Testing Conditional Asset Pricing Models Using a Markov Chain Monte Carlo Approach

We use Markov Chain Monte Carlo (MCMC) methods for the parameter estimation and the testing of conditional asset pricing models. In contrast to traditional approaches, it is truly conditional because the assumption that time variation in betas is driven by a set of conditioning variables is not necessary. Moreover, the approach has exact finite sample properties and accounts for errors‐in‐variables. Using S&P 500 panel data, we analyse the empirical performance of the CAPM and the Fama and French (1993) three‐factor model. We find that time‐variation of betas in the CAPM and the time variation of the coefficients for the size factor (SMB) and the distress factor (HML) in the three‐factor model improve the empirical performance. Therefore, our findings are consistent with time variation of firm‐specific exposure to market risk, systematic credit risk and systematic size effects. However, a Bayesian model comparison trading off goodness of fit and model complexity indicates that the conditional CAPM performs best, followed by the conditional three‐factor model, the unconditional CAPM, and the unconditional three‐factor model.     

Conditional coskewness and asset pricing

We explore the empirical usefulness of conditional coskewness to explain the cross-section of equity returns. We find that coskewness is an important determinant of the returns to equity, and that the pricing relationship varies through time. In particular we find that when the conditional market skewness is positive investors are willing to sacrifice 7.87% annually per unit of gamma (a standardized measure of coskewness risk) while they only demand a premium of 1.80% when the market is negatively skewed. A similar picture emerges from the coskewness factor of Harvey and Siddique (Harvey, C., Siddique, A., 2000a. Conditional skewness in asset pricing models tests. Journal of Finance 65, 1263–1295.) (a portfolio that is long stocks with small coskewness with the market and short high coskewness stocks) which earns 5.00% annually when the market is positively skewed but only 2.81% when the market is negatively skewed. The conditional two-moment CAPM and a conditional Fama and French (Fama, E., French, K., 1992. The cross-section of expected returns. Journal of Finance 47,427465.) three-factor model are rejected, but a model which includes coskewness is not rejected by the data. The model also passes a structural break test which many existing asset pricing models fail.     

Evaluating asset pricing models in the Korean stock market

This paper evaluates and compares asset pricing models in the Korean stock market. The asset pricing models considered are the CAPM, APT-motivated models, the Consumption-based CAPM, Intertemporal CAPM-motivated models, and the Jagannathan and Wang conditional CAPM model. By using various test portfolios as well as individual stocks, we conduct time-series tests and cross-sectional regression tests based on individual t-tests, the joint F-tests, the Hansen and Jagannathan (1997) distance, and R-squares. Overall, the Fama and French (1993) five-factor model performs most satisfactorily among the asset pricing models considered in explaining the intertemporal and cross-sectional behavior of stock returns in Korea. The Fama and French (1993) three-factor model, the Chen et al. (2010) three-factor model, and the Campbell (1996) model are the next. The results indicate that the two bond portfolios, term spread and default spread, play an important role in explaining stock returns in Korea.     

Conditional Asset Pricing and Stock Market Anomalies in Europe

This study provides European evidence on the ability of static and dynamic specifications of the Fama‐French (1993) three‐factor model to price 25 size‐B/M portfolios. In contrast to US evidence, we detect a small‐growth premium and find that the size effect is still present in Europe. Furthermore, we document strong time variation in factor risk loadings. Incorporating these risk fluctuations in conditional specifications of the three‐factor model clearly improves its ability to explain time variation in expected returns. However, the model still fails to completely capture cross‐sectional variation in returns as it is unable to explain the momentum effect.     

A Comparison of the Efficacy of Liquidity,Momentum, Size and Book‐to‐Market Value Factors in Equity Pricing on a Heterogeneous Sample: Evidence from Asia

This paper compares the size and book‐to‐market value factors of Fama and French (1993) alongside Momentum of Jagadeesh and Titman ( 1993 ) with two Liu ( 2006 ) liquidity factors formed from 1 year rebalancing and 1 month rebalancing respectively. A heterogeneous and comprehensive sample of the top blue chip stocks of all national Asian equity markets with further differentiation undertaken between sub samples formed for Japan only and Asia excluding Japan for period January 2000 to August 2014. Our empirical results suggest that multifactor time invariant pricing models based on augmented capital asset pricing model (CAPM) framework are ineffective in explaining the cross section of stock returns in the presence of significant inter and intra‐market segmentation. However an alternative model specification based on a time varying parameter specification and using same sets of factors yields significant enhancements in explaining cross section of stock returns across universe. We find that momentum factor largely lacks significance while a time varying two factor model, based on CAPM plus liquidity factor, is optimal. The liquidity factor being that of Liu (2006) and annually rebalanced. Our findings are important for investment managers seeking appropriate factors and modelling techniques to hedge against risks as well as firm's financial managers seeking to reduce costs of equity capital.     

