Asset returns and economic risk

The capital asset pricing model (CAPM), favored by financial researchers and practitioners fifteen years ago, holds that the extra return on a risky asset comes from bearing market risk only. But newer evidence supports the intertemporal CAPM (I-CAPM) theory (Merton 1973), which suggests that the premium on any risky asset is related not only to market risk but also to additional economic variables. ; This article reviews and interprets recent advances in the asset pricing literature. The study seeks to shed light on the sources of economic risk that investors should track and hedge against and the sign of the risk premia commanded by economic and financial risks. ; The author empirically measures the impact of prespecified financial and economic variables on the risk-return trade-off by looking at how they affect (or predict) the mean and the variance of asset returns. The analysis shows that variables such as the market portfolio, the term structure, the default premium, and the consumption-aggregate wealth ratio positively affect average asset returns and command positive risk premia while the inflation portfolio negatively affects returns and commands a negative premium. ; The article also provides extensive evidence of time variation in economic risk premia, showing that expected compensation for bearing different sorts of risk is larger at some times and smaller at others depending on economic conditions.Capital assets pricing model ; Risk

The exact distribution of the Hansen-Jagannathan bound

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.

Asset-pricing models and economic risk premia: a decomposition

The risk premia assigned to economic (nontraded) 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 nontraded components of the candidate pricing kernel of a given model and the factors; and (iii) (minus) the mispricing 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 nontraded 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 nontraded factors. We conclude that the economic risk premia assigned by multi-beta models with nontraded factors can be very unreliable. Conversely, the risk premia on maximum-correlation portfolios provide more reliable indications of whether a nontraded risk factor is priced. These results hold for both the constant and the time-varying components of the factor risk premia.

Minimum-variance kernels, economic risk premia, and tests of multi-beta models

This paper uses minimum-variance (MV) admissible kernels to estimate risk premia associated with economic risk variables and to test multi-beta models. Estimating risk premia using MV kernels is appealing because it avoids the need to 1) identify all relevant sources of risk and 2) assume a linear factor model for asset returns. Testing multi-beta models in terms of restricted MV kernels has the advantage that 1) the candidate kernel has the smallest volatility and 2) test statistics are easy to interpret in terms of Sharpe ratios. The authors find that several economic variables command significant risk premia and that the signs of the premia mostly correspond to the effect that these variables have on the risk-return trade-off, consistent with the implications of the intertemporal capital asset pricing model (I-CAPM). They also find that the MV kernel implied by the I-CAPM, while formally rejected by the data, consistently outperforms a pricing kernel based on the size and book-to-market factors of Fama and French (1993).Risk ; Asset pricing ; Econometric models

Specification tests of asset pricing models using excess returns

We discuss the impact of different formulations of asset pricing models on the outcome of specification tests that are performed using excess returns. It is generally believed that when only excess returns are used for testing asset pricing models, the mean of the stochastic discount factor (SDF) does not matter. We show that the mean of the candidate SDF is only irrelevant when the model is correct. When the model is misspecified, the mean of the SDF can be a very important determinant of the specification test statistic, and it also heavily influences the relative rankings of competing asset pricing models. We point out that the popular way of specifying the SDF as a linear function of the factors is problematic because the specification test statistic is not invariant to an affine transformation of the factors and 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 only excess returns are used. 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. We provide 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. Finally, we propose a simple methodology for computing the standard errors of the estimated SDF parameters that are robust to model misspecification.

Model comparison using the Hansen-Jagannathan distance

Although it is of interest to empirical researchers to test whether or not a particular asset-pricing model is true, a more useful task 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 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 are nested or nonnested. 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 the same data as in Hodrick and Zhang (2001), we show that the commonly used returns and factors are, for the most part, too noisy to conclude that one model is superior to the other models in terms of Hansen-Jagannathan distance. 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.

Mimicking portfolios, economic risk premia, and tests of multi-beta models

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.

Playing the field: Geomagnetic storms and international stock markets

This paper documents the impact of geomagnetic storms (GMS) on world and country-specific stock market returns. For the world index and for most of the international indices in our sample, we find that the previous week's unusually high levels of geomagnetic activity have a negative, statistically and economically significant impact on today's stock returns. Our results are consistent with psychological theories of "misattribution of mood," since GMS have been found to negatively affect people's judgment and behavior.Stock market

Financial market frictions

Market frictions, which exist even in efficient markets and change over time, impede trade but also offer profit opportunities. To provide a framework for understanding market frictions, the authors classify frictions into five categories.Financial markets

The price of inflation and foreign exchange risk in international equity markets

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.Hedging (Finance) ; Asset pricing ; Foreign exchange ; Risk