Government Bond Returns,Measurement of Interest Rate Risk,and the Arbitrage Pricing Theory

Empirical tests are reported for Ross' arbitrage pricing theory using monthly data for U.S. Treasury securities during the 1960–1979 period. We find that mean returns on bond portfolios are linearly related to at least two factor loadings. Multivariate test results, however, are not consistent with the APT. Our sample data in the U.S. Treasury securities market are also not consistent with either version of the CAPM. One-month-ahead forecasts of excess returns using factor-generating models are compared with corresponding naive predictions or predictions using the “market model” with various market portfolios.     

An Asset-Pricing Theory Unifying the CAPM and APT

This study shows that the competitive-equilibrium version of the APT may be extended to develop an exact model if idiosyncratic risks obey the Ross separating distribution. The results indicate that one only need add the market portfolio as an extra factor to the factor model in order to obtain an exact asset-pricing relation. Thus, this study presents an extension and integration of the CAPM and APT. The “empirical” APT is also generalized to allow for some factors to be omitted from the econometric model employed to test the theory. The developed model is extremely robust and may be reduced to the CAPM or expanded to approximate Ross's APT depending upon the number of omitted factors. Further, the importance of the market portfolio is shown to be a monotonic increasing function of the number of omitted factors. Finally, the study demonstrates that, in a finite economy, the pricing-error bound of the Ross APT in a correlated-residuals factor structure is an increasing function of the absolute value of market-residual beta, rather than the weight of the asset in the market portfolio as is the case of uncorrelated factor residuals. However, under the normality assumption, the pricing error becomes an extra component related to the market-portfolio factor, and the exact asset-pricing relation is once again obtained.     

Cross‐sectional Tests of Conditional Asset Pricing Models: Evidence from the German Stock Market

We study the performance of conditional asset pricing models and multifactor models in explaining the German cross‐section of stock returns. We focus on several variables, which (according to previous research) are associated with market expectations on future market excess returns or business cycle conditions. Our results suggest that the empirical performance of the Capital Asset Pricing Model (CAPM) can be improved when allowing for time‐varying parameters of the stochastic discount factor. A conditional CAPM using the term spread explains the returns on our size and book‐to‐market sorted portfolios about as well as the Fama‐French three‐factor model and performs best in terms of the Hansen‐Jagannathan distance. Structural break tests do not necessarily indicate parameter instability of conditional model specifications. Another major finding of the paper is that the Fama‐French model – despite its generally good cross‐sectional performance – is subject to model instability. Unconditional models, however, do a better job than conditional ones at capturing time‐series predictability of the test portfolio returns.     

Does It Pay to Bet Against Beta? On the Conditional Performance of the Beta Anomaly

Prior studies find that a strategy that buys high‐beta stocks and sells low‐beta stocks has a significantly negative unconditional capital asset pricing model (CAPM) alpha, such that it appears to pay to “bet against beta.” We show, however, that the conditional beta for the high‐minus‐low beta portfolio covaries negatively with the equity premium and positively with market volatility. As a result, the unconditional alpha is a downward‐biased estimate of the true alpha. We model the conditional market risk for beta‐sorted portfolios using instrumental variables methods and find that the conditional CAPM resolves the beta anomaly.     

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.     

The effect of time-varying covariances on asset risk premia

In this article we examine an intertemporal capital asset pricing model (CAPM) that allows for time-varying conditional covariances that are assumed to follow a multivariate integrated generalized autoregressive conditional heteroscedastic (IGARCH) process. The resulting pricing equation includes idiosyncratic risk premia in addition to the usual market beta. Empirical analysis based on ten size and ten industry portfolios reveals significant idiosyncratic premia for most portfolios. Overall, we reject the static CAPM in favor of the intertemporal CAPM.     

The Arbitrage Pricing Theory: Is it Testable?

This paper challenges the view that the Arbitrage Pricing Theory (APT) is inherently more susceptible to empirical verification than the Capital Asset Pricing Model (CAPM). The usual formulation of the testable implications of the APT is shown to be inadequate, as it precludes the very expected return differentials which the theory attempts to explain. A recent competitive-equilibrium extension of the APT may be testable in principle. In order to implement such a test, however, observation of the return on the true market portfolio appears to be necessary.     