Idiosyncratic Consumption Risk and the Cross Section of Asset Returns

This paper investigates the importance of idiosyncratic consumption risk for the cross‐sectional variation in asset returns. We find that besides the rate of aggregate consumption growth, the cross‐sectional variance of consumption growth is also a priced factor. This suggests that consumers are not fully insured against idiosyncratic consumption risk, and that asset returns reflect their attempts to reduce their exposure to this risk. The resulting two‐factor consumption‐based asset pricing model significantly outperforms the CAPM, and its performance compares favorably with that of the Fama–French three‐factor model.     

TRANSITORY MARKET STATES AND THE JOINT OCCURRENCE OF MOMENTUM AND MEAN REVERSION

In this article we derive and investigate the implications of the Fama–French and Poterba–Summers model—in which the market price of equity contains permanent and temporary components—to explain cross‐sectional differences in equity risk premia and returns. Shocks to the transitory component are regarded a Merton risk factor. We obtain estimates from a simple Kalman decomposition of the market price. The transitory component estimate is used in a conditional capital asset pricing model to test implications of the model related to predictability, cross‐sectional performance, and the existence of momentum and mean reversion.     

It takes a model to beat a model: Volatility bounds

Models like the CAPM and Fama–French three-factor models are commonly used as benchmarks for calculating cost of capital and evaluating portfolio performance, despite the empirical evidence to reject them. For many practical purposes, “it takes a model to beat a model.” In this paper we derive restrictions on models that could “beat” a bench-mark model but might still be misspecified. In these “takes-a-model-to-beat-a-model” (TMBM) bounds, model A beats model B if model A's quadratic form of pricing errors is smaller. The bounds generalize the Hansen–Jagannathan bound and distance measure. We use the TMBM bounds to evaluate various linear factor models and consumption-based models. The failure of the power utility model is much less extreme when it is compared with the CAPM and Fama–French model. For reasonable utility curvature, the Ferson–Constantinides model and Epstein–Zin model perform best among the consumption-based models, beating the model of Campbell and Cochrane, in which model the value of the persistence parameter that matches the time-series properties of aggregate stock market returns seems too low for cross-sectional asset pricing.     

Long-Run Performance Persistence of Investment Funds

This article analyzes the long-run persistence of returns and risk of investment in the assets of money, bound, and stock funds recorded on the Polish market in 2000–12. Portfolios of safe, hybrid, and stock classes are formed on the basis of tested funds. The persistence of returns and the Sharpe ratio are investigated in rolled five-year sub-periods, with one year step. Also, persistence in performance is assessed using classic CAPM and Fama and French models, which allow for evaluating management skills. We find the occurrence of the Sharpe ratio long-run persistence of money and bound funds. The study does not explicitly show long-run persistence in hybrid and stock fund portfolios. The CAPM and Fama and French models simulations of returns on stock and hybrid funds indicate varying management skills during five-year periods.     

Constructing and Testing Alternative Versions of the Fama–French and Carhart Models in the UK

This paper constructs and tests alternative versions of the Fama–French and Carhart models for the UK market with the purpose of providing guidance for researchers interested in asset pricing and event studies. We conduct a comprehensive analysis of such models, forming risk factors using approaches advanced in the recent literature including value‐weighted factor components and various decompositions of the risk factors. We also test whether such factor models can at least explain the returns of large firms. We find that versions of the four‐factor model using decomposed and value‐weighted factor components are able to explain the cross‐section of returns in large firms or in portfolios without extreme momentum exposures. However, we do not find that risk factors are consistently and reliably priced.     

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.     

The Performance of Hedge Fund Strategies and the Asymmetry of Return Distributions

We present hedge fund performance estimates that adjust for stale prices, Fama‐French risk factors and skewness. We contrast these new performance estimates with traditional performance measures. Using three‐factor models to adjust for staleness in prices and to incorporate Fama‐French factors along with the Harvey‐Siddique (2000) two‐factor model that incorporates skewness, we find that for the period 1990–2003, all hedge fund categories achieve above average performance when measured against an aggregate market index. More significantly, however, when we estimate performance at the individual hedge fund level, we discover that only 40 to 47% of the funds are shown to achieve an above average performance over that time period depending on the model used. These results have important implications for investors, endowments and pensions when they choose hedge fund managers.     

