Test Assets Research Articles

A Practical Guide to Volatility Forecasting through Calm and Storm

We present a volatility forecasting comparative study within the ARCH class of models. Our goal is to identify successful predictive models over multiple horizons and to investigate how predictive ability is influenced by choices for estimation window length, innovation distribution, and frequency of parameter re-estimation. Test assets include a range of domestic and international equity indices and exchange rates. We find that model rankings are insensitive to forecast horizon and suggestions for estimation best practices emerge. While our main sample spans 1990-2008, we take advantage of the near-record surge in volatility during the last half of 2008 to ask if forecasting models or best practices break down during periods of turmoil. Surprisingly, we find that volatility during the 2008 crisis was well approximated by predictions one-day ahead, and should have been within risk managers' 1% confidence intervals up to one month ahead.

Pricing of liquidity risk: empirical evidence from Finland

This study investigates the pricing of liquidity risk in stock market using conditional Asset Pricing Models (APMs). The estimation is conducted in the Generalized Method of Moment (GMM) framework with a price of risk specification. The main interest is to find out whether liquidity is priced as a systematic source of risk or as an asset-specific characteristic. Tests are conducted on the Finnish stock market known for wide variations in liquidity. The sample period is from 1987 to 2004, and size portfolios are used as test assets. The results indicate that illiquidity is priced as a market-wide systematic risk and not as an asset-specific risk.

Asset pricing with a reference level of consumption: New evidence from the cross-section of stock returns

This paper presents an empirical evaluation of recently proposed asset pricing models which extend the standard preference specification by a reference level of consumption. We motivate an alternative model that accounts for the return on human capital as a determinant of the reference level. Our analysis is based on a broad cross-section of test assets, which provides a level playing field for a comparison to established benchmark models. The reference level model extended by human capital does a good job in explaining size and value premia. Estimated on Fama and French's size and book-to-market sorted portfolios, it outperforms Lettau and Ludvigson's scaled CCAPM and delivers average pricing errors comparable to the Fama–French three-factor model.

A Conditional Asset Pricing Model with the Optimal Orthogonal Portfolio

This paper develops a conditional asset pricing model with latent factors, based on the optimal orthogonal portfolio approach. We construct a factor portfolio that embodies all the latent factors important for pricing a given set of test assets. The out-of-sample performance of this portfolio is evaluated against several conventional factors, using both cross-sectional and time-series regression approaches. Our results show that our suggested factor outperforms all the predefined factors regarding the contribution in return variations as well as the pricing ability. Our suggested methodology may have important applications in risk management, portfolio selection and performance evaluation.

Consumption Volatility Risk

We show that time-variation in macroeconomic uncertainty affects asset prices. Consumption volatility is a negatively priced source of risk for a wide variety of test assets. At the firm level, exposure to consumption volatility risk predicts future returns, generating a spread across quintile portfolios in excess of 7% annually. This premium is explained by cross-sectional differences in the sensitivity of dividend volatility to consumption volatility. Stocks with volatile cash flows in uncertain aggregate times require higher expected returns.

