Do industries matter in explaining stock returns and asset-pricing anomalies?

Industry returns cannot be explained fully by well-known asset pricing models. This study reveals that common factors extracted from industry returns carry significant risk premiums that go beyond the explanatory power of size, book-to-market (BM) ratios, and momentum. In particular, this study shows that (1) the small-firm effect is significant only for firms whose market capitalization is below their industry average; (2) the BM effect is an intra-industry phenomenon; (3) a one-year momentum effect is significant only for firms whose BM ratio is smaller than the industry average and limited to non-January months; and (4) there is seasonality in all effects that cannot be explained by risk-based asset-pricing models. Neither rational nor behavioral theories alone can explain industry returns, and it is perhaps too hasty to attribute asset pricing anomalies to a single driving force.     

Arbitrage risk and the turnover anomaly

A strong turnover premium exists such that stocks with lower turnover have higher future returns in the 5 years following their formation than those with higher turnover. This turnover premium cannot be explained by existing asset-pricing models, a risk-based liquidity factor, or anomalies such as size, book-to-market ratio, or momentum. Further analysis indicates that the turnover premium is greater for stocks with higher idiosyncratic volatility, higher transaction costs, lower institutional ownership, and lower investor sophistication, which implies it is consistent with the mispricing explanation based on arbitrage risk.     

Time-series and cross-sectional momentum in anomaly returns

We find strong evidence of time-series and cross-sectional momentum in the long–short returns of a comprehensive sample of anomalies. Strategies that exploit such persistence deliver significant abnormal returns that are robust to the stock momentum effect, cannot be explained by traditional asset-pricing models, and are more pronounced when arbitrage capital is scarcer or market liquidity is lower. Momentum in anomaly returns dissipates but does not reverse, in the long-run. Our findings are consistent with limits-to-arbitrage and slow-moving capital causing mispricing to persist. Supporting this explanation, we find that both the level and persistence of anomaly returns are positively related to idiosyncratic volatility.     

Do relative leverage and relative distress really explain size and book-to-market anomalies?

In a capital asset pricing model (CAPM) framework, Ferguson and Shockley [2003. Equilibrium “anomalies”. Journal of Finance 58, 2549–2580] propose two factors constructed on relative leverage and relative distress, and show that the two factors subsume Fama and French's [1993. Common risk factors in the returns on stocks and bonds. Journal of Financial Economics 33, 3–56] factors constructed on size and book-to-market (BM) in explaining the cross-sectional average returns of the 25 size-BM portfolios. Based on tests on individual securities, we find that all factors fail to fully explain the common asset-pricing anomalies. In the spirit of Merton's [1973. An intertemporal capital asset pricing model. Econometrica 41, 867–887] intertemporal CAPM, we propose an augmented five-factor model, which incorporates Ferguson and Shockley's [2003. Equilibrium “anomalies”. Journal of Finance 58, 2549–2580] factors into the Fama–French three-factor model. The empirical results show that a simple conditional version of the augmented model is able to explain most well-known asset-pricing anomalies.     

Testing for a rational bubble under long memory

We analyse the time series properties of the S&P500 dividend–price ratio in the light of long-memory, structural breaks and rational bubbles. We find an increase in the long-memory parameter in the early 1990s by applying a test recently proposed by Sibbertsen and Kruse [J. Time Series Anal., 2009, 30, 263–285]. An application of the unit root test against long memory of Demetrescu et al. [Econometr. Theory, 2008, 24, 176–215] suggests that the pre-break data can be characterized by long memory, while the post-break sample contains a unit root. These results reconcile two empirical findings that are seen as contradictory: on the one hand, they confirm the existence of fractional integration in the S&P500 log-dividend–price ratio and, on the other, they are consistent with the existence of a rational bubble. The result of a changing memory parameter in the dividend–price ratio has an important implication for the literature on return predictability: the shift from a stationary dividend–price ratio to a unit root process in 1991 is likely to have caused the well-documented failure of conventional return prediction models since the 1990s.     

