Improvement in finite sample properties of the Hansen–Jagannathan distance test

Jagannathan and Wang [Jagannthan, R., and Wang, Z., “The conditional CAPM and the cross-section of expected returns.” Journal of Finance, 51 (1996), 3–53] derive the asymptotic distribution of the Hansen–Jagannathan distance (HJ-distance) proposed by Hansen and Jagannathan [Hansen, L.P., and Jagannathan, R., Assessing specific errors in stochastic discount factor models." Journal of Finance, 52 (1997), 557–590], and develop a specification test of asset pricing models based on the HJ-distance. While the HJ-distance has several desirable properties, Ahn and Gadarowski [Ahn, S.C., and Gadarowski, C., “Small sample properties of the GMM specification test based on the Hansen–Jagannathan distance.” Journal of Empirical Finance, 11 (2004), 109–132] find that the specification test based on the HJ-distance overrejects correct models too severely in commonly used sample size to provide a valid test. This paper proposes to improve the finite sample properties of the HJ-distance test by applying the shrinkage method [Ledoit, O., and Wolf, M., “Improved estimation of the covariance matrix of stock returns with an application to portfolio selection.” Journal of Empirical Finance, 10 (2003), 603–621] to compute its weighting matrix. The proposed method improves the finite sample performance of the HJ-distance test significantly.     

Small sample properties of the GMM specification test based on the Hansen–Jagannathan distance

Following Hansen and Jagannathan (J. Finance 52 (1997) 557), Jagannathan and Wang (J. Finance 51 (1996) 3) propose a distance measure that estimates the maximum pricing error generated by a linear asset model. Jagannathan and Wang propose a test of this HJ-distance using an empirical p-value as an alternative generalized method of moments (GMM) measure to Hansen's (Econometrica 50 (1982) 1029) GMM specification test. Using Monte Carlo analysis, we examine the finite sample properties of these specification tests. While the Hansen test mildly overrejects correct models in commonly used sample size, the empirical p-value of the HJ-distance rejects correct models too severely in such samples to provide a valid test of such models.     

A Critique of the Stochastic Discount Factor Methodology

In this paper, we point out that the widely used stochastic discount factor (SDF) methodology ignores a fully specified model for asset returns. As a result, it suffers from two potential problems when asset returns follow a linear factor model. The first problem is that the risk premium estimate from the SDF methodology is unreliable. The second problem is that the specification test under the SDF methodology has very low power in detecting misspecified models. Traditional methodologies typically incorporate a fully specified model for asset returns, and they can perform substantially better than the SDF methodology.     

Tests of the Relations Among Marketwide Factors,Firm-Specific Variables,and Stock Returns Using a Conditional Asset Pricing Model

In this article we generalize Harvey's (1989) empirical specification of conditional asset pricing models to allow for both time-varying covariances between stock returns and marketwide factors and time-varying reward-to-covariabilities. The model is then applied to examine the effects of firm size and book-to-market equity ratios. We find that the traditional asset pricing model with commonly used factors can only explain a small portion of the stock returns predicted by firm size and book-to-market equity ratios. The results indicate that allowing time-varying covariances and time-varying reward-to-covariabilities does little to salvage the traditional asset pricing models.     

Tests of market models: heteroskedasticity or misspecification?

This paper investigates the nature and the incidence of heteroskedasticity and misspecification in the market models by utilizing tests that are generally applicable. The results show that heteroskedasticity appears more frequently than misspecification even though both are serious problems. The evidence also indicates that the use of a quadratic market model or equally weighted market returns may lead to a smaller percentage of heteroskedastic cases but that, in general, this advantage has to be offset against an increase in the occurrence of specification errors. Small firms and January returns are also observed to produce a higher incidence of both heteroskedasticity and misspecification.     

An examination of alternative CAPM-based models in UK stock returns

We evaluate the performance of unconditional and conditional versions of seven stochastic discount factor models in UK stock returns between January 1975 and December 2001. We find that the conditional four-moment capital asset pricing model (CAPM) has the best performance among the models we consider in terms of the lowest [Hansen, L.P., Jagannathan, R., 1997. Assessing specification errors in stochastic discount factor models. Journal of Finance 52, 591–607] distance measure and explaining the time-series predictability of industry portfolio excess returns. Conditional models also do a better job than unconditional models. However we find that the superior performance of the conditional four-moment CAPM, and conditional models in general, arises in part due to overfitting the data.     