A Note on the Estimation of Asset Pricing Models Using Simple Regression Betas

Working Paper 2009-12 March 2009 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 asset 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. JEL classification: G12 Key words: two-pass cross-sectional regressions, risk premia, model misspecification, simple regression betas, multivariate betas Introduction In the empirical asset pricing literature, the popular two-pass cross-sectional regression (CSR) methodology developed by Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973) is often used for estimating risk premia and testing pricing models that relate expected security returns to security betas on economic factors (beta pricing models). Although there are many variations of this two-pass methodology, its basic approach always involves two steps. In the first pass, the betas of the test assets are estimated using the usual ordinary least squares (OLS) time series regression of returns on some common factors. In the second pass, the returns on test assets are regressed on the estimated betas obtained from the first pass. By running this second-pass CSR on a period-by-period basis, we obtain time series of the intercept and the slope coefficients. The average values of the intercept and the slope coefficients are then used as estimates of the zero-beta rate and the risk premia. Usually, asset betas are defined as the OLS slope coefficients in the multiple regression of asset returns on factors and are referred to as multiple regression or multivariate betas. However, there is a potential issue with the use of multiple regression betas: unless the factors are uncorrelated, the beta of an asset with respect to a particular factor in general depends on what other factors are included in the first-pass time series OLS regression. As a result, a factor can possess additional explanatory power for the cross-sectional differences in expected returns but yet have a zero risk premium in a model with multiple factors. This makes it problematic to use the risk premium of a factor for the purpose of model selection. To overcome this problem, Chen, Roll, and Ross (1986) and Jagannathan and Wang (1996, 1998) define the beta of an asset with respect to a given factor as the OLS slope coefficient in a simple regression of its return on the factor. These betas are normally referred to as simple regression or univariate betas. In models with simple regression betas, adding or deleting a factor in a model will not change the values of the betas corresponding to the other factors and selecting models based on risk premia becomes more meaningful. (1) Jagannathan and Wang (1998) present an asymptotic theory for models with simple regression betas. (2) However, their asymptotic results rest on the assumption that expected returns are exactly linear in the betas, i.e., the beta pricing model is correctly specified. It is difficult to justify this assumption when estimating the zero-beta rate and risk premia parameters for many different models because some (if not all) of the models are bound to be misspecified. Since asset pricing models are, at best, approximations of reality, it is inevitable that we will often, knowingly or unknowingly (since asset pricing tests have limited power), estimate an expected return relation that departs from exact linearity in the betas. …

Long-Horizon Consumption Risk and the Cross-Section of Returns: New Tests and International Evidence

This paper investigates whether measuring consumption risk over long horizons can improve the empirical performance of the Consumption CAPM for size and value premia in international stock markets (US, UK, and Germany). In order to account for commonalities in size and book-tomarket sorted portfolios, we also include industry portfolios in our set of test assets. Our results show that, contrary to the findings of Parker and Julliard (2005), the model falls short of providing an accurate description of the cross-section of returns under our modified empirical approach. At the same time, however, measuring consumption risk over longer horizons typically yields lower risk-aversion estimates. Thus, our results suggest that more plausible parameter estimates - as opposed to lower pricing errors - can be regarded as the main achievement of the long-horizon Consumption CAPM.

Global Asset Pricing: Is There a Role for Long-Run Consumption Risk?

We estimate long-run consumption-based asset pricing models using a comprehensive set of international test assets, including broad equity market portfolios, international value/growth portfolios, and international bond portfolios. We find that differences in returns across assets within a country are sometimes (and most prominently for the U.S.) better captured by the assets' exposure to long-run consumption risk as opposed to their exposure to one-period changes in consumption (the canonical consumption CAPM). Across countries, however, exposure to long-run consumption risk does not provide a better fit than the canonical consumption CAPM. Thus, when characterizing the cross-country distribution of returns, long-run consumption risk does not seem to play any particular role, even if long-run risk is important for explaining the cross section of expected returns in the U.S. Furthermore, we show that consumption growth is more predictable over short to medium-run horizons than over longer horizons and that empirical evidence of a declining risk aversion parameter estimate in long-run risk models has to be interpreted with care.

EVALUATING THE ACCURACY OF FAMA-FRENCH MODEL VERSUS LIQUIDITY-BASED THREE-FACTOR MODELS IN FORECASTING PORTFOLIO RETURNS

This paper evaluates the forecasting accuracy of the Fama-French three-factor model versus two liquidity-based three-factor models, referred as SiLiq and DiLiq, that have been developed as potential improvements on the Fama-French model. The study uses the period of 1987:01 to 2000:12 for estimation and sets the period of 2001:01 to 2004:12 as the forecast sample. The test assets are 27 portfolios nine each formed from the intersections of the following firm characteristics: (i) size and book-to-market ratio (B/M), (ii) size and share turnover (TURN), and (iii) B/M and TURN. Once the models are estimated using multiple time-series regressions, the forecasting accuracy of the competing models are evaluated using three error metrics; mean absolute errors (MAE), mean absolute percentage errors (MAPE), and Theil’s U statistics. Our results suggest that in predicting the Malaysian stock returns, the Fama-French model is dominated by its liquiditybased model counterparts, specifically, the DiLiq model.