Some Empirical Tests of the Theory of Arbitrage Pricing

We estimate the parameters of Ross's Arbitrage Pricing Theory (APT). Using daily return data during the 1963–78 period, we compare the evidence on the APT and the Capital Asset Pricing Model (CAPM) as implemented by market indices and find that the APT performs well. The theory is further supported in that estimated expected returns depend on estimated factor loadings, and variables such as own variance and firm size do not contribute additional explanatory power to that of the factor loadings.     

Currency risk premia and uncovered interest parity in the International CAPM

Zero-investment uncovered interest parity (UIP) portfolio positions provide perfect factor-mimicking portfolios for currency risk in the International CAPM context. Their returns are the currency risk premia. Since the UIP positions on average provide low returns, the currency risk premia must be low so that currency risk appears not to be priced in an unconditional model. However, previous research has shown that UIP returns are predictable and may be quite substantial conditionally. We use this observation to generate a specific conditional version of the International CAPM. A GMM approach shows that the conditional model performs well, while the unconditional International CAPM is (marginally) rejected. The paper thus argues that previous rejections of the International CAPM stem from the fact that currency risk premia are by nature low over extended periods of time and do not provide evidence against the International CAPM.     

APT VS. CAPM ESTIMATES OF THE RETURN-GENERATING FUNCTION PARAMETERS FOR REGULATED PUBLIC UTILITIES

In public utility rate hearings, there are extensive arguments concerning the most appropriate model of the return-generating function. Bower, Bower, and Logue (1984) suggest that the APT is superior to the CAPM, but their results have troublesome ranking differences between the two models when applied to returns from electric versus natural gas utilities. The purposes of this paper are to develop forward estimates of the parameters for both of these models applied to five different utility portfolios of electric and natural gas companies at a point in time, and to test whether these estimates are valid during a subsequent or future period. Also, forecasting errors for each model are compared to determine which model is best and to ascertain if there are any ranking conflicts. There are no ranking conflicts with the models as the market model consistently underestimates the actual return. Thus, the analysis suggests that the arbitrage model is a superior representation of the return-generating process of these utilities.     

Some Tests of APT Mispricing Using Mimicking Portfolios

Cross-sectional and time-series tests using mimicking portfolios are used to assess the exactness of the APT with(out) a residual market factor. The first factor seems to be sufficient to span the efficient set, whether the model is estimated using (un)conditional variance-covariance matrices that are (un)adjusted for nonsynchronous trading. Although the conditional standard deviations of the mimicking portfolios significantly explain the time-variability of security volatilities, the residuals of the mean equation still exhibit heteroskedasticity. Similar results are obtained for portfolios of CAPM-betaranked securities, and for randomly selected individual securities.     

Capital Asset Pricing Model and Stochastic Volatility: A Case Study of India

The existing literature demonstrates that under a general equilibrium model, the performance of the Capital Asset Pricing Model (CAPM) can be improved significantly by using conditional consumption and market return volatilities as factors. This article tests the validity of these factors explaining stock return differences using a less developed country (India) as a case study. While the earlier studies used panel data to test CAPM, we use portfolios sorted by size and book-to-market equity (BE/ME) ratio. We found that conditional volatility has a limited effect on firms with large capitalization but a significant impact on small-growth and small-value firms.     

Portfolio performance of linear SDF models: an out-of-sample assessment

We evaluate linear stochastic discount factor models using an ex-post portfolio metric: the realized out-of-sample Sharpe ratio of mean–variance portfolios backed by alternative linear factor models. Using a sample of monthly US portfolio returns spanning the period 1968–2016, we find evidence that multifactor linear models have better empirical properties than the CAPM, not only when the cross-section of expected returns is evaluated in-sample, but also when they are used to inform one-month ahead portfolio selection. When we compare portfolios associated to multifactor models with mean–variance decisions implied by the single-factor CAPM, we document statistically significant differences in Sharpe ratios of up to 10 percent. Linear multifactor models that provide the best in-sample fit also yield the highest realized Sharpe ratios.     

