Unconditional CAPM Research Articles

Testing the Conditional CAPM Using Short-Window Regressions : A Critique

Using short-window regressions, prior studies have shown that the conditional CAPM performs as poorly as the unconditional CAPM and that unconditional alphas are too large to be explained by the covariance between conditional betas and market risk premium. I examine the extent to which these results are driven by estimation biases in short-window regressions. Even when the true time-varying beta has highly transient components, beta estimates from these short-window regressions can be estimated to highly persistent because of yearly portfolio reformulations that are commonly employed in empirical studies. I show that, under these circumstances, large non-zero alpha estimates from short-window regressions are consistent with the conditional CAPM and the covariance estimates between conditional betas and market risk premium are biased downward and can have large estimation errors.

Observable Implications of the Conditional CAPM

The derivation of observable implications of the conditional CAPM theory often includes the joint (internally inconsistent) hypothesis that the stock portfolio used in the tests is the theoretical, mean-variance efficient, market portfolio. The present paper generalizes this derivation by avoiding this joint hypothesis. The generalization reveals that the conditional CAPM plausibly explains asset pricing anomalies, such as the unconditional alphas and betas of momentum, value, and size portfolios, while the unconditional CAPM theory is still rejected by portfolios with negative unconditional betas and positive unconditional alphas. Hence, relaxing this joint assumption does not render the CAPM theory untestable.

Observable Implications of the Conditional CAPM

The derivation of observable implications of the conditional CAPM theory often includes the joint (internally inconsistent) hypothesis that the stock portfolio used in the tests is the theoretical, mean-variance efficient, market portfolio. The present paper generalizes this derivation by avoiding this joint hypothesis. The generalization reveals that the conditional CAPM plausibly explains asset pricing anomalies, such as the unconditional alphas and betas of momentum, value, and size portfolios, while the unconditional CAPM theory is still rejected by portfolios with negative unconditional betas and positive unconditional alphas. Hence, relaxing this joint assumption does not render the CAPM theory untestable.

A dynamic conditional regime-switching GARCH CAPM for energy and financial markets

This paper develops a methodology for estimating a time-varying conditional version of the CAPM with regime changes in conditional variance dynamics. Our research goal is related to documenting the power of the beta when it is estimated dynamically. The empirical performance is tested across a sample of 81 financial, energy, and other commodity markets for the period August 1999–January 2018. The conditional regime-switching GARCH CAPM, with time-varying betas explaining both bull and bear markets, outperforms the unconditional (static) CAPM. Among stocks, there are significant time variations in betas across our models and regimes. This empirical feature is even more pronounced in the USA, the UK, Germany, France, China, and Malaysia. Among energy and other commodities, we find similar variations in the market price of risk. The direction of the relation with market returns for Crude Oil, Gold, Copper, Tin, Rubber, Aluminum, and Platinum is the same across our nested models. This result also holds for aggregate markets indices. Secondly, we provide a ranking by mean filtered volatility series where Natural Gas stands out at a high level. Average pricing errors are inferior in the case of the conditional model, and for Crude Oil. Lastly, we demonstrate that the regime-switching model delivers better estimates of one-day-ahead Value-at-Risk than its non-switching counterpart. Our results shed light on the supremacy of the market factor alone associated with time variation in risk premia across the energy and financial markets.

Mutual Fund Performance When It Really Matters Most

Motivated by asset pricing evidence that disappointment periods in aggregate consumption growth are very good proxies for high marginal utility states, we examine whether equity fund performance exhibits state dependence. We find that the quintile of funds with the highest (lowest) unconditional CAPM alpha exhibits the biggest decrease (increase) in risk-adjusted performance during disappointment months. As a result, the alpha differential between unconditional winner and loser funds disappears when it matters most in utility terms. Our results indicate that the unconditional CAPM alpha is a highly misspecified performance measure from the viewpoint of a disappointment averse investor. To the contrary, state dependence is considerably attenuated when the 3-factor Fama-French alpha is used as performance measure. We conclude that the latter is the least misspecified unconditional performance measure, as it better aligns managerial incentives with the preferences of a disappointment averse investor. These findings are particularly important for fund performance measurement in light of the recent evidence that investors primarily evaluate funds on the basis of their CAPM alpha.