News and the cross-section of expected corporate bond returns

We study the cross-section of expected corporate bond returns using an inter-temporal CAPM (ICAPM) with three-factors: innovations in future excess bond returns, future real interest rates and future expected inflation. Our test assets are a broad range of corporate bond market index portfolios. We find that two factors – innovations about future inflation and innovations about future real interest rates – explain the cross-section of expected corporate bond returns in our sample. Our model provides an alternative to the ad hoc risk factor models used, for example, in evaluating the performance of bond mutual funds.

Long-horizon consumption risk and the cross-section of returns: new tests and international evidence

This paper investigates whether measuring consumption risk over long horizons can improve the empirical performance of the consumption-based capital asset pricing model (CCAPM) for size and value premia in international stock markets (USA, UK, and Germany). In order to account for commonalities in size and book-to-market sorted portfolios, we also include industry portfolios in our set of test assets. Our results show that, contrary to the findings of Parker and Julliard [2005. Consumption risk and the cross- section of expected returns. Journal of Political Economy 113, no. 1: 185–222], the model falls short of providing an accurate description of the cross-section of returns under our modified empirical approach. At the same time, however, measuring consumption risk over longer horizons typically yields lower risk-aversion estimates. Thus, our results suggest that more plausible parameter estimates – as opposed to lower pricing errors – can be regarded as the main achievement of the long-horizon CCAPM.

News and the Cross-Section of Expected Corporate Bond Returns

We study the cross-section of expected corporate bond returns using an inter-temporal CAPM (ICAPM) with three factors: innovations in future excess bond returns, future real interest rates and future expected inflation. Our test assets are a broad range of corporate bond market index portfolios. We find that two factors - innovations about future inflation and innovations about future real interest rates - explain the cross-section of expected corporate bond returns in our sample. Our model provides an alternative to the ad hoc risk factor models used, for example, in evaluating the performance of bond mutual funds.

Evaluating Asset Pricing Models Using the Second Hansen-Jagannathan Distance

We develop a systematic approach for evaluating asset pricing models based on the second Hansen-Jagannathan distance (HJD), which requires a good asset pricing model to not only have small pricing errors but also be arbitrage free. Our approach includes a specification test and a sequence of model selection procedures for non-nested, overlapping, and nested models. While the former can test whether a given model is correctly specified, the latter can compare relative performances of potentially misspecified models. Our methods are more powerful than existing ones in (i) detecting misspecified models that have small pricing errors but are not arbitrage free; and (ii) differentiating models that have similar pricing errors of a given set of test assets. Simulation studies show that our tests have reasonably good finite sample performances for typical sample sizes considered in the literature. Using the Fama-French size and book-to-market portfolios or hedge fund portfolios that exhibit option-like returns, we reach dramatically different conclusions on model performances based on our approach and existing methods.

Empirical Evaluation of Asset Pricing Models: Arbitrage and Pricing Errors in Contingent Claims

Hansen and Jagannathan (1997) have developed two measures of pricing errors for asset-pricing models: the maximum pricing error in all static portfolios of the test assets and the maximum pricing error in all contingent claims of the assets. In this paper, we develop simulation-based Bayesian inference for these measures. While the literature reports that the time-varying extensions substantially reduce pricing errors of classic models on the standard test assets, our analysis shows that the reduction is much smaller based on the second measure. Those time-varying models have large pricing errors on the contingent claims of the test assets because their stochastic dis- count factors are often negative and admit arbitrage opportunities.

Long-Run Stockholder Consumption Risk and Asset Returns

We provide new evidence on the success of long-run risks in asset pricing by focusing on the risks borne by stockholders. Exploiting micro-level household consumption data, we show that long-run stockholder consumption risk better captures cross-sectional variation in average asset returns than aggregate or non-stockholder consumption risk, and provides more plausible economic magnitudes. We find that risk aversion estimates around 10 can match observed risk premia for the wealthiest stockholders across sets of test assets that include the 25 Fama and French size and value portfolios, the market portfolio, bond portfolios, and the entire cross-section of stocks.

