Risk evaluations with robust approximate factor models

Approximate factor models and their extensions are widely used in economic analysis and forecasting due to their ability to extracting useful information from a large number of relevant variables. In these models, candidate predictors are typically subject to some common components. In this paper we propose a new method for robustly estimating the approximate factor models and use it in risk assessments. We consider a class of approximate factor models in which the candidate predictors are additionally subject to idiosyncratic large uncommon components such as jumps or outliers. By assuming that occurrences of the uncommon components are rare, we develop an estimation procedure to simultaneously disentangle and estimate the common and uncommon components. We then use the proposed method to investigate whether risks from the latent factors are priced for expected returns of Fama and French 100 size and book-to-market ratio portfolios. We find that while the risk from the common factor is priced for the 100 portfolios, the risks from the idiosyncratic factors are not. However, we find that model uncertainty risks of the idiosyncratic factors are priced, suggesting that with effective diversifications, only the predictable idiosyncratic risks can be reduced, but the unpredictable ones may still exist. We also illustrate how the proposed method can be adopted on evaluating value at risk (VaR) and find it can delivery comparable results as the conventional methods on VaR evaluations.     

Downside beta and the cross section of equity returns: A decade later

This study reexamines the relation between downside beta and equity returns in the United States. First, we replicate the 2006 work of Ang, Chen, and Xing who find a positive relation between downside beta and future equity returns for equal‐weighted portfolios of NYSE stocks. We show that this relation doesn't hold after using value‐weighted returns or controlling for various return determinants. We also extend the original sample, add AMEX/NASDAQ stocks or utilize alternative downside beta measures and still find no downside risk premium. We focus on factor analysis results, persistence of downside beta, and various subsamples to understand the economic reasons behind the findings.     

Convertible Bond Arbitrage: Risk and Return

Abstract:  This paper specifies a simulated convertible bond arbitrage portfolio to characterise the risks in convertible bond arbitrage. For comparison the risk profile of convertible bond arbitrage hedge fund indices at both monthly and daily frequencies is also examined. Results indicate that convertible bond arbitrage is positively related to default and term structure risk factors. These risk factors are augmented with the simulated convertible bond arbitrage portfolio, mimicking a passive investment in convertible bond arbitrage, to assess the risk and return of individual hedge funds. We provide estimates of the performance of two hedge fund indices (an equally weighted and value weighted index) and a sample of convertible bond arbitrage hedge funds using a factor model methodology. Lagged and contemporaneous observations of the risk factors are specified, controlling for illiquidity in the securities held by funds. Our results cover two time periods. Initially we find evidence of abnormal risk adjusted returns in the individual hedge fund data and the equally weighted hedge fund index and no evidence of abnormal risk adjusted returns in the value weighted hedge fund index. When we examine performance during the credit crisis of 2007 and 2008 we find evidence of negative abnormal returns amongst individual hedge funds and the hedge fund indices.     

Dynamic jump intensities and risk premiums: Evidence from S&P500 returns and options

We build a new class of discrete-time models that are relatively easy to estimate using returns and/or options. The distribution of returns is driven by two factors: dynamic volatility and dynamic jump intensity. Each factor has its own risk premium. The models significantly outperform standard models without jumps when estimated on S&P500 returns. We find very strong support for time-varying jump intensities. Compared to the risk premium on dynamic volatility, the risk premium on the dynamic jump intensity has a much larger impact on option prices. We confirm these findings using joint estimation on returns and large option samples.     

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.     

Estimation of the underlying structure of systematic risk with the use of principal component analysis and factor analysis

We present an improved methodology to estimate the underlying structure of systematic risk in the Mexican Stock Exchange with the use of Principal Component Analysis and Factor Analysis. We consider the estimation of risk factors in an Arbitrage Pricing Theory (APT) framework under a statistical approach, where the systematic risk factors are extracted directly from the observed returns on equities, and there are two differentiated stages, namely, the risk extraction and the risk attribution processes. Our empirical study focuses only on the former; it includes the testing of our models in two versions: returns and returns in excess of the riskless interest rate for weekly and daily databases, and a two-stage methodology for the econometric contrast. First, we extract the underlying systematic risk factors by way of both, the standard linear version of the Principal Component Analysis and the Maximum Likelihood Factor Analysis estimation. Then, we estimate simultaneously, for all the system of equations, the sensitivities to the systematic risk factors (betas) by weighted least squares. Finally, we test the pricing model with the use of an average cross-section methodology via ordinary least squares, corrected by heteroskedasticity and autocorrelation consistent covariances estimation. Our results show that although APT is very sensitive to the extraction technique utilized and to the number of components or factors retained, the evidence found partially supports the APT according to the methodology presented and the sample studied.     