Risk-managed 52-week high industry momentum,momentum crashes and hedging macroeconomic risk

This is the first study to investigate the profitability of Barroso and Santa-Clara’s [J. Financial Econ., 2015, 116, 111–120] risk-managing approach for George and Hwang’s [J. Finance, 2004, 59, 2145–2176] 52-week high momentum strategy in an industrial portfolio setting. The findings indicate that risk-managing adds value as the Sharpe ratio increases, and the downside risk decreases notably. Even after controlling for the spread of the traditional 52-week high industry momentum strategy in association with standard risk factors, the risk-managed version generates economically and statistically significant pay-offs. Notably, the risk-managed strategy is partially explained by changes in cross-sectional return dispersion, whereas the traditional strategy does not appear to be exposed to such economic risks.     

Time-varying long-run mean of commodity prices and the modeling of futures term structures

The exploration of the mean-reversion of commodity prices is important for inventory management, inflation forecasting and contingent claim pricing. Bessembinder et al. [J. Finance, 1995, 50, 361–375] document the mean-reversion of commodity spot prices using futures term structure data; however, mean-reversion to a constant level is rejected in nearly all studies using historical spot price time series. This indicates that the spot prices revert to a stochastic long-run mean. Recognizing this, I propose a reduced-form model with the stochastic long-run mean as a separate factor. This model fits the futures dynamics better than do classical models such as the Gibson–Schwartz [J. Finance, 1990, 45, 959–976] model and the Casassus–Collin-Dufresne [J. Finance, 2005, 60, 2283–2331] model with a constant interest rate. An application for option pricing is also presented in this paper.     

Econometric analysis of microscopic simulation models

Microscopic simulation models are often evaluated based on visual inspection of the results. This paper presents formal econometric techniques to compare microscopic simulation (MS) models with real-life data. A related result is a methodology to compare different MS models with each other. For this purpose, possible parameters of interest, such as mean returns, or autocorrelation patterns, are classified and characterized. For each class of characteristics, the appropriate techniques are presented. We illustrate the methodology by comparing the MS model developed by He and Li [J. Econ. Dynam. Control, 2007, 31, 3396–3426, Quant. Finance, 2008, 8, 59–79] with actual data.     

The independence axiom and asset returns

This paper integrates models of atemporal risk preference that relax the independence axiom into a recursive intertemporal asset-pricing framework. The resulting models are amenable to empirical analysis using market data and standard Euler equation methods. We are thereby able to provide the first nonlaboratory-based evidence regarding the usefulness of several new theories of risk preference for addressing standard problems in dynamic economics. Using both stock and bond returns data, we find that a model incorporating risk preferences that exhibit first-order risk aversion accounts for significantly more of the mean and autocorrelation properties of the data than models that exhibit only second-order risk aversion. Unlike the latter class of models which require parameter estimates that are outside of the admissible parameter space, e.g., negative rates of time preference, the model with first-order risk aversion generates point estimates that are economically meaningful. We also examine the relationship between first-order risk aversion and models that employ exogenous stochastic switching processes for consumption growth.     

Myopic loss aversion,reference point,and money illusion

We use the portfolio selection model presented in He and Zhou [Manage. Sci., 2011, 57, 315–331] and the NYSE equity and US treasury bond returns for the period 1926–1990 to revisit Benartzi and Thaler’s myopic loss aversion theory. Through an extensive empirical study, we find that in addition to the agent’s loss aversion and evaluation period, his reference point also has a significant effect on optimal asset allocation. We demonstrate that the agent’s optimal allocation to equities is consistent with market observation when he has reasonable values of degree of loss aversion, evaluation period and reference point. We also find that the optimal allocation to equities is sensitive to these parameters. We then examine the implications of money illusion for asset allocation. Finally, we extend the model to a dynamic setting.     

Term Structure Models: A Perspective from the Long Rate

Term structure models based on dynamic asset-pricing theory are discussed by taking a perspective from the long rate. This paper partially answers two questions about the asymptotic behavior of yields on default-free zero-coupon bonds: in frictionless markets having no arbitrage, what should the behavior be; and, in known term structure models, what can the behavior be.