Volatility Risk Premium, Risk Aversion and the Cross-Section of Stock Returns

We test if innovations in investor risk aversion are a priced factor in the stock market as is predicted by models incorporating habit formation in preferences. Our proxy for time-varying risk aversion is based on the volatility risk premium series constructed by Bollerslev et al. (2007). Time-series tests show that a mimicking portfolio tracking innovations in risk aversion partly captures the strong momentum effect in stock returns and produces only two significant alphas for 25 momentum portfolios. Furthermore, using 25 portfolios sorted on book-to-market and size as test assets in Fama-MacBeth regressions, our new factor together with the market factor explains 64% of the variation in average returns compared to 60% for the Fama-French three factor model. The new factor is generally significant with an estimated risk premium close to its time series mean also when industry portfolios and portfolios sorted on previous returns are included among the test assets.

Pervasive Liquidity Risk

While there is no equilibrium framework for defining liquidity risk per se, several plausible arguments suggest that liquidity risk is pervasive and thus may be priced. For example, market frictions increase the cost of hedging strategies requiring frequent portfolio rebalancing. Also, liquidity risk is likely to play a role whenever the market declines and investors are prevented from hedging via short positions. Using monthly return data from 1963-2000, and a broad set of test assets, we examine six candidate factor representations of aggregate liquidity risk, and test whether any one of these are priced. The results are interesting. First, with the surprising exception of the recent measure proposed by Pastor and Stambaugh (2001), liquidity factor shocks induce co-movements in individual stocks' liquidity measure (commonality in liquidity). The commonality is similar to that found in the extant literature (Chordia, Roll, and Subrahmanyam (2000)), which so far has been restricted to a single year of data. Second, again with the exception of the Pastor-Stambaugh measure, the liquidity factors receive statistically significant betas when added to the Fama-French model. Third, maximum-likelihood estimates of the risk premium are significant for the measure based on bid-ask spreads, contemporaneous turnover, as well as the Pastor-Stambaugh measure, which exploits price reversals following volume shocks. Overall, the simple-to-compute, low-minus-high turnover factor first proposed by Eckbo and Norli (2000) appears to do as least as well as the other factor measures.

A Stochastic Discount Factor Volatility Upper Bound in a Mean-Variance-Skewness World: No Good Deal Implications for Multi-Factor Models Estimates

Based on an upper bound on investors’ risk aversion, this paper derives a stochastic discount factor (SDF) volatility upper bound that limits attainable maximal Sharpe ratios. The bound and a no-arbitrage condition can be used to rule out “good deals” in incomplete markets without the need to observe investors’ optimal portfolios. The usefulness of these restrictions is shown by imposing them on multifactor models nonlinear in the market return. Empirical results show that, under the bound, the price of coskewness risk is much reduced and the annualized coskewness risk premium drops, in absolute value, from -2.6 to -1.6 percent. When the test assets include managed portfolios and option-like strategies, conditional versions of a model that nests the Fama and French (1996) 3-factor model and the quadratic market model either violate no-good deal restrictions or are not empirically admissible.

Asset Pricing with a Reference Level of Consumption: New Evidence from the Cross-Section of Stock Returns

This paper presents an empirical evaluation of recently proposed asset pricing models which extend the standard preference specification by a reference level of consumption. We motivate an alternative model that accounts for the return on human capital as a determinant of the reference level. Our analysis is based on a broad cross-section of test assets which provides a level playing field for a comparison to established benchmark models. The human capital extended reference level model does a good job in explaining size and value premia. Estimated on Fama and French's size and book-to-market sorted portfolios it outperforms Lettau and Ludvigson's scaled CCAPM and delivers average pricing errors comparable to the Fama-French three-factor model.

Can Risk-Based Theories Explain the Value Premium?*

This paper shows that some of the most prominent risk-based theories offered as explanation for the value premium are at odds with data. The models proposed by Fama and French (1993), Lettau and Ludvingson (2001), Campbell and Vuolteenaho (2004), and Yogo (2006) can capture the cross section of returns of portfolios sorted on book-to-market ratio and size, but not of portfolios sorted on book-to-market ratio and institutional ownership. These models generate economically large pricing errors in all the institutional ownership quintiles and each statistical test indicates that these pricing errors are significant. More generally, these results show that a minor alteration of the test assets can lead to a dramatically different answer regarding the validity of a given asset pricing model.