Papers in international peer-reviewed journals

F. Ortu, P. Reggiani, F. Severino (2025) Persistence-based portfolio choice along the FOMC cycle. The Quarterly Journal of Finance 15(1), 2550005. https://doi.org/10.1142/S2010139225500053. A previous CIRANO Working paper.

Abstract. The Federal Reserve holds Federal Open Market Committee and Board Meetings, with six- and two-week cadence respectively. The financial literature associates these meetings with stock market cycles of corresponding frequencies. These can be exploited through a portfolio strategy that invests in the market at alternate weeks. Since this strategy lacks theoretical foundations, we provide a rigorous framework for detecting market cycles and determining optimal portfolios that profit from them. We isolate uncorrelated components of stock returns associated with two- and six-week cycles, we replicate them and design an optimal portfolio that maximizes the investor’s wealth by properly exploiting such cyclicality.

F. Severino (2025) Long-term risk with stochastic interest rates. Mathematical Finance 35(1), 3-39. https://doi.org/10.1111/mafi.12440

Abstract. In constant-rate markets, the average stochastic discount factor growth rate coincides with the instantaneous rate. When interest rates are stochastic, this average growth rate is given by the long-term yield of zero-coupon bonds, which cannot serve as instantaneous discount rate. We show how to reconcile the stochastic discount factor growth with the instantaneous relations between returns and rates in stochastic-rate markets. We factorize no-arbitrage prices and isolate a rate adjustment that captures the short-term variability of rates. The rate-adjusted stochastic discount factor features the same long-term growth as the stochastic discount factor in the market but has no transient component in its Hansen–Scheinkman decomposition, capturing the long-term interest rate risk. Moreover, we show how the rate adjustment can be used for managing the interest rate risk related to fixed-income derivatives and life insurances.

M. Madotto, F. Severino (2023) Heterogeneous awareness in financial markets.  Journal of Economic Behavior and Organization 216, 26-41. https://doi.org/10.1016/j.jebo.2023.09.029. Accepted manuscript.

Abstract. The overlook of some economic scenarios may result in unforeseen negative outcomes for investors. In this paper, we consider an order-driven financial market in which a fraction of the traders is only partially aware of the possible payoffs of a risky asset, but is aware of the possibility of facing unknown contingencies. Investors decide whether to acquire a costly signal about the payoff of a risky asset and whether to buy such asset given their awareness level and their perceived relations among signals, order flows, and prices. We show that as unawareness becomes more severe, the value of the signal to the partially aware traders diminishes. In turn, through its impact on the price, the reduced number of partially aware informed investors increases the incentives of the fully aware to acquire the signal. This may partly or fully offset the previous effect, so that the overall proportion of informed investors in the market is (weakly) decreasing in the unawareness level. As for the equilibrium price, a lower amount of informed traders makes it more difficult for market makers to distinguish between good and bad signals, and this brings the conditional expectations of the price closer to the unconditional one and reduces the price variance.

S. Cerreia-Vioglio, F. Ortu, F. Severino, C. Tebaldi (2023) Multivariate Wold decompositions: a Hilbert A-module approach. Decisions in Economics and Finance 46, 45-96. https://doi.org/10.1007/s10203-023-00392-3. Accepted manuscript.

Abstract. Orthogonal decompositions are essential tools for the study of weakly stationary time series. Some examples are given by the Classical Wold Decomposition of Wold (1938) and the Extended Wold Decomposition of Ortu, Severino, Tamoni and Tebaldi (2020), which permits to disentangle shocks with heterogeneous degrees of persistence from a given weakly stationary process. The analysis becomes more involved when dealing with vector processes because of the presence of different simultaneous shocks. In this paper, we recast the standard treatment of multivariate time series in terms of Hilbert A-modules (where matrices replace the field of scalars) and we prove the Abstract Wold Theorem for self-dual pre-Hilbert A-modules with an isometric operator. This theorem allows us to easily retrieve the Multivariate Classical Wold Decomposition and the multivariate version of the Extended Wold Decomposition. The theory helps in handling matrix coefficients and computing orthogonal projections on closed submodules. The orthogonality notion is key to decompose the given vector process into uncorrelated subseries and it implies a variance decomposition.

F. Severino, M.A. Cremona, É. Dadié (2022) COVID-19 effects on the Canadian term structure of interest rates. Review of Economic Analysis 14(4), 471-502. https://doi.org/10.15353/rea.v14i4.4962

Abstract. In Canada, COVID-19 pandemic triggered exceptional monetary policy interventions by the central bank, which in March 2020 made multiple unscheduled cuts to itstarget rate. In this paper we assess the extent to which Bank of Canada interventions affected the determinants of the yield curve. In particular, we apply Functional Principal Component Analysis to the term structure of interest rates. We find that, during the pandemic, the long-run dependence of level and slope components of the yield curve is unchanged with respect to previous months, although the shape of the mean yield curve completely changed after target rate cuts. Bank of Canada was effective in lowering the whole yield curve and correcting the inverted hump of previous months, but it was not able to reduce the exposure to already existing long-run risks.

