Notes on dynamic factor pricing models

These notes discuss three aspects of dynamic factor pricing (i.e., APT) models. First, the diversifiable component of returns is unpredictable in a no-arbitrage world. Second, conditional factor loadings or betas have an unconditional factor structure when returns follow an unconditional factor structure, which provides a link between conditional and unconditional factor pricing models. Third, the estimation of dynamic factor pricing models is easily simplified in large cross sections when returns follow an unconditional factor structure. These results aid in the interpretation of existing applications and identify some of the issues in the formulation and estimation of dynamic factor pricing models.     

The conditional CAPM does not explain asset-pricing anomalies

Recent studies suggest that the conditional CAPM holds, period by period, and that time-variation in risk and expected returns can explain why the unconditional CAPM fails. In contrast, we argue that variation in betas and the equity premium would have to be implausibly large to explain important asset-pricing anomalies like momentum and the value premium. We also provide a simple new test of the conditional CAPM using direct estimates of conditional alphas and betas from short-window regressions, avoiding the need to specify conditioning information. The tests show that the conditional CAPM performs nearly as poorly as the unconditional CAPM, consistent with our analytical results.     

INTERTEMPORAL ASSET PRICING WITHOUT CONSUMPTION DATA: EMPIRICAL TESTS

In this paper I conduct tests of an intertemporal asset pricing model using variables that forecast stock returns as the risk factors. I document that the forecasting variables are priced so that expected excess returns are related to their conditional covariances with the forecasting variables. The variability in the covariance risk fails to explain the cross-sectional and time-series variation in expected stock returns. Evidence rejects restrictions on the prices of covariance risk imposed by the model with constant volatilities. I also find that an extended model that allows time-varying conditional volatilities is misspecified.     

Sources of risk and expected returns in global equity markets

This paper empirically examines multifactor asset pricing models for the returns and expected returns on eighteen national equity markets. The factors are chosen to measure global economic risks. Although previous studies do not reject the unconditional mean variance efficiency of a world market portfolio, our evidence indicates that the tests are low in power, and the world market betas do not provide a good explanation of cross-sectional differences in average returns. Multiple beta models provide an improved explanation of the equity returns.     

The specification of conditional expectations

This paper explores different specifications of conditional expectations. The most common specification, linear least squares, is contrasted with nonparametric techniques that make no assumptions about the distribution of the data. Nonparametric regression is successful in capturing some nonlinearities in financial data, in particular, asymmetric responses of security returns to the direction and magnitude of market returns. The technique is ideally suited for empirically modeling returns of securities that have complicated embedded options. The conditional mean and variance of the NYSE market return are also examined. Forecasts of market returns are not improved with the nonparametric techniques which suggests that linear conditional expectations are a reasonable approximation in conditional asset pricing research. However, the linear model produces a disturbing number of negative expected excess returns. My results also indicate that the relation between the conditional mean and variance depends on the specification of the conditional variance. Furthermore, a linear model relating mean to variance is rejected and these tests are not sensitive to the expectation generating mechanism nor the conditioning information. Rejections are driven by the distinct countercyclical variation in the ratio of the conditional mean to variance.     

Integrating Factor Models

This paper develops a comprehensive framework to address uncertainty about the correct factor model. Asset pricing inferences draw on a composite model that integrates over competing factor models weighted by posterior probabilities. Evidence shows that unconditional models record near-zero probabilities, while postearnings announcement drift, quality-minus-junk, and intermediary capital are potent factors in conditional asset pricing. Out-of-sample, the integrated model performs well, tilting away from subsequently underperforming factors. Model uncertainty makes equities appear considerably riskier, while model disagreement about expected returns spikes during crash episodes. Disagreement spans all return components involving mispricing, factor loadings, and risk premia.     

ON THE RATIONALITY OF COMMON STOCK RETURN VOLATILITY

This paper derives the relationship between the population unconditional variance of common stock returns and the variance of expected returns conditional on a well-specified information set. As a consequence, a lower bound is obtained for the variance of common stock returns. The sample counterpart of this bound is then empirically tested against the sample variance of returns. The paper's main conclusion can be stated as follows: the observed volatility of real (inflation-adjusted) common stock returns is not “irrationally” large. The paper admits of this conclusion because the point estimate of the lower-bound variance derived in this model is actually larger than the point estimate of common stock return volatility. However, since these point estimates are found to have a statistically insignificant difference, equality of the two variances cannot be ruled out. Hence, “rationality” of common stock returns—as implied by a utility-based valuation conditional on a specified information set—cannot be rejected.     

Conditional Skewness in Asset Pricing Tests

If asset returns have systematic skewness, expected returns should include rewards for accepting this risk. We formalize this intuition with an asset pricing model that incorporates conditional skewness. Our results show that conditional skewness helps explain the cross-sectional variation of expected returns across assets and is significant even when factors based on size and book-to-market are included. Systematic skewness is economically important and commands a risk premium, on average, of 3.60 percent per year. Our results suggest that the momentum effect is related to systematic skewness. The low expected return momentum portfolios have higher skewness than high expected return portfolios.     

How Does Information Quality Affect Stock Returns?

Using a simple dynamic asset pricing model, this paper investigates the relationship between the precision of public information about economic growth and stock market returns. After fully characterizing expected returns and conditional volatility, I show that (i) higher precision of signals tends to increase the risk premium, (ii) when signals are imprecise the equity premium is bounded above independently of investors' risk aversion, (iii) return volatility is U-shaped with respect to investors' risk aversion, and (iv) the relationship between conditional expected returns and conditional variance is ambiguous.     

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.     