Idiosyncratic Cash Flows and Systematic Risk

We show that unpriced cash flow shocks contain information about future priced risk. A positive idiosyncratic shock decreases the sensitivity of firm value to priced risk factors and simultaneously increases firm size and idiosyncratic risk. A simple model can therefore explain book‐to‐market and size anomalies, as well as the negative relation between idiosyncratic volatility and stock returns. Empirically, we find that anomalies are more pronounced for firms with high idiosyncratic cash flow volatility. More generally, our results imply that any economic variable correlated with the history of idiosyncratic shocks can help to explain expected stock returns.     

Size Anomalies in U.S. Bank Stock Returns

The largest commercial bank stocks, ranked by total size of the balance sheet, have significantly lower risk‐adjusted returns than small‐ and medium‐sized bank stocks, even though large banks are significantly more levered. We uncover a size factor in the component of bank returns that is orthogonal to the standard risk factors, including small minus big, which has the right covariance with bank returns to explain the average risk‐adjusted returns. This factor measures size‐dependent exposure to bank‐specific tail risk. These findings are consistent with government guarantees that protect shareholders of large banks, but not small banks, in disaster states.     

A Nonlinear Factor Analysis of S&P 500 Index Option Returns

Growing evidence suggests that extraordinary average returns may be obtained by trading equity index options, and that at least part of this abnormal performance is attributable to volatility and jump risk premia. This paper asks whether such priced risk factors are alone sufficient to explain these average returns. To provide an answer in as general as possible a setting, I estimate a flexible class of nonlinear models using all S&P 500 Index futures options traded between 1986 and 2000. The results show that priced factors contribute to these expected returns but are insufficient to explain their magnitudes, particularly for short‐term out‐of‐the‐money puts.     

Effects of uncertainty and risk aversion on the exposure of investment-style factor returns to real activity

How do uncertainty and risk aversion affect the behavior of investment-style factors? We argue that a significant channel through which both uncertainty and risk aversion impact aggregate risk factors is the exposure of factor returns to real activity. We analyze this issue using mixed data sampling decomposition of the sensitivity of factor returns to real activity into high- and low-frequency components. We find a positive and significant relation between uncertainty and risk aversion for the low-frequency component of the sensitivity of factor returns to economic activity. More importantly, risk aversion significantly amplifies the effects of uncertainty on real activity exposure. The quality-based factor is an important exception to these findings.     

Size,value, and momentum in developed country equity returns: Macroeconomic and liquidity exposures

The paper investigates value and momentum factors in 23 developed international stock markets. We find that typically value and momentum premia are smaller and more negatively correlated for large market capitalization stocks relative to small. Momentum factors are more highly correlated internationally relative to value. We provide international evidence on three sets of risk exposures of value and momentum returns: macroeconomic risk, funding liquidity risk, and stock market liquidity risk. We find that value returns are typically lower prior to a recession while momentum returns often exhibit little sensitivity. Value returns are typically lower in times of poor funding liquidity, whereas, with notable exceptions, momentum returns are typically unaffected. Lastly, for almost all countries, value returns are high in poor stock market liquidity conditions.     

Characterizing the Risk of IPO Long‐Run Returns: The Impact of Momentum,Liquidity, Skewness,and Investment

We study 6,686 initial public offerings (IPOs) spanning the period 1981‐2005 and find that the new issues puzzle disappears in a Fama‐French three‐factor framework. IPOs do not underperform in the aftermarket on a risk‐adjusted basis and do not underperform a matched sample of nonissuers. IPO underperformance is concentrated in the 1980s and early 1990s, and IPOs either perform the same as the market or outperform on a risk‐adjusted basis from 1998 to 2005. We find that outperformance in the later period is driven by large firms. Factors for momentum, investment, liquidity, and skewness help to explain aftermarket returns, although size and book‐to‐market tend to proxy for skewness. IPO investors receive smaller expected returns due to negative momentum and investment exposure and in exchange for higher liquidity.     

Systematic risk and the cross section of hedge fund returns

This paper investigates the extent to which market risk, residual risk, and tail risk explain the cross-sectional dispersion in hedge fund returns. The paper introduces a comprehensive measure of systematic risk (SR) for individual hedge funds by breaking up total risk into systematic and fund-specific or residual risk components. Contrary to the popular understanding that hedge funds are market neutral, we find that systematic risk is a highly significant factor explaining the dispersion of cross-sectional returns while at the same time measures of residual risk and tail risk seem to have little explanatory power. Funds in the highest SR quintile generate 6% more average annual returns compared with funds in the lowest SR quintile. After controlling for a large set of fund characteristics and risk factors, systematic risk remains positive and highly significant, whereas the relation between residual risk and future fund returns continues to be insignificant. Hence, systematic risk is a powerful determinant of the cross-sectional differences in hedge fund returns.     