In frictionless markets having no arbitrage, yields of all maturities should be positive and uniformly bounded from above. The yield curve should level out as term to maturity increases. Slopes with large absolute values occur only in the early maturities. In a continuous-time framework, the longer the maturity of the yield is, the less volatile it will be. The long rate should be a nondecreasing process. Furthermore, the long rate in continuous-time factor models with nonsingular volatility matrices should be a nondecreasing deterministic function.

In the Black, Derman, and Toy model and factor models with the short rate having the mean reversion property, yields of all maturities are uniformly bounded from above. The long rate in the Duffie and Kan model with the mean reversion property is a constant. The long rate in the Heath, Jarrow, and Morton model can be infinite or a nondecreasing process. Examples with the long rate increasing are given in this paper. A model with the long rate and short rate as two state variables is then obtained.     

Violation of the iid-normal assumption: Effects on tests of asset-pricing models using Australian data

Financial data are typically not identically, independently and normally distributed (iid-normal). Yet, standard tests of asset-pricing models are based on this assumption, and we have little information on how sensitive the tests are to violations of iid-normality. Recent evidence suggests that test outcomes may be sensitive to these violations. In this paper, we use Australian data to compare the standard test results with those that do not require iid-normality: the GMM-J test and bootstrap-based tests. We find that different tests produce differences in prob values at least as large as those in US studies but that test outcomes are generally robust.     

An improved convolution algorithm for discretely sampled Asian options

We suggest an improved FFT pricing algorithm for discretely sampled Asian options with general independently distributed returns in the underlying. Our work complements the studies of Carverhill and Clewlow [Risk, 1990, 3(4), 25–29], Benhamou [J. Comput. Finance, 2002, 6(1), 49–68], and Fusai and Meucci [J. Bank. Finance, 2008, 32(10), 2076–2088], and, if we restrict our attention only to log-normally distributed returns, also Ve?e? [Risk, 2002, 15(6), 113–116]. While the existing convolution algorithms compute the density of the underlying state variable by moving forward on a suitably defined state space grid, our new algorithm uses backward price convolution, which resembles classical lattice pricing algorithms. For the first time in the literature we provide an analytical upper bound for the pricing error caused by the truncation of the state space grid and by the curtailment of the integration range. We highlight the benefits of the new scheme and benchmark its performance against existing finite difference, Monte Carlo, and forward density convolution algorithms.     

Algebraic structure of vector fields in financial diffusion models and its applications

High-order discretization schemes of SDEs using free Lie algebra-valued random variables are introduced by Kusuoka [Adv. Math. Econ., 2004, 5, 69–83], [Adv. Math. Econ., 2013, 17, 71–120], Lyons–Victoir [Proc. R. Soc. Lond. Ser. A Math. Phys. Sci., 2004, 460, 169–198], Ninomiya–Victoir [Appl. Math. Finance, 2008, 15, 107–121] and Ninomiya–Ninomiya [Finance Stochast., 2009, 13, 415–443]. These schemes are called KLNV methods. They involve solving the flows of vector fields associated with SDEs and it is usually done by numerical methods. The authors have found a special Lie algebraic structure on the vector fields in the major financial diffusion models. Using this structure, we can solve the flows associated with vector fields analytically and efficiently. Numerical examples show that our method reduces the computation time drastically.     

Fast Ninomiya–Victoir calibration of the double-mean-reverting model

Abstract

We consider the three-factor double mean reverting (DMR) option pricing model of Gatheral [Consistent Modelling of SPX and VIX Options, 2008], a model which can be successfully calibrated to both VIX options and SPX options simultaneously. One drawback of this model is that calibration may be slow because no closed form solution for European options exists. In this paper, we apply modified versions of the second-order Monte Carlo scheme of Ninomiya and Victoir [Appl. Math. Finance, 2008, 15, 107–121], and compare these to the Euler–Maruyama scheme with full truncation of Lord et al. [Quant. Finance, 2010, 10(2), 177–194], demonstrating on the one hand that fast calibration of the DMR model is practical, and on the other that suitably modified Ninomiya–Victoir schemes are applicable to the simulation of much more complicated time-homogeneous models than may have been thought previously.     