The CAPM Holds

When the cost of hedging is nil, the conditional CAPM holds (Merton, 1973). We empirically test the conditional CAPM by regressing asset returns onto the product of their conditional betas and market returns. Estimated intercepts are not statistically different from zero, implying that the conditional CAPM successfully explains the conditional level of asset returns. Yet, unconditional betas do not explain the cross-section of average asset returns; the unconditional CAPM fails. We show why and how the success of the conditional CAPM actually explains the failure of the unconditional CAPM, thereby rationalizing the coexistence of these two intriguing results.

Short-Term and Long-Term Discount Rates for Commercial Real Estate

How should executives discount commercial real estate cash flows up to 30 years in the future? In this paper, we develop a novel methodology to estimate the term structure of discount rates for commercial real estate cash flows. We find that the average term structure is downward sloping: longer maturity cash flows carry less risk, and the appropriate discount rate for these cash flows is quite often lower than that estimated from the unconditional single period CAPM. These findings are consistent with recent theory suggesting that rare-catastrophic events can lead to an inverted term structure of discount rates in real estate.

Carry and Trend Following Returns in the Foreign Exchange Market

Recent research has confirmed the behaviour of traders that significant excess returns can be achieved from following the predictions of the carry trade which involves buying currencies with relatively high short-term interest rates, or equivalently a high forward premium, and selling those with relatively low interest rates. This paper shows that similar-sized excess returns can be achieved by following a trend-following strategy which buys long positions in currencies that have achieved positive returns and otherwise holds cash. We demonstrate that market risk is an important determinant of carry returns but that the standard unconditional CAPM is inadequate in explaining the cross-section of forward premium ordered portfolio returns. We also show that the downside risk CAPM fails to explain this cross-section, in contrast to recent literature. A conditional CAPM which makes the impact of the market return as a risk factor depend on a measure of market liquidity performs very well in explaining more than 90% of the variation in portfolio returns and more than 90% of the average returns to the carry trade. Trend following is found to provide a significant hedge against these risks. The performance of the trend following factor is more surprising given that it does not have the negative skewness or maximum drawdown characteristic which is shown by the carry trade factor.

Indexing CNX NIFTY 50 Momentum Effects

The empirical literature indicates that momentum-style investing is a more effective approach than value-based or growth-based strategies. To confirm this, this article makes an attempt to construct a Momentum Index for the Indian equity market. The CNX NIFTY 50 Momentum Index is designed by calculating the volatility and volume-adjusted Momentum Index for each security in the CNX NIFTY 50 Parent Index. The estimated Momentum Index returns are compared with the CNX NIFTY 50 Index in terms of volatility, Sharpe Ratio and Treynor Ratio. Using VAR methodology, and macroeconomic, firm-specific factors which influence the momentum, index returns are analysed. This study also examined the Fama–French unconditional CAPM by including the Momentum Index return as the fourth factor alongside price–earnings, price–book ratio and dividend yield in estimating excess market returns. JEL: G11, G12, G14

Time-Varying Beta and the Value Premium: A Single-Index Varying-Coefficient Model Approach

We revisit conditional CAPM by modeling alpha and beta as flexible functions of state variables identified via formal variable selection. In post-1963 sample, beta of the value premium comoves strongly with unemployment, inflation, and price-earnings ratio in a countercyclical manner. We also uncover a novel nonlinear dependence of alpha on business conditions: It falls sharply and becomes even negative during severe economic downturns but is positive and flat otherwise. Conditional CAPM performs better than unconditional CAPM but does not fully explain the value premium. Our findings are consistent with a conditional CAPM with rare disasters or a multi-factor model.