Estimation of expected return: CAPM vs. Fama and French

Most practitioners favour a one-factor model (CAPM) when estimating expected return for an individual stock. For estimation of portfolio returns, academics recommend the Fama and French three-factor model. The main objective of this paper is to compare the performance of these two models for individual stocks. First, estimates for individual stock returns based on CAPM are obtained using different time frames, data frequencies, and indexes. It is found that 5 years of monthly data and an equal-weighted index, as opposed to the commonly recommended value-weighted index, provide the best estimate. However, performance of the model is very poor; it explains on average 3% of differences in returns. Then, estimates for individual stock returns are obtained based on the Fama and French model using 5 years of monthly data. This model, however, does not do much better; independent of the index used, it explains on average 5% of differences in returns. These results therefore bring into question the use of either model for estimation of individual expected stock returns.     

On the differences in measuring SMB and HML in the UK – Do they matter?

The Fama–French (FF) three factor model expands the capital asset pricing model (CAPM) to include two additional factors to the market factor – SMB, employed to capture a firm size effect in returns and HML employed to capture book-to-market effects in returns. In the UK, different researchers use different ways of calculating SMB and HML in the context of empirical applications of the three factor model, or extensions of it, perhaps because they believe the differences in the construction of the SMB and HML factors to be relatively unimportant from an empirical standpoint. We investigate whether indeed factor construction methods are unimportant. Our conclusion is that they do matter.     

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.     

Pricing Model Performance and the Two‐Pass Cross‐Sectional Regression Methodology

Over the years, many asset pricing studies have employed the sample cross‐sectional regression (CSR) R² as a measure of model performance. We derive the asymptotic distribution of this statistic and develop associated model comparison tests, taking into account the impact of model misspecification on the variability of the CSR estimates. We encounter several examples of large R² differences that are not statistically significant. A version of the intertemporal capital asset pricing model (CAPM) exhibits the best overall performance, followed by the Fama–French three‐factor model. Interestingly, the performance of prominent consumption CAPMs is sensitive to variations in experimental design.     

Industry Cost of Equity Capital: UK Evidence

Abstract:  This paper explores the industry cost of equity capital for the UK. We replicate the Fama and French (1997) US analysis for UK industries, but additionally investigate the industry cost of equity capital obtained from a conditional CAPM, the Cahart (1997) four factor model, and the Al-Horani, Pope and Stark (2003) R&D model. In line with the Fama-French US results, the out of sample performance of all the models is disappointing Whilst the FF3F model has a somewhat higher explanatory power than the CAPM in terms of explaining past returns, the SMB and HML factor slopes show considerable variability through time. However, all our models of the cost of equity capital in the UK outperform a simple 'beta one' model, a result that has implications for the regulatory process. There is also some evidence to suggest that a conditional CAPM may be of interest to regulators. The new R&D model of Al-Horani et al. clearly has potential, in that over the limited period for which data is available it yields return errors not dissimilar to those found under the FF3F model, but exhibits slope coefficients on the fourth R&D factor that seem to be relatively stable.     

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 Really Long-Run Performance of Initial Public Offerings: The Pre-Nasdaq Evidence

Financial economists have intensely debated the performance of IPOs using data after the formation of Nasdaq. This paper sheds light on this controversy by undertaking a large, out‐of‐sample study: We examine the performance for five years after listing of 3,661 U.S. IPOs from 1935 to 1972. The sample displays some underperformance when event‐time buy‐and‐hold abnormal returns are used. The underperformance disappears, however, when cumulative abnormal returns are utilized. A calendar‐time analysis shows that over the entire period, IPOs return as much as the market. The intercepts in CAPM and Fama–French regressions are insignificantly different from zero, suggesting no abnormal performance.     

New Paradigms in Stock Market Indexing

Considerable recent interest has been shown in a new set of stock‐market indices that are weighted by fundamental factors such as sales, earnings, dividends or book values, rather than by capitalization. In this paper, we analyze the performance of Fundamental Indexing? (“FI”). First, we show that the source of FI's recent excellent performance is not from its ability to systematically arbitrage mispricing in a noisy market but from increasing the portfolio's exposure to stocks with low price‐to‐book values and with small capitalizations. We find that FI does not produce a positive alpha when its excess returns are explained by the Fama‐French three‐factor model of CAPM beta, the value premium and the size premium. Second, we show that it is possible to construct a portfolio of exchange‐traded funds with similar factor loadings that can replicate, and sometimes, even outperform FI. However, we caution investors not to expect consistent outperformance from portfolios tilted towards value and small‐cap stocks. Historical data shows evidence of mean reversion in the performance of such strategies.