Sebastien Daniel, Vincent Haller, Benoit Bellone, QuantCube Technology Research Paper, December 2023


This research note exhibits a new seasonal adjustment methodology developed at QuantCube Technology: Seasonal Trend And Holiday decom- position with Loess (STAHL). Derived from the STL procedure introduced by R. B. Cleveland et al. (1990), STAHL aims to be applied to alternative data series at multiple frequencies. It is able to proceed to Working Day Adjustment coping with time-varying or periodic calendars such as the Chinese New Year, to handle structural or periodic missing values, and to provide a point-in-time procedure to generate unrevised trend and sea- sonal components.

In a first part, we describe the STAHL framework and its different key innovative steps: spectral identification of multiple seasonal frequencies, industrial preprocessing including resampling, seasonal adjustment with missing value handling, specific holiday adjustment and point in time seasonal trend extraction.

In the second part, we provide multiple empirical illustrations based on high frequency data. We notably focus on the US Weekly Initial claims series during the outstanding periods of Covid outbreaks which raised critical issues for real-time seasonality extraction. As such we discuss the consequences of our point-in-time (ie. no revision) principle compared to the adjusted series produced by the US Department of Labour. Second, we focus on many different high frequency alternative data series to explore how STAHL deals with multiple seasonality and holidays. We notably focus on periodic missing value treatments and measure the Chinese Lunar Calendar impact on human activity captured through daily measures of NO2 Air pollution.

Keywords: Seasonal adjustment, Calendar adjustment, Loess, High-frequency, Alternative data, Point-in-time estimations, Missing values


Key Findings:

Benoit Bellone, Raul Leote de Carvalho, Journal of Investing, February 2022 , Vol. 31, (2) 75-93

  1. The spread between valuations of value stocks relative to their expensive peers reached levels last seen in the 2000 tech bubble in every region and sector investigated. This expansion of value spreads explains the recent underperformance of value stocks.
  2. The expansion of value spreads reflected an increasing difference between earnings growth forecasts for expensive and value stocks. Value spreads and earnings growth forecast differences peaked in 2020, suggesting we may have entered a regime of value spread compression.
  3. Value spread compression periods are characterized by the strongest outperformance of value stocks relative to expensive peers and by outperformance of smaller cap stocks relative to larger cap stocks. Other sector-neutral styles and their multifactor combinations also do well.


Value stocks endured a period of severe underperformance until recently. We show that the value spreads between valuations of value stocks and their most expensive peers expanded in all regions and sectors during this period of underperformance, reaching the same extreme high levels last seen at the peak of the tech bubble in 2000. Investors have re-rated expensive stocks relative to their value peers reflecting an expanding difference in their respective earnings growth forecasts.

There are signs this trend may now have changed. Value spreads may have started a new period of compression at the end of 2020, a trend led by shrinking differences in earnings growth forecasts. A compression in value spreads would be favorable for value stocks, smaller capitalization stocks and for multi-factor strategies.

Keywords: Factor investing, Equities, Value, Value stocks, Growth stocks, Value spread, Smart

Read on Ivey Value Investing Research Center, View Abstract on SSRN

Frederic Abergel, Benoit Bellone and François Soupé, (2022), Journal of Risk, Volume 24, Number 4 (April 2022)


This note presents a novel, practical approach to risk management
for multi-factor equity investment strategies. Our approach lies in the
construction of a cross-sectional risk model using the stock return betas
and a small number of style factors and macro-sectors indicator functions
as explanatory variables in a cross-sectional regression.

The model leads to a covariance structure that incorporates in an intuitive fashion the
stocks’ characteristics while at the same time possesses good conditioning
properties leading to robust optimization problems. Various portfolio
constructions are analyzed in details, and some concrete examples are

Keywords: factor investing, risk model, portfolio construction, cross-section of returns

Download, View on SSRN

Benoit Bellone, Thomas Heckel, François Soupé and Raul Leote de Carvalho, (2021), BNP Paribas Asset Management Working Paper


We investigate the possible sources of the recent underperformance of multi-factor equity strategies reported by many equity quant managers. We considered the value, quality, low risk and momentum factor styles in mid to large-capitalisation World, USA and European stock universes. When looking at the historical performance of the factors and multi-factor combinations, we find that this is not the first time factor strategies have experienced a period of poor performance. The tech bubble of the late 90s and the great financial crisis of 2008 were other difficult periods for some of the factors and multi-factor combinations.