A Test for the Number of Factors in an Approximate Factor Model

An important issue in applications of multifactor models of asset returns is the appropriate number of factors. Most extant tests for the number of factors are valid only for strict factor models, in which diversifiable returns are uncorrelated across assets. In this paper we develop a test statistic to determine the number of factors in an approximate factor model of asset returns, which does not require that diversifiable components of returns be uncorrelated across assets. We find evidence for one to six pervasive factors in the cross-section of New York Stock Exchange and American Stock Exchange stock returns.     

The Impact of Jumps in Volatility and Returns

This paper examines continuous‐time stochastic volatility models incorporating jumps in returns and volatility. We develop a likelihood‐based estimation strategy and provide estimates of parameters, spot volatility, jump times, and jump sizes using S&P 500 and Nasdaq 100 index returns. Estimates of jump times, jump sizes, and volatility are particularly useful for identifying the effects of these factors during periods of market stress, such as those in 1987, 1997, and 1998. Using formal and informal diagnostics, we find strong evidence for jumps in volatility and jumps in returns. Finally, we study how these factors and estimation risk impact option pricing.     

Risk factor and industry effects in the cross-country comovement of momentum returns

This paper examines the sources of cross-country comovement of momentum returns over the 1975–2004 period. Using data on more than 17,000 individual firms across 100 industries from 40 countries, we document the profitability of country-neutral individual firm, industry, and industry-adjusted return momentum. We show that country-neutral momentum returns are significantly correlated across countries, the correlation is time-varying, and that comovement among industries cannot explain the comovement of country-neutral momentum returns. However, we find that standard risk factor models do explain a significant portion of the cross-country comovement of momentum returns, even though they do not explain average momentum returns.     

Shrinking the cross-section

We construct a robust stochastic discount factor (SDF) summarizing the joint explanatory power of a large number of cross-sectional stock return predictors. Our method achieves robust out-of-sample performance in this high-dimensional setting by imposing an economically motivated prior on SDF coefficients that shrinks contributions of low-variance principal components of the candidate characteristics-based factors. We find that characteristics-sparse SDFs formed from a few such factors—e.g., the four- or five-factor models in the recent literature—cannot adequately summarize the cross-section of expected stock returns. However, an SDF formed from a small number of principal components performs well.     

Liquidity and asset pricing: Evidence from the Hong Kong stock market

This study investigates the role of liquidity in pricing stock returns in the Hong Kong stock market. Our results show that liquidity is an important factor for pricing returns in Hong Kong after taking well-documented asset pricing factors into consideration. The results are robust to adding portfolio residuals and higher moment factor in the factor models. The results are also robust to seasonality, and conditional-market tests. We also compare alternative factor models and find that the liquidity four-factor model (market excess return, size, book-to-market ratio, and liquidity) is the best model to explain stock returns in the Hong Kong stock market, while the momentum factor is not found to be priced.     

Exchange Rates and the Conversion of Currency‐Specific Risk Premia

How do the risk factors that drive asset prices influence exchange rates? Are the parameters of asset price processes relevant for specifying exchange rate processes? Most international asset pricing models focus on the analysis of asset returns given exchange rate processes. Little work has been done on the analysis of exchange rates dependent on asset returns. This paper uses an international stochastic discount factor (SDF) framework to analyse the interplay between asset prices and exchange rates. So far, this approach has only been implemented in international term structure models. We find that exchange rates serve to convert currency‐specific discount factors and currency‐specific prices of risk – a result linked to the international arbitrage pricing theory (IAPT). Our empirical investigation of exchange rates and stock markets of four countries presents evidence for the conversion of currency‐specific risk premia by exchange rates.     

Banks’ equity performance and the term structure of interest rates

Using an extensive global sample, this paper investigates the impact of the term structure of interest rates on bank equity returns. Decomposing the yield curve to its three constituents (level, slope and curvature), the paper evaluates the time‐varying sensitivity of the bank's equity returns to these constituents by using a diagonal dynamic conditional correlation multivariate GARCH framework. Evidence reveals that the empirical proxies for the three factors explain the variations in equity returns above and beyond the market‐wide effect. More specifically, shocks to the long‐term (level) and short‐term (slope) factors have a statistically significant impact on equity returns, while those on the medium‐term (curvature) factor are less clear‐cut. Bank size plays an important role in the sense that exposures are higher for SIFIs and large banks compared to medium and small banks. Moreover, banks exhibit greater sensitivities to all risk factors during the crisis and post‐crisis periods compared to the pre‐crisis period; though these sensitivities do not differ for market‐oriented and bank‐oriented financial systems.