S. Cerreia-Vioglio, F. Ortu, F. Rotondi, F. Severino (2024) On horizon-consistent mean-variance portfolio allocation. Annals of Operations Research 336(1), 797-828. https://doi.org/10.1007/s10479-022-04798-x. Accepted manuscript.

Abstract. We analyze the problem of constructing multiple buy-and-hold mean-variance portfolios over increasing investment horizons in continuous-time arbitrage-free stochastic interest rate markets. The orthogonal approach to the one-period mean-variance optimization of Hansen and Richard (1987) requires the replication of a risky payoff for each investment horizon. When many maturities are considered, a large number of payoffs must be replicated, with an impact on transaction costs. In this paper, we orthogonally decompose the whole processes defined by asset returns to obtain a mean-variance frontier generated by the same two securities across a multiplicity of horizons. Our risk-adjusted mean-variance frontier rests on the martingale property of the returns discounted by the log-optimal portfolio and features a horizon consistency property. The outcome is that the replication of a single risky payoff is required to implement such frontier at any investment horizon. As a result, when transaction costs are taken into account, our risk-adjusted mean-variance frontier may outperform the traditional mean-variance optimal strategies in terms of Sharpe ratio. Realistic numerical examples show the improvements of our approach in medium- or long-term cashflow management, when a sequence of target returns at increasing investment horizons is considered.

F. Ortu, F. Severino, A. Tamoni, C. Tebaldi (2020) A persistence-based Wold-type decomposition for stationary time series.  Quantitative Economics 11(1), 203-230. https://doi.org/10.3982/QE994

Abstract. This paper shows how to decompose weakly stationary time series into the sum, across time scales, of uncorrelated components associated with different degrees of persistence. In particular, we provide an Extended Wold Decomposition based on an isometric scaling operator that makes averages of process innovations. Thanks to the uncorrelatedness of components, our representation of a time series naturally induces a persistence-based variance decomposition of any weakly stationary process. We provide two applications to show how the tools developed in this paper can shed new light on the determinants of the variability of economic and financial time series.

M. Marinacci, F. Severino (2018) Weak time-derivatives and no-arbitrage pricing. Finance and Stochastics 22(4), 1007-1036. https://doi.org/10.1007/s00780-018-0371-9. Accepted manuscript.

Abstract. We prove a risk-neutral pricing formula for a large class of semimartingale processes through a novel notion of weak time-differentiability that permits to differentiate adapted processes. In particular, the weak time-derivative isolates drifts of semimartingales and is null for martingales. Weak time-differentiability enables us to characterize no arbitrage prices as solutions of differential equations, where interest rates play a key role. Finally, we reformulate the eigenvalue problem of Hansen and Scheinkman (2009) by employing weak time-derivatives.

F. Severino (2016) Isometric operators on Hilbert spaces and Wold decomposition of stationary time series. Decisions in Economics and Finance 39(2), 203-234. https://doi.org/10.1007/s10203-016-0181-5. A preliminary version.

Abstract. The Wold Theorem plays a fundamental role in the decomposition of weakly stationary time series. It provides a moving average representation of the process under consideration in terms of uncorrelated innovations, whatever the nature of the process is. From an empirical point of view, this result enables to identify orthogonal shocks, for instance in macroeconomic and financial time series. More theoretically, the decomposition of weakly stationary stochastic processes can be seen as a special case of the Abstract Wold Theorem, that allows to decompose Hilbert spaces by using isometric operators. In this work we explain this link in detail, employing the Hilbert space spanned by a weakly stationary time series and the lag operator as isometry. In particular, we characterize the innovation subspace by exploiting the adjoint operator. We also show that the isometry of the lag operator is equivalent to weak stationarity. Our methodology, fully based on operator theory, provides novel tools useful to discover new Wold-type decompositions of stochastic processes, in which the involved isometry is no more the lag operator. In such decompositions the orthogonality of innovations is ensured by construction since they are derived from the Abstract Wold Theorem.

Book chapters

F. Severino, S. Thierry (2022) Robo-advisors: A big data challenge. In book: Big Data in finance: Opportunities and challenges of financial digitalization by T. Walker, F. Davis and T. Schwartz, Palgrave-Macmillan. https://doi.org/10.1007/978-3-031-12240-8_7. Accepted manuscript.