Turbocharging Monte Carlo pricing for the rough Bergomi model

The rough Bergomi model, introduced by Bayer et al. [Quant. Finance, 2016, 16(6), 887–904], is one of the recent rough volatility models that are consistent with the stylised fact of implied volatility surfaces being essentially time-invariant, and are able to capture the term structure of skew observed in equity markets. In the absence of analytical European option pricing methods for the model, we focus on reducing the runtime-adjusted variance of Monte Carlo implied volatilities, thereby contributing to the model’s calibration by simulation. We employ a novel composition of variance reduction methods, immediately applicable to any conditionally log-normal stochastic volatility model. Assuming one targets implied volatility estimates with a given degree of confidence, thus calibration RMSE, the results we demonstrate equate to significant runtime reductions—roughly 20 times on average, across different correlation regimes.     

The performance of enhanced-return index funds: evidence from bootstrap analysis

We apply the bootstrap technique proposed by Kosowski et al. [J. Finance, 2006, 61, 2551–2595] in conjunction with Carhart's [J. Finance, 1997, 52, 57–82] unconditional and Ferson and Schadt's [J. Finance, 1996, 51, 425–461] conditional four-factor models of performance to examine whether the performances of enhanced-return index funds over the 1996 to 2007 period are based on luck or superior ‘enhancing’ skills. The advantages of using the bootstrap to rank fund performance are many. It eliminates the need to specify the exact shape of the distribution from which returns are drawn and does not require estimating correlations between portfolio returns. It also eliminates the need to explicitly control for potential ‘data snooping’ biases that arise from an ex-post sort. Our results show evidence of enhanced-return index funds with positive and significant alphas after controlling for luck and sampling variability. The results are robust to both stock-only and derivative-enhanced index funds, although the spread of cross-sectional alphas for derivative-enhanced funds is slightly more pronounced. The study also examines various sub-periods within the sample horizon.     

Risk-managed industry momentum and momentum crashes

This paper investigates Barroso and Santa-Clara’s [J. Financ. Econ., 2008, 116, 111–120] risk-managed momentum strategy in an industry momentum setting. We investigate several traditional momentum strategies including that recently proposed by Novy-Marx [J. Financ. Econ., 2012, 103, 429–453]. We moreover examine the impact of different variance forecast horizons on average pay-offs and also Daniel and Moskowitz’s [J. Financ. Econ., 2016, 122, 221–247] optionality effects. Our results show in general that neither plain industry momentum strategies nor the risk-managed industry momentum strategies are subject to optionality effects, implying that these strategies have no time-varying beta. Moreover, the benefits of risk management are robust across volatility estimators, momentum strategies and subsamples. Finally, the ‘echo effect’ in industries is not robust in subsamples as the strategy works only during the most recent subsample.     

The role of volume in order book dynamics: a multivariate Hawkes process analysis

We show that multivariate Hawkes processes coupled with the nonparametric estimation procedure first proposed in Bacry and Muzy [IEEE Trans. Inform. Theory, 2016, 62, 2184–2202] can be successfully used to study complex interactions between the time of arrival of orders and their size observed in a limit order book market. We apply this methodology to high-frequency order book data of futures traded at EUREX. Specifically, we demonstrate how this approach is amenable not only to analyse interplay between different order types (market orders, limit orders, cancellations) but also to include other relevant quantities, such as the order size, into the analysis, showing also that simple models assuming the independence between volume and time are not suitable to describe the data.     

Book reviews

Public Sector Management Norman Flynn. Harvester Wheatsheaf, Hemel Hempstead, UK (1990). 201 pp. £9.95. ISBN 0–7450–0594–2.

CIPFA Guide to the Community Charge R. Hale and C. Stewart (Eds). Longman, Harlow, UK (1990). Price £225. ISBN 0–582–063–54X.

Ethics in the British Civil Service Richard A. Chapman. Routledge, London ( 1988). pp. xix + 338. £30.