What is different this time around is that poor performance can be mainly attributed to the underperformance of value factors. We also find that long-only portfolios, which tend to be exposed to smaller-capitalisation stocks in their construction, have suffered additionally from that exposure. Not only did the size factor fail to generate a premium in mid to large-capitalisation universes in the long term, but also the recent underperformance of smaller-capitalisation stocks and the consequent increase in the concentration of benchmarks was an additional source of difficulty in long-only benchmarked portfolios.

Finally, we discuss the impact of a number of choices available to managers of factor strategies and show that the neutralisation of sectors, neutralisation of beta, control of tracking error and diversification of factors in styles play an important role in improving the performance of equity factor strategies.

Keywords: factor investing, risk model, portfolio construction, cross-section of returns

Download, View on SSRN

Benoit Bellone and Raul Leote de Carvalho, (2020), BNP Paribas Asset Management Working Paper


Ten years after showing that the low volatility anomaly in the performance of stocks is a phenomenon that should be considered in each sector as opposed to on an absolute basis ignoring sectors, we present evidence that this observation has held up well, and that if anything, has become even more valid.

Keywords: Low Volatility, Low Risk Anomaly, Minimum Variance, Minimum Volatility, Factor Investing, Equities, Smart Beta, Sectors

Download, View on SSRN

Benoit Bellone, Philippe Declerck, Mounir Nordine and Thomas Vy The Journal of Portfolio Management, Multi-Asset Special Issue 2023, jpm.2023.1.470


Carry, Value and Momentum factors are said « to be everywhere » according to a growing body of research. As such they may be the most robust styles across asset classes and history. In this research paper, we look forward to clearing up the following questions: how to describe multi-asset styles performance across time and across different market regimes? How multi-asset styles should be expected to behave during alternative phases of the Stock Market cycle?

Are cross-asset styles sensitive to volatility conditions? Are there different responses to changes in bond yields? Is there any style likely to be structurally more cyclical or defensive? Eventually, we would like to contribute to the current debate opposing Style Rotation to Diversification: is there a case for more time-varying and concentrated Multi-Asset style portfolio constructions?

Keywords: Factor Investing, Cross-asset Alternative Risk Premia, Regimes

Download on JPM website, View abstract on SSRN

Benoit Bellone, (2017), Research Note


This note provides a simplified framework to design Intertemporal Consumption and Portfolio Plans. Following Munk (2013), I start from simple assumptions (constant drift and volatility) with one risk asset(equity) in continuous time. From here, using CRRA utility functions, the Hamilton-Jacobi-Bellman (HJB) program can be solved analytically and forms of the consumption/saving and wealth processes can be exhibited. Those results are generalized to time-varying deterministic processes.

Such a tractable model leads to the following conclusions:

1) a rationale investor with constant risk-aversion and expectations will have to invest a constant share of its wealth in the risky asset in retirement,

2) the consumption rate expressed as a percentage of the wealth is an increasing function of time converging toward unity,

3) the lower the expected risk-free rate, the lower the risk aversion, the lower the expected risky asset Sharpe Ratio, the higher the time preference for the present, the higher the risk of consuming all the wealth before expiration,

4) the higher the risk-free rate, the higher the prospective sharpe ratio of the risky asset, the higher the expected consumption at retirement.

Appendix provides analytical formula in discrete time extending the results of Demange and Rochet (1992) in a stochastic framework.

Keywords: Stochastic Optimal Control, Hamilton-Jacobi-Bellman, Dynamic Asset Allocation, Optimal Portfolio Choice, Continous and Discrete time


Benoit Bellone, (2011), Research Note


When should investors hold passive currency risk ? Under which conditions is there a clear gain for currency hedging ? What about prospective Sharpe ratios of both unhedged and hedged investments ? This note aims to answer those questions.

It so happens that theoretical relations derived from a very simple model stick with the intuition : the gain from currency hedging depends in a non-linear way from the prospective prices of risk of the currency and the local asset, the volatility of the currency, the ratio of volatilities between currency and the local asset and the correlation between local asset and currency returns.

If an investor is eager to maximize the Sharpe ratio of its foreign portfolio, such a model suggests that the case for hedging should be all the stronger as :

1) the correlation between a local asset performance and its currency return is elevated and positive,

2) the local asset’s prospective Sharpe ratio is large,

3) the currency’s prospective Sharpe ratio is small,

4) the currency volatility is large relative to the local asset price volatility.

