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Abstract:
Explaining movements in daily stock prices is one of the most difficult tasks in modern finance. This paper contributes to the existing literature by documenting the impact of geomagnetic storms on daily stock market returns. A large body of psychological research has shown that geomagnetic storms have a profound effect on people's moods, and, in turn, people's moods have been found to be related to human behavior, judgments and decisions about risk. An important finding of this literature is that people often attribute their feelings and emotions to the wrong source, leading to incorrect judgments. Specifically, people affected by geomagnetic storms may be more inclined to sell stocks on stormy days because they incorrectly attribute their bad mood to negative economic prospects rather than bad environmental conditions. Misattribution of mood and pessimistic choices can translate into a relatively higher demand for riskless assets, causing the price of risky assets to fall or to rise less quickly than otherwise. The authors find strong empirical support in favor of a geomagnetic-storm effect in stock returns after controlling for market seasonals and other environmental and behavioral factors. Unusually high levels of geomagnetic activity have a negative, statistically and economically significant effect on the following week's stock returns for all U.S. stock market indices. Finally, this paper provides evidence of substantially higher returns around the world during periods of quiet geomagnetic activity.

Stock returns, geomagnetic storms, seasonal affective disorders, misattribution of mood, behavioral finance

Abstract:
In this paper the author formulates and tests an international intertemporal capital asset pricing model in the presence of deviations from purchasing power parity (II-CAPM[PPP]). He finds evidence in favor of at least mild segmentation of international equity markets in which only global market risk appears to be priced. When using the Hansen & Jagannathan (1991, 1997) variance bounds and distance measures as testing devices, the author finds that, while all international asset pricing models are formally rejected by the data, their pricing implications are substantially different. The superior performance of the II-CAPM (PPP) is mainly attributable to significant hedging against inflation risk.

international intertemporal capital asset pricing model, purchasing power parity, hedging demands

Abstract:
In this paper, I study the behavior of an investor with unit risk aversion who maximizes a utility function defined over the mean and the variance of a portfolio's return. Conditioning information is accessible without cost and an unconditionally riskless asset is available in the market.

The proposed approach makes it possible to compare the performance of a benchmark tangency portfolio formed from the set of unrestricted estimates of portfolio weights) to the performance of a restricted tangency portfolio which uses single-index and multi-index asset pricing models to constrain the first moments of asset returns.

The main findings of the paper are summarized as follows: i) The estimates of the constant and time-varying tangency portfolio weights are extremely volatile and imprecise. Using an asset pricing model to constrain mean asset returns eliminates extreme short positions in the underlying securities and improves the precision of the estimates of the weights. ii) Partially restricting mean asset returns according to single-index and multi-index asset pricing models improves the out-of-sample performance of the tangency portfolio. iii) Active investment
strategies (i.e., strategies that incorporate the role played by conditioning information in investment decisions) strongly dominate passive investment strategies in-sample but do not provide any convincing pattern of improved out-of-sample performance.

asset allocation, conditioning information, dynamic strategies, tangency portfolio

Abstract:
In this paper, we discuss the impact of different formulations of asset pricing models on the outcome of specification tests that are performed using excess returns. We point out that the popular way of specifying the stochastic discount factor (SDF) as a linear function of the factors is problematic because (1) the specification test statistic is not invariant to an affine transformation of the factors, and (2) the SDFs of competing models can have very different means. In contrast, an alternative specification that defines the SDF as a linear function of the de-meaned factors is free from these two problems and is more appropriate for model comparison. In addition, we suggest that a modification of the traditional Hansen-Jagannathan distance (HJ-distance) is needed when we use the de-meaned factors. The modified HJ-distance uses the inverse of the covariance matrix (instead of the second moment matrix) of excess returns as the weighting matrix to aggregate pricing errors. Asymptotic distributions of the modified HJ-distance and of the traditional HJ-distance based on the de-meaned SDF under the correctly specified model and the misspecified models are provided. Finally, we propose a simple methodology for computing the standard errors of the estimated SDF parameters that are robust to model misspecification. We show that failure to take model misspecification into account is likely to understate the standard errors of the estimates of the SDF parameters and lead us to erroneously conclude that certain factors are priced.