Pricing errors and estimates of risk premia in factor models

In this paper, we consider the effect of the theoretical pricing error in the arbitrage pricing model on estimates of risk premia implied by the model. Under arbitrage pricing, the pricing error satisfies a strong bounding condition where for an infinite set of assets, the sum of squared pricing errors is bounded. We characterize the pricing error in terms of orders of probability and estimate an expected returns model which allows for pricing errors less than order one in probability. The principal finding of the paper is that misspecification of the pricing error and misspecification of the factor structure has no effect on the bias or mean squared error of the dominant risk premium. This implies that an exact form of arbitrage pricing can be used to estimate risk premia.     

Market proxies as factors in linear asset pricing models: Still living with the roll critique

A new model misspecification measure for linear asset pricing models is proposed for the case where misspecification maps to latency of one of the pricing factors; in this case, the market return. This measure is suited both for testing models that include the market return as a pricing factor in a traditional sense (i.e., whether the chosen model does or does not price a collection of risky assets) and ranking those models (i.e., determining which model performs best). The proposed measure is used in pricing portfolios reflecting the size, value, and momentum premia. The conditional CAPM of Jagannathan and Wang (1996) is found to best the performance of both the simple CAPM and the ICAPM of Petkova (2006). Moreover, it is discovered that winner stocks in a momentum portfolio may have higher market betas than loser stocks.     

Consumption-based equity valuation

Using a CCAPM-based risk-adjustment model, we perform yearly valuations of a large sample of stocks listed on NYSE, AMEX, and NASDAQ over a 30-year period. The model differs from standard valuation models in the sense that it adjusts forecasted residual income for risk in the numerator rather than through a risk-adjusted cost of equity in the denominator. The risk adjustments are derived based on assumptions about the time-series properties of residual income returns and aggregate consumption rather than on historical stock returns. We compare the performance of the model with several implementations of standard valuation models, both in terms of median absolute valuation errors (MAVE) and in terms of excess returns on simple investment strategies based on the differences between model and market prices. The CCAPM-based valuation model yields a significantly lower MAVE than the best performing standard valuation model. Both types of models can identify investment strategies with subsequent excess returns. The CCAPM-based valuation model yields time-series of realized hedge returns with more and higher positive returns and fewer and less negative returns compared with the time-series of realized hedge returns based on the best performing standard valuation model for holding periods from 1 to 5 years. In a statistical test of 1-year-ahead excess return predictability based on the models’ implied pricing errors, the CCAPM-based valuation model is selected as the better model. Using the standard series of aggregate consumption and the nominal price index, a reasonable level of relative risk aversion, and calibrated growth rates in the continuing value at each valuation date, the CCAPM-based valuation model produces small risk adjustments to forecasted residual income and low continuing values. Compared with standard valuation models, it relies less on estimated parameters and speculative elements when aggregating residual earnings forecasts into a valuation.     

Macroeconomic sources of foreign exchange risk in new EU members

We address the issue of foreign exchange risk and its macroeconomic determinants in several new EU members. We derive the observable macroeconomic factors—consumption and inflation—using the stochastic discount factor (SDF) approach. The joint distribution of excess returns in the foreign exchange market and the factors are modeled using a multivariate GARCH-in-mean specification. Our findings show that both real and nominal factors play important roles in explaining the variability of the foreign exchange risk premium. Both types of factors should be included in monetary general equilibrium models employed to study excess returns. To contribute to the further stability of domestic currencies, the new EU members should strive to implement stabilization policies aimed at achieving nominal as well as real convergence with the core EU members.     

Testing conditional asset pricing models: An emerging market perspective

The CAPM as the benchmark asset pricing model generally performs poorly in both developed and emerging markets. We investigate whether allowing the model parameters to vary improves the performance of the CAPM and the Fama–French model. Conditional asset pricing models scaled by conditioning variables such as Trading Volume and Dividend Yield generally result in small pricing errors. However, a graphical analysis reveals that the predictions of conditional models are generally upward biased. We demonstrate that the bias in prediction may be the consequence of ignoring frequent large variation in asset returns caused by volatile institutional, political and macroeconomic conditions. This is characterised by excess kurtosis. An unconditional Fama–French model augmented with a cubic market factor performs the best among some competing models when local risk factors are employed. Moreover, the conditional models with global risk factors scaled by global conditioning variables perform better than the unconditional models with global risk factors.     