Learning about beta: Time-varying factor loadings, expected returns, and the conditional CAPM

We amend the conditional CAPM to allow for unobservable long-run changes in risk factor loadings. In this environment, investors rationally “learn” the long-run level of factor loadings from the observation of realized returns. As a consequence of this assumption, we model conditional betas using the Kalman filter. Because of its focus on low-frequency variation in betas, our approach circumvents recent criticisms of the conditional CAPM. When tested on portfolios sorted by size and book-to-market, our learning-augmented conditional CAPM passes the specification tests.     

Time-varying risk The case of the American computer industry

A bivariate GARCH-in-mean model for individual stock returns and the market portfolio is designed to model volatility and to test the conditional Capital Asset Pricing Model versus the conditional Residual Risk Model. We find that a univariate model of volatility for individual stock returns is misspecified. A joint modelling of the market return and the individual stock return shows that a major force driving the conditional variances of individual stocks is the history contained in the market return variance. We find that a conditional residual risk model, where the variance of the individual stock return is used to explain expected returns, is preferred to a conditional CAPM. We propose a partial ordering of securities according to their market risk using first and second order dominance criteria.     

Testing conditional factor models

Using nonparametric techniques, we develop a methodology for estimating and testing conditional alphas and betas and long-run alphas and betas, which are the averages of conditional alphas and betas, respectively, across time. The estimators and tests can be implemented for a single asset or jointly across portfolios. The traditional Gibbons, Ross, and Shanken (1989) test arises as a special case of no time variation in the alphas and factor loadings and homoskedasticity. As applications of the methodology, we estimate conditional CAPM and multifactor models on book-to-market and momentum decile portfolios. We reject the null that long-run alphas are equal to zero even though there is substantial variation in the conditional factor loadings of these portfolios.     

The numeraire portfolio: a new perspective on financial theory

The numeraire portfolio, also called the optimal growth portfolio, allows simple derivations of the main results of financial theory. The prices of self financing portfolios, when the optimal growth portfolio is the numeraire, are martingales in the ‘true’ (historical) probability. Given the dynamics of the traded securities, the composition of the numeraire portfolio as well as its value are easily computable. Among its numerous properties, the numeraire portfolio is instantaneously mean variance efficient. This key feature allows a simple derivation of standard continuous time CAPM, CCAPM, APT and contingent claim pricing. Moreover, since the Radon-Nikodym derivatives of the usual martingale measures are very simple functions of the numeraire portfolio, the latter provides a convenient link between the standard Capital Market Theory a la Merton and the probabilistic approach a la Harrison-Kreps-Pliska.     

Cashflow news,the value premium and an asset pricing view on European stock market integration

The decomposition of national CAPM market betas of European countries’ value and growth portfolio returns into cashflow and discount rate news driven components reveals that i) high average returns on value portfolios are associated with disproportionately high sensitivity to national cashflow news which corroborates recent evidence for the U.S. and ii) two-beta variants of national CAPMs capture the cross-sectional dispersion in European stock returns. The latter finding is suggestive of relatively well integrated stock markets among the core European countries and reflects basic asset pricing theory. One (national) discount factor should price any (international) asset.     

CAPM over the long run: 1926–2001

A conditional one-factor model can account for the spread in the average returns of portfolios sorted by book-to-market ratios over the long run from 1926 to 2001. In contrast, earlier studies document strong evidence of a book-to-market effect using OLS regressions over post-1963 data. However, the betas of portfolios sorted by book-to-market ratios vary over time and in the presence of time-varying factor loadings, OLS inference produces inconsistent estimates of conditional alphas and betas. We show that under a conditional CAPM with time-varying betas, predictable market risk premia, and stochastic systematic volatility, there is little evidence that the conditional alpha for a book-to-market trading strategy is different from zero.     

Asset Pricing with Conditioning Information: A New Test

This paper presents a new test of conditional versions of the Sharpe-Lintner CAPM, the Jagannathan and Wang (1996) extension of the CAPM, and the Fama and French (1993) three-factor model. The test is based on a general nonparametric methodology that avoids functional form misspecification of betas, risk premia, and the stochastic discount factor. Our results provide a novel view of empirical performance of these models. In particular, we find that a nonparametric version of the Fama and French model performs well, even when challenged by momentum portfolios.