Does Money Explain Asset Returns? Theory and Empirical Analysis

A cash-in-advance model of a monetary economy is used to derive a money-based CAPM (M-CAPM), which allows us to implement tests of asset pricing restrictions without consumption data. A test as in Fama and MacBeth of the model suggests that the money betas have some explanatory power for the cross-sectional variation of expected returns; however, the model is rejected using conditional information. Consistent with our predictions, estimates of the curvature parameter are lower than those of the consumption CAPM (C-CAPM) and pricing errors of the M-CAPM tend to be smaller than those of the C-CAPM.     

What explains the investment growth anomaly?

We examine if an existing asset pricing model in an unconditional or conditional setting can explain the investment growth anomaly, as represented by higher returns on stocks of the firms with lower growth in capital expenditures. Our results indicate that the conditional Fama–French 3-factor model that allows factor loadings to be time-varying and further linked to firm-level characteristics and the business cycle can explain the anomaly.     

Time-varying market,interest rate,and exchange rate risk premia in the US commercial bank stock returns

This paper examines the role of market, interest rate, and exchange rate risks in pricing a sample of the US Commercial Bank stocks by developing and estimating a multi-factor model under both unconditional and conditional frameworks. Three different econometric methodologies are used to conduct the estimations and testing. Estimations based on nonlinear seemingly unrelated regression (NLSUR) via GMM approach indicate that interest rate risk is the only priced factor in the unconditional three-factor model. However, based on ‘pricing kernel’ approach by Dumas and Solnik [(1995). J. Finance 50, 445–479], strong evidence of exchange rate risk is found in both large bank and regional bank stocks in the conditional three-factor model with time-varying risk prices. Finally, estimations based on the multivariate GARCH in mean (MGARCH-M) approach where both conditional first and second moments of bank portfolio returns and risk factors are estimated simultaneously show strong evidence of time-varying interest rate and exchange rate risk premia and weak evidence of time-varying world market risk premium for all three bank portfolios, namely those of Money Center bank, Large bank, and Regional bank.     

Exact distribution-free tests of mean-variance efficiency

This paper develops exact distribution-free tests of unconditional mean-variance efficiency. These new tests allow for unknown forms of non-normalities, conditional heteroskedasticity, and other non-linear temporal dependencies among the absolute values of the error terms in the asset pricing model. Exactness here rests on the assumption that the joint temporal error density is symmetric around zero. This still leaves open the possibility of return distribution asymmetry via coskewness with the benchmark portfolio. A simulation study shows that the new tests have very good power relative to that of many commonly used tests. The inference procedures developed are further illustrated by tests of the mean-variance efficiency of a market index using a 42-year sample of monthly returns on ten U.S. equity portfolios.     

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.     

The Correlation Structure of Unexpected Returns in U.S. Equities

We examine the correlations between unexpected market moves and unexpected equity portfolio moves conditional on market performance. We derive unexpected returns from a two-stage regime switching model. The model allows for time-varying expected returns where the market portfolio alone dictates the regime switching process. Portfolios exhibit a natural hedge where correlations during extreme unexpected market downturns are generally negative. During unexpected market upswings, correlations increase. Using the unconditional analysis would lead to overhedging during market downturns and underhedging during market upswings. The adjustments to the unconditional hedging strategy conditional on extreme market movements frequently exceed ±10%.     

Consumption habit and international stock returns

We use the consumption-based asset pricing model with habit formation to study the predictability and cross-section of returns from the international equity markets. We find that the predictability of returns from many developed countries' equity markets is explained in part by changing prices of risks associated with consumption relative to habit at the world as well as local levels. We also provide an exploratory investigation of the cross-sectional implications of the model under the complete world market integration hypothesis and find that the model performs mildly better than the traditional consumption-based model, the unconditional and conditional world CAPMs and a three-factor international asset pricing model.     

Size,value and momentum in stock returns: evidence from India

This paper examines the effects of size, value and momentum on the cross-sectional relation between expected returns and risk in the Indian stock market. We find that the conditional Carhart four-factor model empirically describes the variation of cross-section of return better than the unconditional model. When size, book-to-market and momentum effects are controlled in the conditional model, the positive relation of market beta, book-to-market and momentum with expected returns remains economically and statistically significant. However, this evidence is found to be subject to characteristics of test portfolios. The expected returns are sensitive to changes in predictive macroeconomic variables.     

Are the Latent Variables in Time-Varying Expected Returns Compensation for Consumption Risk?

Multibeta asset pricing models are examined using proxies for economic state variables in a framework which exploits time-varying expected returns to estimate conditional betas. Examples include multiple consumption-beta models and models where asset returns proxy for the state variables. When the state variables are not specified, the tests indicate two or three time-varying expected risk premiums in the sample of quarterly asset returns. Conditional betas relative to consumption generate less striking evidence against the model than betas relative to asset returns, but both the consumption and the market variables fail to proxy for the state variables.     

Varying the VaR for unconditional and conditional environments

Accurate forecasting of risk is the key to successful risk management techniques. Using the largest stock index futures from 12 European bourses, this paper presents VaR measures based on their unconditional and conditional distributions for single and multi-period settings. These measures underpinned by extreme value theory are statistically robust explicitly allowing for fat-tailed densities. Conditional tail estimates accounting for volatility clustering are obtained by adjusting the unconditional extreme value procedure with GARCH filtered returns. The conditional modelling results in iid returns allowing for the use of a simple and efficient multi-period extreme value scaling law. The paper examines the properties of these distinct conditional and unconditional trading models. The paper finds that the biases inherent in unconditional single and multi-period estimates assuming normality extend to the conditional setting.