Misreaction or misspecification? A re-examination of volatility anomalies

Existing research examines the impact of volatility shocks on the relative pricing of long-term vs. short-term options and documents patterns of “short-horizon underreaction” and “long-horizon overreaction” in the options market. These studies, however, rely on implied volatilities derived from specific option-pricing models and are thus subject to model specification errors. In this paper, we show that these anomalous patterns are the result of model misspecification as opposed to market misreaction. We provide evidence that these patterns are consistent with, in both direction and magnitude, inherent biases in the misspecified models. We also apply a model-free approach to re-examine the anomalous patterns and find no evidence of market misreaction.     

Liquidity and asset pricing: Evidence from the Hong Kong stock market

This study investigates the role of liquidity in pricing stock returns in the Hong Kong stock market. Our results show that liquidity is an important factor for pricing returns in Hong Kong after taking well-documented asset pricing factors into consideration. The results are robust to adding portfolio residuals and higher moment factor in the factor models. The results are also robust to seasonality, and conditional-market tests. We also compare alternative factor models and find that the liquidity four-factor model (market excess return, size, book-to-market ratio, and liquidity) is the best model to explain stock returns in the Hong Kong stock market, while the momentum factor is not found to be priced.     

Explaining abnormal returns in stock markets: An alpha-neutral version of the CAPM

This paper develops a behavioural asset pricing model in which traders are not fully rational as is commonly assumed in the literature. The model derived is underpinned by the notion that agents’ preferences are affected by their degree of optimism or pessimism regarding future market states. It is characterized by a representation consistent with the Capital Asset Pricing Model, augmented by a behavioural bias that yields a simple and intuitive economic explanation of the abnormal returns typically left unexplained by benchmark models. The results we provide show how the factor introduced is able to absorb the “abnormal” returns that are not captured by the traditional CAPM, thereby reducing the pricing errors in the asset pricing model to statistical insignificance.     

Options as a predictor of common stock price changes

Since rather novel techniques such as neural nets allow investigation of nonlinear model specification previously untested, it may be that traditional models of price formation underperform through misspecification rather than market efficiency. This paper explores whether a multilayer backpropagation model offers exploitable profit opportunities for some limited period. Using an intradaytransaction dataset obtained from the European Options Exchange (Amsterdam), We attempted to predict the return on Philips. Two neural nets are contrasted to ordinary linear regression analysis on the basis of three benchmarks (MSE, and net realized returns). An adaptively trained 33-14-1 architecture scored best on all criteria and yielded an annualized 11% return following a simple one-period trading strategy.     

Does information risk affect the implied cost of equity capital? An analysis of PIN and adjusted PIN

Using a unique dataset of Korean listed companies for which trade initiators are correctly identifiable, we estimate bias-free PIN (probability of informed trading) that is no longer subject to the trade misspecification problem and test whether it is related to expected returns. Unlike prior studies, we find that bias-free AdjPIN, the adjusted PIN purged of a liquidity component, is positively related to implied cost of equity. Our findings suggest that the errors in PIN variables hamper a proper identification of PIN pricing in prior studies.     

An Examination of Alternative Factor Models in UK Stock Returns

This paper examines the mean-variance efficiency of a number offactor models in UK stock returns. The paper also explores, using theapproach of MacKinlay (1995), whether missing risk factors ornonrisk-based explanations best explain the pricing errors of thedifferent factor models. The evidence in the paper suggests that themean-variance efficiency of each factor model is rejected and missing riskfactors are unable to explain the pricing errors of any of the models.Some nonrisk-based explanations, which posit a wide spread in abnormalreturns, may be a more plausible source of explaining the pricing errorsof the factor models.     

Model uncertainty and the Forward Premium Puzzle

This paper studies the Forward Premium Puzzle in a setting where investors doubt the specification of their models, and thus engage in robust portfolio strategies (Hansen and Sargent, 2008). It shows that an empirically plausible concern for model misspecification can explain the Forward Premium Puzzle. In particular, the paper shows that Hansen and Jagannathan (1991) volatility bounds can be attained with both reasonable degrees of risk aversion and reasonable detection error probabilities. Hence, observed excess returns in the foreign exchange market appear to be primarily driven by a model uncertainty premium.     

Market-wide illiquidity and the distribution of non-parametric stochastic discount factors

Employing out-of-sample non-parametric estimation techniques, we show that market-wide liquidity risk matters for asset pricing independently of the specific functional form of the stochastic discount factor (SDF) and, therefore, of the asset pricing model specification. Market-wide illiquidity significantly affects the distribution of the SDF. Specifically, it boosts up the volatility of the SDF, causing minor effects on higher moments of its distribution. This finding is robust to the use of different sets of test assets in the estimation of the SDF, including equity and corporate bond portfolios, and the use of a high-dimensional data estimation procedure.