to explicitly decompose the explanatory power of the model into two components, namely, the relative entropy of the pricing kernel and that corresponding to its correlation with asset returns. This makes the relative entropy a versatile tool for designing robust tests in asset pricing.

scholarly journals Data Envelopment Analysis and Multifactor Asset Pricing Models

2020 ◽  
Vol 8 (2) ◽  
pp. 24
Author(s):  
Pablo Solórzano-Taborga ◽  
Ana Belén Alonso-Conde ◽  
Javier Rojo-Suárez
Keyword(s):  
Data Envelopment Analysis ◽  
Asset Pricing ◽  
Least Squares ◽  
Explanatory Power ◽  
Ordinary Least Squares ◽  
Efficiency Factor ◽  
Data Envelopment ◽  
Pricing Models ◽  
Cross Sectional ◽  
Asset Pricing Models

Recent literature shows that market anomalies have significantly diminished, while research on market factors has largely improved the performance of asset pricing models. In this paper we study the extent to which data envelopment analysis (DEA) techniques can help improve the performance of multifactor models. Specifically, we test the explanatory power of the Fama and French three-factor model, combined with an additional factor based on DEA, on a sample of 2101 European equity funds, for the period from 2001 to 2016. Accordingly, we first form the fund portfolios that constitute our test assets and create the efficiency factor. Secondly, we estimate the prices of risk tied to the four factors using ordinary least squares (OLS) on a two-stage cross-sectional regression. Finally, we use the R-squared statistic estimated by generalized least squares (GLS), as well as the Gibbons Ross and Shanken test and the J-test for overidentifying restrictions in order to study the performance of the model, including and omitting the efficiency factor. The results show that the efficiency factor improves the performance of the model and reduces the pricing errors of the assets under consideration, which allows us to conclude that the efficiency index may be used as a factor in asset pricing models.

Using Stocks or Portfolios in Tests of Factor Models

2019 ◽  
Vol 55 (3) ◽  
pp. 709-750 ◽  
Author(s):  
Andrew Ang ◽  
Jun Liu ◽  
Krista Schwarz
Keyword(s):  
Asset Pricing ◽  
Risk Premia ◽  
Factor Models ◽  
Idiosyncratic Volatility ◽  
Standard Errors ◽  
Coefficient Estimates ◽  
Pricing Models ◽  
Cross Sectional ◽  
Factor Loadings ◽  
Asset Pricing Models

We examine the efficiency of using individual stocks or portfolios as base assets to test asset pricing models using cross-sectional data. The literature has argued that creating portfolios reduces idiosyncratic volatility and allows more precise estimates of factor loadings, and consequently risk premia. We show analytically and empirically that smaller standard errors of portfolio beta estimates do not lead to smaller standard errors of cross-sectional coefficient estimates. Factor risk premia standard errors are determined by the cross-sectional distributions of factor loadings and residual risk. Portfolios destroy information by shrinking the dispersion of betas, leading to larger standard errors.

The Bias in Two-Pass Regression Tests of Asset-Pricing Models in Presence of Idiosyncratic Errors with Cross-Sectional Dependence

2019 ◽  
Vol 22 (02) ◽  
pp. 1950012
Author(s):  
Thomas Gramespacher ◽  
Armin Bänziger
Keyword(s):  
Asset Pricing ◽  
Risk Premium ◽  
Measurement Errors ◽  
Factor Model ◽  
Pricing Models ◽  
Time Series Regression ◽  
Cross Sectional ◽  
Asset Pricing Models ◽  
Slope Estimator ◽  
Regression Tests

In two-pass regression-tests of asset-pricing models, cross-sectional correlations in the errors of the first-pass time-series regression lead to correlated measurement errors in the betas used as explanatory variables in the second-pass cross-sectional regression. The slope estimator of the second-pass regression is an estimate for the factor risk-premium and its significance is decisive for the validity of the pricing model. While it is well known that the slope estimator is downward biased in presence of uncorrelated measurement errors, we show in this paper that the correlations seen in empirical return data substantially suppress this bias. For the case of a single-factor model, we calculate the bias of the OLS slope estimator in the presence of correlated measurement errors with a first-order Taylor-approximation in the size of the errors. We show that the bias increases with the size of the errors, but decreases the more the errors are correlated. We illustrate and validate our result using a simulation approach based on empirical data commonly used in asset-pricing tests.