Turnover Premium, Foreign Institutional Ownership, and Time-Varying Risk Premium in Taiwan Equity Markets

The low turnover premium found in U.S. equity markets is also found in Taiwan market, unlike the mixed evidence for other stylized effects such as size, book-to-market ratio and momentum. Consistent with investor overconfidence hypothesis proposed by Odean (1998, 1999), the percentage of foreign institutional shareholdings in a stock is found to vary inversely with turnover premium. This inverse relation is robust to the influence of other forces that may interact with turnover rate, such as market capitalization, book-to-market ratio and 6-month past returns, respectively. Time-varying risk premium, particularly in low turnover-low foreign institutional shareholdings percentage portfolio, provides partial explanation for the phenomenon, but the inverse relation persists after risk adjustment by models such as unconditional CAPM, Fama-French three factor model and conditional CAPM.

CAPM Condicional: Betas Variantes no Tempo no Mercado Brasileiro

O CAPM condicional pressupõe a variação temporal do beta de mercado. À luz de modelos espaço-estado, a dinâmica de beta pode ser modelada como um processo estocástico combinado com variáveis condicionantes relativas ao ciclo econômico e estimada através do filtro de Kalman. Este artigo analisa modelagens alternativas no que se refere ao ajuste aos dados de carteiras ordenadas por valor de mercado e razão book-to-market no mercado brasileiro, bem como à capacidade de explicação dos erros de apreçamento em relação ao CAPM incondicional através de testes sob abordagens de séries temporais e cross-sectional. O modelo em que beta segue passeio aleatório combinado com variáveis condicionantes é o que apresenta melhor resultado ao reduzir erros de apreçamento, mas, apesar da redução, estes permanecem ainda significativos. Testes cross-sectional indicam que a variável book-to-market perde poder na explicação dos retornos, mas evidenciam uma influência de variável relativa a retornos passados.

External Equity Financing Shocks, Financial Flows, and Asset Prices

The ability of corporations to raise external equity varies with macroeconomic conditions, suggesting that the cost of equity issuance is time-varying. Using cross sectional data on U.S. publicly traded firms, we construct an empirical proxy of an aggregate shock to the cost of equity issuance, which we interpret as a financial shock. We show that this shock captures systematic risk, and that exposure to this shock helps price the cross section of stock returns including book-to-market, investment, and size portfolios. We propose a dynamic investment-based model with time-varying external financing frictions to interpret the empirical findings. Our central finding is that time variation in external equity financing costs is important for the model to quantitatively capture the joint dynamics of firms’ asset prices, real quantities, and financing flows. In the model, growth firms, high investment firms, and big firms, can substitute more easily debt financing for equity financing when it becomes more costly to raise external equity, hence these firms are less risky in equilibrium. The model also replicates the failure of the unconditional CAPM in pricing the cross section of stock returns.

Explaining Momentum and Value Simultaneously

This paper proposes a unified risk-based explanation for momentum profits and the value premium in a neoclassical investment-based model. Winner firms have higher short-term profitability and investment commitment, and hence more negative exposure to the price of investment goods than loser firms. Value firms have lower long-term profitability and higher operating leverage, and hence higher sensitivity to neutral productivity shocks than growth firms. The model reproduces the coexistence of momentum profits and the value premium, the failure of the unconditional CAPM, the predictability of momentum profits by market states, and the long-term reversal of momentum profits.

Specification Errors of Asset Pricing Models for a Market Characterized with Large Capitalization Firms

The evaluation for the specification errors of asset pricing models is conducted using size-BM, size-MOM and industry portfolios (21) for Finnish stock market. The Finnish market is taken as a test case for equity markets where few firms dominate the total market capitalization. We report diverging risk-returns tradeoffs for the average tendencies of the stocks and for the actual growth in them. The results suggest the poor cross-sectional ability of unconditional CAPM is improved if the parameters of the stochastic discount factor (SDF) are allowed to vary through time. Nonetheless, the Carhart (1997) model SDF produces the lowest Hansen and Jagannathan (1997) distance for stock returns across all tested specifications. The Fama and French (1993) model augmented with macro variables, and January scaled CAPM produce matching performances to Carhart model with equal and capitalized weighting respectively. The evidence is stable under the employed diagnostics checks.