Hansen-Jagannathan distance, excess returns, stochastic discount factors

Abstract:
The risk premia assigned to economic (non-traded) risk factors can be decomposed into three parts: i) the risk premia on maximum-correlation portfolios mimicking the factors; ii) (minus) the covariance between the non-traded components of the candidate pricing kernel of a given model and the factors; and iii) (minus) the mis-pricing assigned by the candidate pricing kernel to the maximum-correlation mimicking portfolios. The first component is the same across asset-pricing models, and is typically estimated with little (absolute) bias and high precision. The second component, on the other hand, is essentially arbitrary, and can be estimated with large (absolute) biases and low precisions by multi-beta models with non-traded factors. This second component is also sensitive to the criterion minimized in estimation. The third component is estimated reasonably well, both for models with traded and non-traded factors. We conclude that the economic risk premia assigned by multi-beta models with non-traded factors can be very unreliable. Conversely, the risk premia on maximum-correlation portfolios provide more reliable indications of whether a non-traded risk factor is priced. These results hold for both the constant and the time-varying components of the factor risk premia.

economic risk premia, non-traded factors, maximum-correlation portfolios

Abstract:
The risk premia assigned to economic (non-traded) risk factors can be decomposed into three parts: i) the risk premia on maximum-correlation portfolios mimicking the factors; ii) (minus) the covariance between the non-traded components of the candidate pricing kernel of a given model and the factors; and iii) (minus) the mis-pricing assigned by the candidate pricing kernel to the maximum-correlation mimicking portfolios. The first component is the same across asset-pricing models, and is typically estimated with little (absolute) bias and high precision. The second component, on the other hand, is essentially arbitrary, and can be estimated with large (absolute) biases and low precisions by multi-beta models with non-traded factors. This second component is also sensitive to the criterion minimized in estimation. The third component is estimated reasonably well, both for models with traded and non-traded factors. We conclude that the economic risk premia assigned by multi-beta models with non-traded factors can be very unreliable. Conversely, the risk premia on maximum-correlation portfolios provide more reliable indications of whether a non-traded risk factor is priced. These results hold for both the constant and the time-varying components of the factor risk premia.

economic risk premia, non-traded factors, maximum-correlation portfolios

Abstract:
This paper considers two alternative formulations of the linear factor model (LFM) with nontraded factors. The first formulation is the traditional LFM, where the estimation of risk premia and alphas is performed by means of a cross-sectional regression of average returns on betas. The second formulation (LFM*) replaces the factors with their projections on the span of excess returns. This formulation requires only time-series regressions for the estimation of risk premia and alphas. We compare the theoretical properties of the two approaches and study the small-sample properties of estimates and test statistics. Our results show that when estimating risk premia and testing multi-beta models, the LFM* formulation should be considered in addition to, or even instead of, the more traditional LFM formulation.

mimicking portfolios, economic risk premia, multi-beta models

Abstract:
Under the assumption of multivariate normality of asset returns, this paper presents a geometrical interpretation and the finite-sample distributions of the sample Hansen-Jagannathan (1991) bounds on the variance of admissible stochastic discount factors, with and without the nonnegativity constraint on the stochastic discount factors. In addition, since the sample Hansen-Jagannathan bounds can be very volatile, we propose a simple method to construct confidence intervals for the population Hansen-Jagannathan bounds. Finally, we show that the analytical results in the paper are robust to departures from the normality assumption.

Hansen-Jagannathan Bound, No Arbitrage, Positivity, Exact Distribution

Abstract:
Although it is of interest to test whether or not a particular asset pricing model is literally true, a more useful task for empirical researchers is to determine how wrong a model is and to compare the performance of competing asset pricing models. In this paper, we propose a new methodology to test whether or not two competing linear asset pricing models have the same Hansen-Jagannathan distance. We show that the asymptotic distribution of the test statistic depends on whether the competing models are correctly specified or misspecified, and on whether the competing models are nested or non-nested. In addition, given the increasing interest in misspecified models, we propose a simple methodology for computing the standard errors of the estimated stochastic discount factor parameters that are robust to model misspecification. Using monthly data on 25 size and book-to-market ranked portfolios and the one-month T-bill, we show that the commonly used returns and factors are, for the most part, too noisy for us to conclude that one model is superior to the other models in terms of Hansen-Jagannathan distance. Specifically, there is little evidence that conditional and intertemporal CAPM-type specifications outperform the simple unconditional CAPM. In addition, we show that many of the macroeconomic factors commonly used in the literature are no longer priced once potential model misspecification is taken into account.

Hansen-Jagannathan Distance, Asset-pricing Models, Model Misspecification, Risk Premia

Abstract:
We consider two formulations of the linear factor model with non-traded factors. In the first formulation (LFM), risk premia and alphas are estimated by a cross-sectional regression of average returns on betas. In the second formulation (LFM*), the factors are replaced by their projections on the span of excess returns, and risk premia and alphas are estimated by time-series regressions. We compare the two formulations and study the small-sample properties of estimates and test statistics. We conclude that the LFM* formulation should be considered in addition to, or even instead of, the more traditional LFM formulation.