Minimum-Relative-Entropy Calibration of Asset-Pricing Models

1998 ◽  
Vol 01 (04) ◽  
pp. 447-472 ◽  
Author(s):  
Marco Avellaneda
Keyword(s):  
Asset Pricing ◽  
Relative Entropy ◽  
Smooth Curve ◽  
Contingent Claims ◽  
Fixed Income ◽  
Pricing Models ◽  
Forward Rates ◽  
Asset Pricing Models ◽  
Minimum Relative Entropy ◽  
Input Prices

We present an algorithm for calibrating asset-pricing models to the prices of benchmark securities. The algorithm computes the probability that minimizes the relative entropy with respect to a prior distribution and satisfies a finite number of moment constraints. These constraints arise from fitting the model to the prices of benchmark prices are studied in detail. We find that the sensitivities can be interpreted as regression coefficients of the payoffs of contingent claims on the set of payoffs of the benchmark instruments. We show that the algorithm has a unique solution which is stable, i.e. it depends smoothly on the input prices. The sensitivities of the values of contingent claims with respect to varriations in the benchmark instruments, in the risk-neutral measure. We also show that the minimum-relative-entropy algorithm is a special case of a general class of algorithms for calibrating models based on stochastic control and convex optimization. As an illustration, we use minimum-relative-entropy to construct a smooth curve of instantaneous forward rates from US LIBOR swap/FRA data and to study the corresponding sensitivities of fixed-income securities to variations in input prices.

Firm Characteristics, Cross-Sectional Regression Estimates, and Asset Pricing Tests

2019 ◽  
Vol 10 (2) ◽  
pp. 290-334 ◽  
Author(s):  
Chris Kirby
Keyword(s):  
Asset Pricing ◽  
Stock Returns ◽  
Nonlinear Effects ◽  
Firm Characteristics ◽  
Pricing Models ◽  
Cross Sectional ◽  
Portfolio Returns ◽  
Asset Pricing Models ◽  
Formidable Challenge ◽  
Expected Stock Returns

Abstract I test a number of well-known asset pricing models using regression-based managed portfolios that capture nonlinearity in the cross-sectional relation between firm characteristics and expected stock returns. Although the average portfolio returns point to substantial nonlinearity in the data, none of the asset pricing models successfully explain the estimated nonlinear effects. Indeed, the estimated expected returns produced by the models display almost no variation across portfolios. Because the tests soundly reject every model considered, it is apparent that nonlinearity in the relation between firm characteristics and expected stock returns poses a formidable challenge to asset pricing theory. (JEL G12, C58)

scholarly journals Modelos de Precificação de Ativos e o Efeito Liquidez: Evidências Empíricas no Mercado Acionário Brasileiro

2011 ◽  
Vol 9 (3) ◽  
pp. 383 ◽  
Author(s):  
Márcio André Veras Machado ◽  
Otávio Ribeiro de Medeiros
Keyword(s):  
Asset Pricing ◽  
Stock Returns ◽  
Factor Model ◽  
Five Factor Model ◽  
Explanatory Power ◽  
Liquidity Premium ◽  
Pricing Models ◽  
Portfolio Returns ◽  
Asset Pricing Models ◽  
Three Factor

This paper is aims to analyze whether a liquidity premium exists in the Brazilian stock market. As a second goal, we include liquidity as an extra risk factor in asset pricing models and test whether this factor is priced and whether stock returns were explained not only by systematic risk, as proposed by the CAPM, by Fama and French’s (1993) three-factor model, and by Carhart’s (1997) momentum-factor model, but also by liquidity, as suggested by Amihud and Mendelson (1986). To achieve this, we used stock portfolios and five measures of liquidity. Among the asset pricing models tested, the CAPM was the least capable of explaining returns. We found that the inclusion of size and book-to-market factors in the CAPM, a momentum factor in the three-factor model, and a liquidity factor in the four-factor model improve their explanatory power of portfolio returns. In addition, we found that the five-factor model is marginally superior to the other asset pricing models tested.

scholarly journals A Synthesis of Two Factor Estimation Methods

2015 ◽  
Vol 50 (4) ◽  
pp. 825-842 ◽  
Author(s):  
Gregory Connor ◽  
Robert A. Korajczyk ◽  
Robert T. Uhlaner
Keyword(s):  
Fixed Point ◽  
Asset Pricing ◽  
Risk Premia ◽  
Estimation Methods ◽  
Errors In Variables ◽  
Pricing Models ◽  
Cross Sectional ◽  
Asset Pricing Models ◽  
The Common ◽  
Factor Estimation

AbstractTwo-pass cross-sectional regression (TPCSR) is frequently used in estimating factor risk premia. Recent papers argue that the common practice of grouping assets into portfolios to reduce the errors-in-variables (EIV) problem leads to loss of efficiency and masks potential deviations from asset pricing models. One solution that allows the use of individual assets while overcoming the EIV problem is iterated TPCSR (ITPCSR). ITPCSR converges to a fixed point regardless of the initial factors chosen. ITPCSR is intimately linked to the asymptotic principal components (APC) method of estimating factors since the ITPCSR estimates are the APC estimates, up to a rotation.

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