Empirical Evidence for State and Time Separable Preferences: Case Finland

The study investigates the implications of modified utility specifications developed on the standard power utility assumptions for Finnish representative agent while breaking the state and time separable constraints. The estimations are carried out using returns on equity and bond returns with iterated GMM procedure. The results from Epstein and Zin (1991) and Campbell and Cochrane (1999) models show Finnish risk premia is time varying across the studied samples. We conclude Campbell-Cochrane model outperforms the competing models in producing plausible model parameters while suppressing specification errors. The diagnostic checks show model is able to capture variations in stock returns over time. It also commands a significant price of risk in cross-sectional regressions and even manages to do better than unconditional CAPM.

A Higher Moment Downside Framework for Conditional and Unconditional Capm in the Russian Stock Market

The article presents an empirical validation for mean-variance CAPM, using a Downside and Higher-moment framework of CAPM in the Russian stock market. The authors test the unconditional and conditional CAPM specifications on a sample of weekly returns of the most liquid Russian stocks over the financially stable period of 2004-2007 and over the crisis period of 2008-2009. The primary contribution of this study is ranking the models with respect to their explanatory power of cross-sectional return variations. The unconditional classical CAPM (where market risk is approximated by the beta coefficient) is compared to the downside (mean-semivariance) CAPM extended to incorporate the third (skewness) and fourth (kurtosis) moments. The ranking methodology is based on Fama and MacBeth’s (1973) two-stage estimation procedure. The unconditional CAPMs prove to have low explanatory power for the financially stable period and test results that are not statistically significant for the crisis period. Incorporating additional risk measures of the third and fourth moments and adopting one-sided risk measures only slightly increases the explanatory power. The highest explanatory power is offered by the unconditional CAPM of the Harlow-Rao downside systematic risk measure with zero benchmark. Our study confirms the feasibility of employing conditional CAPMs extended for systematic asymmetry (co-skewness) and systematic kurtosis (co-kurtosis) for the Russian stock market since these models display better explanatory power for cross-sectional return variations.

Information Risk, Conditional Betas, and the Financial Distress Anomaly

Several recent articles find that stocks with high probabilities of bankruptcy or default earn anomalously low returns and negative unconditional CAPM alphas in the post-1980 period. I show that the conditional CAPM resolves the performance difference between high- and low-distress stocks. In particular, financially distressed stocks have relatively low exposure to market risk during bad economic times. I help to explain these findings through a theoretical model in which a levered firm's equity beta is negatively related to uncertainty about the unobserved value of its underlying assets.

Portfolio Choice Implications of Parameter and Model Uncertainty in Factor Models

This paper examines the portfolio choice implications of incorporating parameter and model uncertainty in (conditionally) linear factor models using industry portfolios. I examine a CAPM, a linear factor model with different predictor variables (dividend yield, price to book ratio, price to earnings ratio, and price to sales ratio), and a time-varying CAPM. All approaches incorporate parameter uncertainty in a mean-variance framework. I consider a time-varying CAPM with changing conditional variance. It is shown that taking into account the time variation in market betas improves the portfolio performance as measured by the ex-post Sharpe ratio compared to both an unconditional CAPM and a linear factor model with predictor variables. I also show the implications of using a Black-Litterman framework versus using a standard mean-variance approach in the asset allocation step. Black-Litterman framework can be thought as a model averaging approach and thus helps deal with both the parameter and model uncertainty problems. I show that Black-Litterman approach results in portfolios with a higher Sharpe ratio than those obtained by a standard mean-variance framework using a single model or historical averages.

Learning about Beta: Time-Varying Factor Loadings, Expected Returns, and the Conditional CAPM

This paper explores the theoretical and empirical implications of time-varying and unobservable beta. Investors infer factor loadings from the history of returns via the Kalman filter. Due to learning, the history of beta matters. Even though the conditional CAPM holds, standard OLS tests can reject the model if the evolution of investor's expectations is not properly modelled. We use our methodology to explain returns on the twenty-five size and book-to-market sorted portfolios. Our learning version of the conditional CAPM produces pricing errors that are significantly smaller than standard conditional or unconditional CAPM and the model is not rejected by the data.