Keywords: Stochastic Calculus, Foreign-exchange risk, Hedging , Arbitrage Theory in Continous Time


Benoit Bellone, (2006), Economie et Prévision, 2006/1, (n°172), page 63-81, French Version : Une lecture probabiliste du cycle d’affaires américain


This article explores 35 years of the U.S. business cycle with a multivariate hidden Markov model using monthly data. It identifies ten U.S. time series offering particularly reliable information to detect recessions. It also assesses the performances of different and complementary “recession models” based on Markov processes and draws two main conclusions:

1) simple univariate models are decisive to monitor the business cycle providing that the series are shown to be highly reliable;

2) models adding a multivariate dimension are useful but work only marginally better than a simple summary.

The primary determinant of model quality appears to be the variables’ information content. The author introduces a new reading of the business cycle using a preferred recession model and concludes by discussing the limitations of leading indicators and “real-time detection ».

Note: Downloadable article is in French.

Keywords: Multivariate Markov-Switching Regressions, Hidden markov Models, Business cycle, EM algorithm, Kittagawa-Hamilton Filtering

Download, View on Economie & Prévision

Benoit Bellone, Emmanuel Michaux, (2006), Working Paper


Should we run one regression forecast? We confront the Bayesian Model Averag- ing (BMA) with two major automatic forecasting procedures: the dynamic factor model (DFA) and the ”general-to-specific” (GETS) algorithm, to gauge whether introducing Bayesian model uncertainty significantly improves forecasting. We consider those methods, including the ”Median BMA” strategy to forecast quarterly US GDP growth on an original monthly basis.

All models consistently select the same coincident and leading series, giving a robustness check of the best US GDP predictors. We also assess relative model performance in and out-of-sample using forecast accuracy tests and directional change metrics. Results suggest that the simple BMA approach, the GETS strategy or the DFA model tend to be equivalent.

Keywords: Automatic Model Selection, Bayesian Model Averaging, GETS, Factor models.


Benoit Bellone, Erwan Gautier and Sebastien Le Coent , Banque de France Working Paper No. 128


This article aims at estimating leading indicators of the American economy with financial variables. We use two types of hidden Markov chains models, a quantitative one (Krolzig (1997)) and a qualitative one (Gregoir and Lenglart (2000)). These models provide a robust and reliable framework to build with financial variables a qualitative probabilistic indicator with a 3-to-6 month lead on business and growth cycle. During the last forty years, the financial market rarely proved false signals and identified all recessions which are dated by the NBER and slowdowns periods of the American economy.

Note: Downloadable document is in French.

Keywords: Business cycles, Qualitative multivariate Markov switching models, MS-VAR models, leading indicators

Download, View on SSRN

Benoit Bellone, (2005), Working Paper


This paper introduces an upgraded version of MSVARlib, a Gauss and Ox-Gauss compliant library, focusing on Multivariate Markov Switching Regressions in their most general specification. This new set of procedures allows to estimate, through classical optimization methods, models belonging to the MSI(M)(AH)-VARX “intercept regime dependent” family.

This research enhances the first package MSVARlib 1.1, which has been deeply inspired by the works of Hamilton and Krolzig. Not to mention the extension to a generalized multivariate regression framework, it notably augments the range of models with a possibly unlimited finite number of Markov states, offers automatic or manual intialization procedures and adds new statistical tests.

The first part of this article provides the basic theoretical grounds of the related Markov-switching models. Following sections give some illustrations of the programs through univariate and multivariate examples. One is based on a non-linear reading of the american unemployment rate. A second study is focused on coincident stochastic models of US recessions and slowdowns. The paper concludes on possible extensions and new applications. Detailed guidelines in appendices and tutorial programs are provided to help the reader handling the Gauss package and the joined replication files.

Keywords: Multivariate Markov-Switching Regressions, Hidden markov Models, Open source Gauss library, Business cycle, EM algorithm, Kittagawa-Hamilton Filtering


Benoit Bellone and Erwan Gautier (2004), Working Paper


This paper provides both leading and coincident indicators of the US business and growth cycles through a multivariate qualitative hidden Markov model introduced by Gregoir and Lenglart (2000). The leading model applied to a set of four financial series supplies an unrevised and reliable advanced qualitative probabilistic indicator.

Over the last forty years, it allows to conclude that financial markets have rarely failed to detect economic turning points. In fact, they have foreseen all the American economic slowdowns and especially the seven major recessions dated by the NBER committee. This modelling allows, through the interpretation of market moves, to forewarn economic downturns, with a significant lead varying between 3 to 6 months on a foolproof coincident indicator.

Keywords: Business Cycle, Multivariate qualitative modelling, Hidden Markov Model, Turning points, Asset prices and leading indicators


The views and opinions on this website are my opinions and do not reflect the views of my current or former employers.