Abstract:
The risk premia of linear factor models on economic (non-traded) risk factors can be decomposed into: i) the premium on maximum-correlation portfolios mimicking the factors; ii) (minus) the covariance between the non-traded components of the pricing kernel and the factors; and iii) (minus) the mispricing of the maximum-correlation portfolios. The first component is independent of a model's non-traded variability and mispricing, and is typically estimated with little bias and high precision. We conclude that the premia on maximum-correlation portfolios are appealing alternatives to the risk premia of linear factor models, with the dividend yield being the only economic factor significantly priced.

economic factors, risk premia, pricing kernel, maximum-correlation portfolio

Abstract:
Since Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973), the two-pass cross-sectional regression (CSR) methodology has become the most popular approach for estimating and testing asset pricing models. Statistical inference with this method is typically conducted under the assumption that the models are correctly specified, i.e., expected returns are exactly linear in asset betas. This can be a problem in practice since all models are, at best, approximations of reality and are likely to be subject to a certain degree of misspecification. We propose a general methodology for computing misspecification-robust asymptotic standard errors of the risk premia estimates. We also derive the asymptotic distribution of the sample CSR R2 and develop a test of whether two competing beta pricing models have the same population R2. This provides a formal alternative to the common heuristic of simply comparing the R2 estimates in evaluating relative model performance. Finally, we provide an empirical application which demonstrates the importance of our new results when applied to a variety of asset pricing models.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
Since Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973), the two-pass cross-sectional regression (CSR) methodology has become the most popular approach for estimating and testing asset pricing models. Statistical inference with this method is typically conducted under the assumption that the models are correctly specified, i.e., expected returns are exactly linear in asset betas. This can be a problem in practice since all models are, at best, approximations of reality and are likely to be subject to a certain degree of misspecification. We propose a general methodology for computing misspecification-robust asymptotic standard errors of the risk premia estimates. We also derive the asymptotic distribution of the sample CSR R2 and develop a test of whether two competing linear beta pricing models have the same population R2. This provides a formal alternative to the common heuristic of simply comparing the R2 estimates in evaluating relative model performance. Finally, we provide an empirical application which demonstrates the importance of our new results when applied to a variety of asset pricing models.

R-squared, model misspecification, model comparison, two-pass cross-sectional regressions

Abstract:
The risk premia of linear factor models on economic (non-traded) risk factors can be decomposed into: i) the premium on maximum-correlation portfolios mimicking the factors; ii) (minus) the covariance between the non-traded components of the pricing kernel and the factors; and iii) (minus) the mispricing of the maximum-correlation portfolios. For a given set of assets available for investment, the first component is the same across models and is typically estimated with little bias and high precision. We conclude that the premia on maximum-correlation portfolios are appealing alternatives to the risk premia of linear factor models, with the dividend yield being the only economic factor significantly priced.

economic factors, risk premia, pricing kernel, maximum-correlation portfolio

Abstract:
Since Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973), the two-pass cross-sectional regression (CSR) methodology has become the most popular approach for estimating and testing asset pricing models. Statistical inference with this method is typically conducted under the assumption that the models are correctly specified, i.e., expected returns are exactly linear in asset betas. This can be a problem in practice since all models are, at best, approximations of reality and are likely to be subject to a certain degree of misspecification. We propose a general methodology for computing misspecification-robust asymptotic standard errors of the risk premia estimates. We also derive the asymptotic distribution of the sample CSR R2 and develop a test of whether two competing beta pricing models have the same population R2. This provides a formal alternative to the common heuristic of simply comparing the R2 estimates in evaluating relative model performance. Finally, we provide an empirical application which demonstrates the importance of our new results when applied to a variety of asset pricing models.

Abstract:
Since Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973), the two-pass cross-sectional regression (CSR) methodology has become the most popular tool for estimating and testing beta pricing models. In this paper, we focus on the case in which simple regression betas are used as regressors in the second-pass CSR. Under general distributional assumptions, we derive asymptotic standard errors of the risk premia estimates that are robust to model misspecification. When testing whether the beta risk of a given factor is priced, our misspecification robust standard error and the Jagannathan and Wang (1998) standard error (which is derived under the correctly specified model) can lead to different conclusions.

Asset Pricing Models, Cross-Sectional Regressions, Simple Regression Betas, Model Misspecification

Abstract:
Although it is of interest to test whether or not a particular asset pricing model is literally true, a more useful task for empirical researchers is to determine how wrong a model is and to compare the performance of competing asset pricing models. In this paper, we propose a new methodology to test whether or not two competing linear asset pricing models have the same Hansen-Jagannathan distance. We show that the asymptotic distribution of the test statistic depends on whether the competing models are correctly specified or misspecified, and on whether the competing models are nested or non-nested. In addition, given the increasing interest in misspecified models, we propose a simple methodology for computing the standard errors of the estimated stochastic discount factor parameters that are robust to model misspecification. Using monthly data on 25 size and book-to-market ranked portfolios and the one-month T-bill, we show that the commonly used returns and factors are, for the most part, too noisy for us to conclude that one model is superior to the other models in terms of Hansen-Jagannathan distance. Specifically, there is little evidence that conditional and intertemporal capital asset pricing model (CAPM)-type specifications outperform the simple unconditional CAPM. In addition, we show that many of the macroeconomic factors commonly used in the literature are no longer priced once potential model misspecification is taken into account.

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