Abstract. At the frontier of personal finance and Fintech, robo-advisors aim to provide customized portfolio strategies without human intervention. They typically propose passive strategies that can match the investor’s objectives and risk profile at a low cost. However, digital advisors feature a lack of precision in capturing clients’ attitude towards risk and a (not always suitable) low risk exposure. In this context, leveraging big data and artificial intelligence techniques can improve the main strength of robo-advisors, that is, their ability to automatically provide personalized investment solutions. Text data from dialogue systems, such as chatbots, can be employed to improve the client’s profiling, while recommendation systems can rely on big data from financial social networks to propose targeted investment strategies. Analysis of big data through machine learning methods can also improve the performance of the optimization algorithms employed by digital advisors. The potential for the exploitation of big data and artificial intelligence in automated asset management is still enormous.

D. Di Virgilio, F. Ortu, F. Severino, C. Tebaldi (2019) Optimal asset allocation with heterogeneous persistent shocks and myopic and intertemporal hedging demand. In book: Behavioral finance: the coming of age by I. Venezia, World Scientific. https://doi.org/10.1142/9789813279469_0004. A preliminary version.

Working papers

M.A. Cremona, L. Doroshenko, F. Severino: Functional motif discovery in stock market prices.

Abstract. Financial asset prices display patterns that occur periodically over time and feature similar shapes. This is, for example, the case of the surge of a financial bubble. However, such time series are usually noisy and volatile, making the identification of repetitive patterns challenging. In this study, we embed asset prices in a functional data analysis framework and extend the method of probabilistic K-means with local alignment to discover functional motifs in stock price time series. After illustrating our technique on simulations of mixed causal-noncausal autoregressive processes, we apply it to discover motifs in the prices of S&P 500 top components. 

M.A. Cremona, C.-E. Sarault, F. Severino: Equity market-neutral strategies using variable selection and regularized regression.

Abstract. Equity market-neutral strategies are designed to feature no exposure to market risk. The implementation of such strategies relies upon the estimation of the beta coefficients. Unfortunately, traditional beta estimation methods used to implement these strategies often suffer from weak out-of-sample performance, leading to suboptimal ex-post neutrality. Therefore, we explore how machine learning techniques, particularly variable selection and regularized regression methods, can address the issues faced in the traditional development of equity market-neutral strategies. We test a range of methods, including ridge regression, lasso regression, and stepwise regressions, to construct portfolios that achieve better ex-post neutrality and lower transaction costs when com- pared to strategies based on traditional multiple regression models. The results demonstrate that the tested techniques enhance portfolio performance and help minimize trading costs by selecting an optimal number of risk factors to hedge. Our research contributes to the academic literature on machine learning in asset pricing and offers practical insights for portfolio management.

H. Fathi, M.A. Cremona, F. Severino: Selection of functional predictors and smooth coefficient estimation for scalar-on-function regression models.

Abstract. In the framework of scalar-on-function regression models, in which several functional variables are employed to predict a scalar response, we propose a methodology for selecting relevant functional predictors while simultaneously providing accurate smooth (or more generally regular) estimates of the functional coefficients. We suppose that the functional predictors belong to a real separable Hilbert space, while the functional coefficients belong to a specific subspace of this Hilbert space. Such a subspace can be a Reproducing Kernel Hilbert Space (RKHS) to ensure the desired regularity characteristics, such as smoothness or periodicity, for the coefficient estimates. Our procedure, called SOFIA (Scalar-On-Function Integrated Adaptive Lasso), is based on an adaptive penalized least squares algorithm that leverages functional subgradients to efficiently solve the minimization problem. We demonstrate that the proposed method satisfies an appropriate version of the oracle property adapted to the functional setting, even when the number of predictors exceeds the sample size. SOFIA’s effectiveness in variable selection and coefficient estimation is evaluated through extensive simulation studies and a real-data application to predict GDP growth.

N. Kolani, M. Madotto, A. Pankratov, F. Severino: Unawareness in safety-first portfolio optimization.

Abstract. Loss protection is an important aspect for market investors. However, this objective is severely challenged when the investor lacks complete knowledge of tail events that affect potfolio returns. Moreover, such a partial awareness of portfolio returns may be exploited by a financial advisor who is aware of all market scenarios. In this paper, we assess the impact of the investor’s partial awareness on the optimization of safety-first portfolios. We show that, in the optimum, an investor moderately averse to unawareness opts for cautious portfolio strategies, obtaining lower returns than a portfolio manager can achieve. This leaves room for the manager to impose substantial commissions, contrary to what happens when the investor is unawareness lover. A moderate aversion to unawareness also eliminates the dependence of the safety-first portfolio on the threshold return and the risk tolerance initially set by the investor. Finally, high values of unawareness aversion induce extreme overprotection in portfolio selection.